ANALYTIC AND COORDINATE GEOMETRY
Multiple Connections
Rose Mary Zbiek
Width-length-perimeter graphs and width-length-area graphs.
(889, 1996) 628 - 634
A Geometric Approach to the Discriminant
R. Daniel Hurwitz
Characterizing the number of real solutions to a quadratic equation by investigating
the intersections of a parabola and a line.
(88, 1995) 323 - 325
Investigating Circles and Spirals with a Graphing Calculator
Stuart Moskowitz
Activities involving parametric equations.
(87, 1994) 240 - 243
Geometric Transformations - Part 2
Susan K. Eddins, Evelyn O. Maxwell, and Floramma Stanislaus
Activities. Coordinate approaches to transformations utilizing matrices.
(87, 1994) 258 - 261, 268 - 270
A Quadrilateral Hierarchy to Facilitate Learning in Geometry
Timothy V. Craine and Rheta N. Rubenstein
Creating a "family tree" for quadrilaterals to enable generalization
of results. Analytic proofs are also involved.
(86,1993) 30 - 36
Using a Treasure Hunt to Teach Locus of Points
Linda Hayek
Sharing teaching ideas. Using geometric clues to find
hidden objects.
(86, 1993) 133 - 134
Physical Modeling of Basic Loci
Patricia Frey-Mason
Using students and groups of students to represent geometric objects.
(86, 1993) 216
Square Circles
Judith A. Silver
Examining the set of all points equidistant from a fixed point
using metrics different from the usual metric in a plane.
(86, 1993) 408 - 410
Hidden Treasures in Students' Assumptions
Monte Zerger
Finding the distance between two points separated by an obstacle.
Geometric and trigonometric approaches.
(86, 1993) 567 - 569
Where is My Reference Angle?
Joanne Staulonis
A manipulative for demonstrating the concept of a reference angle.
(85, 1992) 537
Folding Perpendiculars and Counting Slope
Ann Blomquist
Sharing Teaching Ideas. Folding activities to discover relations
between slopes of perpendicular lines.
(85, 1992) 538 - 539
Is the Graph of y = kx Straight?
Alex Friedlander and Tommy Dreyfus
Loci in non-Cartesian coordinate systems.
(84, 1991) 526 - 531
Euclid and Descartes: A Partnership
Dorothy Hoy Wasdovich
Integrating coordinate and synthetic geometry.
(84, 1991) 706 - 709
Coordinate Geometry: A Powerful Tool for Solving Problems
Stanley F. Tabak
Contrasting synthetic and analytic proofs for three theorems.
(83, 1990) 264 - 268
Which Method Is Best?
Edward J. Barbeau
Synthetic, transformational, analytic, vector, and complex number
proofs that an angle inscribed in a semicircle is a right angle.
(81, 1988) 87 - 90
Interdimensional Relationships
Joseph V. Roberti.
A look at relationships suggested by the fact that the derivative of
the area of a circle yields the circumference and the derivative of the
volume of a sphere yields the surface area.
(81, 1988) 96 - 100
Slope As Speed
James Robert Metz
Activities to develop the concept.
(81, 1988) 285 - 289
Another Approach to the Ambiguous Case
Bernard S. Levine
Using the law of cosines to set up a quadratic equation.
80, (1987) 208 - 209.
A Geometric Proof of the Sum-Product Identities for Trigonometric Functions
Joscelyn Jarrett
Utilizing points on a unit circle.
80, (1987) 240 - 244.
Rethinking the Ambiguous Case
Allen L. Peek
Again relating the solution of the problem to the solution of a
quadratic equation.
80, (1987) 372.
Illustrating the Euler Line
James M. Rubillo
Finding the coordinates of the points on the line.
80, (1987) 389 - 393.
Interpreting and Applying the Distance Formula
Richard J. Hopkinson
Applying the usual formula for the distance from a point to a line
to the solution of several typical analytic geometry problems.
80, (1987) 572 - 575, 579.
Distance From a Point to a Line
Donna M. and Enrique A. Gonzalez-Velasco
A derivation of the formula.
79, (1986) 710 - 711.
A Property of Inversion in Polar Coordinates
James N. Boyd
A demonstration of the result that inversion preserves angle size.
78, (1985) 60 - 61.
The Geometry of Microwave Antennas
William R. Parzynski
Reflective properties of parabolas and hyperbolas. An analytic approach.
77, (1984) 294 - 296.
General Equations for a Reflection in a Line
J. Taylor Hollist
An analytic development.
77, (1984) 352 - 353.
Inversion in a Circle: A Different Kind of Transformation
Martin P. Cohen
An analytic introduction to inversion.
76, (1983) 620 - 623.
Two Derivations Of A Formula For Finding The Distance From a Point to A Line
George P. Evanovich
A circle-radius method and a trigonometric method.
72, (1979) 196 - 198.
Writing Equations For Intersecting Circles
Richard J. Hopkinson
A method for guaranteeing that two circles will meet at points
having integer coordinates.
72, (1979) 296 - 298.
Computer Classification Of Triangles and Quadrilaterals - A Challenging
Application
J. Richard Dennis
Computer application, uses coordinates of vertices.
71, (1978) 452 - 458.
Dual Concepts - Graphing With Lines (Points)
Deloyd E. Steretz and Joseph L. Teeters
Point and line coordinates.
70, (1977) 726 - 731.
Coordinates For Lines: An Enrichment Activity
Alan R. Osbourne
Line coordinates in a plane.
69, (1976) 264 - 267.
Equations Of Geometric Figures
Carl S. Johnson, M.M. Ahuja and Leonard Palmer
The relation of the graphs of the union and the intersection of
the figures F and G to the graphs of F and G. Extended to writing
equations for polygons and to higher dimensions.
67, (1974) 741 - 743.
Mission - Tangrams
Charles E. Allen
Activities dealing with coordinate systems, shape, congruence,
similarity and congruence.
66, (1973) 143 - 146.
A Mathematical Vignette
Courtney D. Young, Jr.
A look at some analytic proofs.
65, (1972) 349 - 353.
Circular Coordinates: A Strange New System Of Coordinates
Frederick K. Trask III
A system in which points are represented as the intersection of circles.
Applied mainly to curves which are best represented in polar form.
64, (1971) 402 - 408.
What Points Are Equidistant From Two Skew Lines?
Alexandra Forsythe
An analytic approach.
62, (1969) 97 - 101.
Geometric Techniques For Graphing
Glen Haddock and Donald W. Hight
Graphs of f , g , f + g , f - g , etc.
59, (1966) 2 - 5.
Discovery-Type Investigation For Coordinate Geometry Students
Mary Ellen Schaff
System derived from a circle and a line.
59, (1966) 458 - 460.
The Use Of Transformations In Deriving Equations Of Common Geometric Figures
Clarence R. Perisho
Equations of figures having sharp corners.
58, (1965) 386 - 392.
Coordinate Geometry With An Affine Approach
Harry Sitomer
A brief overview.
57, (1964) 404 - 405.
A Note On Curve Fitting
Joseph F. Santer
Writing an equation for an angle.
56, (1963) 218 - 221.
A Second Note On Curve Fitting
Joseph F. Santer
Writing an equation for a broken line curve.
56, (1963) 307 - 310.
Curves With Corners
Clarence R. Perisho
Equations involving absolute values.
55, (1962) 326 - 329.
Graphing Pictures
Margaret L. Carver
Coordinates presented.
52, (1959) 41 - 43.
Teaching Loci With Wire and Paint
Donald A. Williams
Teaching aids for locus problems.
51, (1958) 562 - 563.
The Functional Approach To Elementary and Secondary Mathematics
William A. Gager
Some geometrical examples.
50, (1957) 30 - 34.
Equations and Geometric Loci: A Logical Synthesis
W. Servais
Relations, some set theory.
50, (1957) 114 - 122.
Notes On Analytic Geometry
William L. Schaff
Bibliography.
46, (1953) 28 - 30.
Using Algebra In Teaching Geometry
Howard F. Fehr
An analytic approach to geometry.
45, (1952) 561 - 566.
Analytic Geometry: The Discovery Of Fermat and Descartes
Carl B. Boyer
History and bibliography.
37, (1944) 99 - 105.
A Lesson On The Parabola, With Emphasis On Its Importance In Modern Life
Chester C. Camp
Analytic approach. Applications.
35, (1942) 59 - 63.
Analytic Geometry In The High School
Arthur F. Leary
Material being taught at the time.
33, (1940) 60 - 68.
A Geometric Representation
E. D. Roe, Jr.
Analytic geometry in space.
10, (1917-1918) 205 - 210.
AREA
Connecting Geometry and Algebra: Geometric Interpretations of Distance
Terry W. Crites
Primarily as areas under curves.
(88, 1995) 292 - 297
Using Similarity to Find Length and Area
James T. Sandefur
Similar figures and scaling factors. Constructing spirals in triangles and squares.
Involvement with the theorem of Pythagoras.
(87, 1994) 319 - 325
Spiral Through Recursion
Jeffrey M. Choppin
Finding areas and perimeters of spirals created through recursive processes.
(87, 1994) 504 - 508
Teaching Relationships between Area and Perimeter with The Geometer's Sketchpad
Michael E. Stone
For all n-gons with the same perimeter, what shape will have the greatest area?
Sketchpad investigations of the problem.
(87, 1994) 590 - 594
Multiple Solutions Involving Geoboard Problems
Lyle R. Smith
Finding areas and perimeters of polygons formed on a geoboard.
(86, 1992) 25 - 29
Area and Perimeter Connections
Jane B. Kennedy
Activities for investigating maximum area rectangles
with fixed perimeter.
(86, 1993) 218 - 221, 231 - 232
The Use of Dot Paper in Geometry Lessons
Ernest Woodward and Thomas Ray Hamel
Area, perimeter, congruence, similarity, Cevians.
(86, 1993) 558 - 561
Looking at Sum k and Sum k*k Geometrically
Eric Hegblom
Using squares and determining area, using cubes
and determining volume.
(86, 1993) 584 - 587
The Generality of a Simple Area Formula
Daniel J. Reinford
Sharing Teaching Ideas. Using the triangle area formula K = rs
to find the areas of polygons which have inscribed circles and
applying the formula to find the area of a circle.
(86, 1993) 738 - 740
A Circle is a Rose
Margaret M. Urban
Area conjectures for a rose curve.
(85, 1992) 114 - 115
Making Connections: Beyond the Surface
Dan Brutlag and Carole Maples
Dealing with scaling-surface area-volume relationships.
(85, 1992) 230 - 235
Determining Area and Calculating Cost: A "Model" Approach
Harry McLaughlin
Activities for discovering the formula for the area of a rectangle
and using the information to calculate various costs.
(85, 1992) 360 - 361, 367 - 370
A Generalized Area Formula
Virginia E. Usnick, Patricia M. Lamphere, and George W. Bright
Looking for a common structure in familiar area formulas.
(85, 1992) 752 - 754
Area and Perimeter Are Independent
Edwin L. Clopton
Sharing Teaching Ideas. A demonstration and laboratory activity.
(84, 1991) 33 - 35
A Geometric Look at Greatest Common Divisor
Melfried Olson
Activities involving area.
(84, 1991) 202 - 208
A Fractal Excursion
Dane R. Camp
Area and perimeter results for the Koch curve and surface area and
volume results for three-dimensional analogs.
(84, 1991) 265 - 275
Pick's Theorem Extended and Generalized
Christopher Polis
The extension is to lattices other than square lattices. The author
was an eighth-grade student at the time the article was written.
(84, 1991) 399 - 401
Counting Squares
David L. Pagni
Finding a relationship between the size of a rectangle and the number
of subsquares cut by a diagonal.
(84, 1991) 754 - 758
Area of a Triangle
Donald W. Stover
Sharing Teaching Ideas. An alternate method for finding the area of
a triangle given the lengths of the sides.
(83, 1990) 120
Seven Ways to Find the Area of a Trapezoid
Lucille Lohmeier Peterson and Mark E. Saul
Sharing Teaching Ideas. Furnishing a hands-on experience in determining
the area of a trapezoid.
(83, 1990) 283 - 286
Areas and Perimeters of Geoboard Polygons
Lyle R. Smith
Finding polygons with specific areas and specific perimeters on
a geoboard.
(83, 1990) 392 - 398
Some Discoveries with Right-Rectangular Prisms
Robert E. Reys
Activities for problem-solving experiences with area and volume.
(82, 1989) 118 - 123
What Do We Mean by Area and Perimeter?
Virginia C. Stimpson
Sharing Teaching Ideas. A lesson designed to reveal misconceptions
about the relationship between area and perimeter.
(82, 1989) 342 - 344
Area Formulas on Isometric Dot Paper
Bonnie H. Litwiller and David R. Duncan
Isometric graph paper as a teaching aid for the concept of area.
(82, 1989) 366 - 369
Interpreting Proportional Relationships
Kathleen A. Cramer, Thomas R Post, and Merlyn J. Behr
Activities which include some discussion of surface area and
map scaling.
(82, 1989) 445 - 452
Designing Dreams In Mathematics
Linda S. Powell
Sharing Teaching Ideas. Informal geometry project involving area
calculations.
(82, 1989) 620
Geometrical Adventures in Functionland
Rina Hershkowitz, Abraham Arcavi, and Theodore Eisenberg
Determining the change in area produced by making a change in some
property of a particular figure.
80, (1987) 346 - 352.
Approximation of Area Under a Curve: A Conceptual Approach
Tommy Dreyfus
Various approaches are presented.
80, (1987) 538 - 543.
Using Sweeps to Find Areas
Donald B. Schultz
A technique related to a theorem of Pappus.
78, (1985) 349 - 351.
Investigating Shapes, Formulas, and Properties With LOGO
Daniel S. Yates
Logo activities leading to results on areas and triangle geometry.
78, (1985) 355 - 360. (See correction p. 472.)
Measuring the Areas of Golf Greens and Other Irregular Regions
W. Gary Martin and Joao Ponto
Divide the region into triangles having a common vertex at an interior
point of the region. BASIC program provided.
78, (1985) 385 - 389.
Ring-Around-A-Trapezoid
Vincent J. Hawkins
Finding the area of a circular ring by transforming it into an
isosceles trapezoid.
77, (1984) 450 - 451.
How Is Area Related to Perimeter?
Betty Clayton Lyon
Relations involving rectangles with integral sides.
76, (1984) 360 - 363.
Understanding Area and Area Formulas
Michael Battista
A sequence of lessons to discourage some common misunderstandings
about area.
75, (1982) 362 - 368, 387.
Area = Perimeter
Lee Markowitz
When will the area of a triangle be equal to its perimeter?
74, (1981) 222 - 223.
The Second National Assessment In Mathematics: Area and Volume
James J. Hirstein
A discussion of student results on the concepts.
74, (1981) 704 - 708.
The Isoperimetric Theorem
Ann E. Watkins
Activities to aid in the discovery that for a given perimeter the
circle encloses the greatest area.
72, (1979) 118 - 122.
A Different Look At pi r*r
William D. Jamski
Dividing a circle into n congruent segments, then reassembling them
into a "quadrilateral".
71, (1978) 273 - 274.
Finding Areas Under Curves With Hand-Held Calculators
Arthur A. Hiatt
Develops (in the appendix) a method for finding the area of a polygon,
given the coordinates of its vertices.
71, (1978) 420 - 423.
Problem Posing and Problem Solving: An Illustration Of Their Interdependence
Marion I. Walter and Stephen I. Brown
Given two equilateral triangles, find a third whose area is the
sum of the areas of the first two. The Pythagorean theorem and a
generalization.
70, (1977) 4 - 13.
Tangram Mathematics
Activities involving area relationships.
70, (1977) 143 - 146.
The Surveyor and The Geoboard
Ronald R. Steffani
Surveyors method for finding area related to the geoboard.
70, (1977) 147 - 149.
Sum Squares On A Geoboard
James J. Cemella
The number of squares on a geoboard and their area.
70, (1977) 150 - 153.
Tangram Geometry
James J. Roberge
Using the tangram pieces to create geometric figures. Looks at
convex quadrilaterals in particular.
70, (1977) 239 - 242.
Volume and Surface Area
Gerald Kulm
Activities involving surface areas and volumes of rectangular
boxes with open tops.
68, (1975) 583 - 586.
Pick's Rule
Christian R. Hirsch
Activities for discovering and using Pick's rule.
67, (1974) 431 - 434, 473.
Area Ratios In Convex Polygons
Gerald Kulm
Area ratios involved when one regular n-gon is derived from
another by joining division points of sides.
67, (1974) 466 - 467.
Problem Number 10
George Lenchner
Find the area of a quadrilateral derived from a right triangle.
67, (1974) 608 - 609.
Some Suggestions For An Informal Discovery Unit On Plane Convex Sets
Alton T. Olson
Activities leading to the discovery of properties and existence
of convex sets.
66, (1973) 267 - 269.
That Area Problem
Benjamin Greenberg
Finding the area of a quadrilateral formed by trisecting the sides
of a given quadrilateral.
64, (1971) 79 - 80.
Area From A Triangular Point Of View
Margaret A. Farrell
Using an equilateral triangle as the unit of area.
63, (1970) 18 - 21.
Two Incorrect Solutions Explored Correctly
Merle C. Allen
Converse of Pythagoras, area of a triangle.
63, (1970) 257 - 258.
The Area Of A Pythagorean Triangle and The Number Six
Robert W. Prielipp
The area of such a triangle is a multiple of six.
62, (1969) 547 - 548.
A Medieval Proof Of Heron's Formula
Yusuf Id and E.S. Kennedy
A proof by Al-Shanni.
62, (1969) 585 - 587.
Pierced Polygons
Charles G. Moore
Regions formed when a polygonal region is cut from the interior of
another polygonal region. Angle relations.
61, (1968) 31 - 35.
The Area Of A Rectangle
Lawrence A. Ringenberg
Formula developed using the square as a unit.
56, (1963) 329 - 332.
The Trapezoid and Area
Wilfred H. Hinkel
An approach to polygonal area formulas.
53, (1960) 106 - 108.
Area Device For A Trapezoid
Emil J. Berger
Teaching aid.
49, (1956) 391.
CIRCLES
Trap a Surprise in an Isosceles Trapezoid
Margaret M. Housinger
Isosceles trapezoids with integral sides in which a circle can be inscribed.
(889, 1996) 12 - 14
Perimeters, Patterns, and Pi
Sue Barnes
Areas and perimeters of inscribed and circumscribed regular polygons.
(889, 1996) 284 - 288
A Mean Solution to an Old Circle Standard
Andrew J. Samide and Amanda M. Warfield
A line is tangent to two tangent circles, find the length of the segment joining the
two points of tangency.
(889, 1996) 411 - 413
Geometry in English Wheatfields
The geometry and diatonic ratios of crop circles.
(88, 1995) 802
Pi Day
Bruce C. Waldner
Mathematically related contests held on March 14 (i.e. 3/14).
(87, 1994) 86 - 87
Investigating Circles and Spirals with a Graphing Calculator
Stuart Moskowitz
Activities involving parametric equations.
(87, 1994) 240 - 243
A Rapidly Converging Recursive Approach to Pi
Joseph B. Dence and Thomas P. Dence
An algorithm for estimating pi from a sequence of inscribed
regular polygons.
(86, 1993) 121 - 124
A Circle is a Rose
Margaret M. Urban
Area conjectures for a rose curve.
(85, 1992) 114 - 115
Circles Revisited
Maurice Burke
Using three theorems about circles to demonstrate eighteen theorems.
(85, 1992) 573 - 577
The Circle and Sphere as Great Equalizers
Steven Schwartzman
Relations between parts of figures and inscribed figures.
(84, 1991) 666 - 672
A New Look at Circles
Dan Bennett
A locus problem from Calvin and Hobbes.
(82, 1989) 90 - 93
Archimedes and Pi
Thomas W. Shilgalis
Developing Archimedes' recursion formulas.
(82, 1989) 204 - 206
Not Just Any Three Points
James M. Sconyers
Sharing Teaching Ideas. Why must three points be noncollinear in
order to determine a circle?
(82, 1989) 436 - 437
Archimedes' Pi - An Introduction to Iteration
Richard Lotspeich
Using inscribed n-gons to develop approximations.
(81, 1988) 208 - 210
Applying the Midpoint Theorem
Richard J. Crouse
Sharing Teaching Ideas. A circle which has as a diameter a segment
with one endpoint on the x-axis and the other endpoint on the y-axis
must pass through the origin.
(81, 1988) 274
Lessons Learned While Approximating Pi
James E. Beamer
Approximations of pi. BASIC, FORTRAN, and TI55-II programs provided.
80, (1987) 154 - 159.
Finding the Area of Regular Polygons
William M. Waters, Jr.
Finding the ratio of the area of one regular polygon to that of
another when they are inscribed in the same circle.
80, (1987) 278 - 280
Circles and Star Polygons
Clark Kimberling
BASIC programs for producing the shapes.
78, (1985) 46 - 51.
A Property of Inversion in Polar Coordinates
James N. Boyd
A demonstration of the fact that inversion preserves angle size.
78, (1985) 60 - 61.
An "Ancient/Modern" Proof of Heron's Formula
William Dunham
Utilizing Heron's inscribed circle and some trigonometric results.
78, (1985) 258 - 259.
The Shoemaker's Knife - an Approach of the Polya Type
Shlomo Libeskind and Johnny W. Lott
The arbelos and some circle geometry. The solution of a given
problem by looking at a transformed problem.
77, (1984) 178 - 182.
A Useful Old Theorem
W. Vance Underhill
Applications of Ptolemy's theorem.
76, (1983) 98 - 100.
Inversion in a Circle: A Different Kind of Transformation
Martin P. Cohen
An analytic introduction to inversion.
76, (1983) 620 - 623.
More Related Geometric Theorems
Joseph V. Roberti
Theorems related to the result on the lengths of segments formed
when secants meet outside a circle.
75, (1982) 564 - 566.
A Present From My Geometry Class
Andy Pauker
A look at the product of segments of secants of a circle.
73, (1980) 119 - 120.
Getting The Most Out Of A Circle
Joe Donegan and Jack Pricken
Polygons determined by six equally spaced points on a circle.
73, (1980) 355 - 358.
Are Circumscribable Polygons Always Inscribable?
Joseph Shin
Develops a condition under which they will be.
73, (1980) 371 - 372.
Writing Equations For Intersecting Circles
Richard J. Hopkinson
A method for guaranteeing that two circles will meet at points
having integer coordinates.
72, (1979) 296 - 298.
A Unification Of Two Famous Theorems From Classical Geometry
Eli Maor
Looks at the product of the lengths of segments of intersecting
secants of a circle.
72, (1979) 363 - 367.
On The Radii Of Inscribed and Escribed Circles Of Right Triangles
David W. Hansen
Develops relations between these radii and the area of a right triangle.
72, (1979) 462 - 464.
A Different Look At pi r*r
William D. Jamski
Dividing a circle into n congruent sectors, then reassembling
into a "quadrilateral".
71, (1978) 273 - 274.
The Three Coin Problem: Tangents, Areas and Ratios
Bonnie H. Litwiller and David R. Duncan
Finding the area of the "triangle" formed by three mutually
tangent circles.
69, (1976) 567 - 569.
Discovering A Congruence Theorem: A Project Of A Geometry For Teachers Class
Malcolm Smith
Demonstrating that corresponding chords of homothetic circles
are parallel.
65, (1972) 750 - 751.
Are Circles Similar?
Paul B. Johnson
Circles in a plane and on a sphere.
59, (1966) 9 - 13.
The Circle Of Unit Diameter
J. Garfunkel and B. Leeds
The use of a circle having diameter one in establishing
geometric results. There is also some trigonometry.
59, (1966) 124 - 127.
Radii Of The Apollonius Contact Circles
C. N. Mills
Development of formula for the radii.
59, (1966) 574 - 576.
How Ptolemy Constructed Trigonometry Tables
Brother T. Brendan
Contains some geometry of the circle.
58, (1965) 141 - 149.
A Deceptively Easy Problem
Jack M. Elkin
Deals with chords of a circle.
58, (1965) 195 - 199.
Some Remarks Concerning Families Of Circles and Radical Axes
James A. Bradley, Jr.
Systems of circles determined by two circles.
57, (1964) 533 - 536.
How To Find The Center Of A Circle
Kardy Tan
Four constructions.
56, (1963) 554 - 556.
A Chain Of Circles
Rodney T. Hood
An application of inversion.
54, (1961) 134 - 137.
Some Related Theorems On Triangles and Circles
J. D. Wiseman, Jr.
Medians of isosceles triangles and chords of circles.
54, (1961) 14 - 16.
The Problem Of Apollonius
N. A. Court
History, solutions, recent developments.
54, (1961) 444 - 452.
A Problem With Touching Circles
John Satterly
Construction of sets of tangent circles.
53, (1960) 90 - 95.
Lengths Of Chords and Their Distances From The Center
Hale Pickett
A theorem and a construction.
50, (1957) 325 - 326.
Teaching The Formula For Circle Area
Jen Jenkins
A suggested method.
49, (1956) 548 - 549.
A Model For Visualizing The Formula For The Area Of A Circle
Clarence Olander
How to construct it.
48, (1955) 245 - 246.
The Problem Of Napoleon
C. N. Mills
Finding the center and radius of a circle.
46, (1953) 344 - 345.
A Circle Device For Demonstrating Facts Which Relate To Inscribed Angles
Emil J. Berger
Construction and use.
46, (1953) 579 - 581.
A Teaching Device For Geometry Related To The Circle
M.H. Ahrendt
A device for working with inscribed polygons.
45, (1952) 67 - 68.
Relations For Radii Of Circles Associated With The Triangle
Herta Taussig Freitag
Inradius, circumradius, etc.
45, (1952) 357 - 360.
Incenter Demonstrator
Emil J. Berger
Its construction and use.
44, (1951) 416 - 417.
Escribed Circles
Joseph Nyberg
Some trigonometric results and geometry of the circle.
40, (1947) 68 - 70.
Dynamic Geometry
John F. Schact and John J. Kinsella
The use of triangle and quadrilateral linkages as teaching
devices. Contains some geometry of the circle.
40, (1947) 151 - 157.
The Hyperbolic Analogues Of Three Theorems On The Circle
Joseph B. Reynolds
Deals with the product of segments formed by two intersecting lines
which meet a circle.
37, (1944) 301 - 303.
The Principle Of Continuity
Francis P. Hennessey
Some results on polygons and circles.
24, (1931) 32 - 40.
Circles Through Notable Points Of The Triangle
Richard Morris
Circles through three, four, five, and six points. A general theorem.
21, (1928) 63 - 71.
Original Solution In Plane Geometry
Robert A. Laird
The points of intersection of external tangents drawn between any
two three circles of different sizes, in turn, lie on a straight line.
15, (1922) 361 - 364.
Inscribing Regular Pentagons and Decagons
Joseph Bowden
Analytic proof of the construction proposed.
8, (1915-1916) 89 - 91.
Approximate Values Of pi
Wilfred H. Sherk
Six approaches.
2, (1909-1910) 87 - 930
COMPLEX NUMBERS AND GEOMETRY
A "Complex" Proof For A Geometric Construction Of A Regular Pentagon
Gary E. Lambert
Uses complex numbers to develop the proof.
72, (1979) 65 - 66.
Line Reflections In The Complex Plane - A Billiard Player's Delight
Gary L. Musser
Applications, complex numbers, reflections, and aiming a cue ball.
71, (1978) 60 - 64.
Real Transformations From Complex Numbers
Robert D. Alexander
Complex numbers and transformation geometry.
69, (1976) 700 - 709.
From The Geoboard To Number Theory To Complex Numbers
Donavan R. Lichtenberg
Geometry related to some aspects of number theory.
68, (1975) 370 - 375.
Solving Problems In Geometry By Using Complex Numbers
J. Garfunkel
Applications to three theorems, gives eight problems.
60, (1967) 731 - 734.
Regular Polygons
Robert C. Yates
Complex numbers and regular polygons.
55, (1962) 112 - 116.
Complex Numbers and Vectors In High School Geometry
A.H. Pedley
Possible applications.
53, (1960) 198 - 201.
John Wallis and Complex Numbers
D.A. Kearns
History and some geometry.
51, (1958) 373 - 374.
Applications Of Complex Numbers To Geometry
Allan A. Shaw
Many of the proofs are much like vector proofs.
25, (1932) 215 - 226.
CONCURRENCY, COLLINEARITY, RATIO OF DIVISION
Mathematics in Weighting
Richard L. Francis
Using templates to investigate several concepts. Included are squaring
problems and the theorem of Pythagoras.
(85, 1992) 388 - 390
Interesting Area Ratios Within A Triangle
Manfried Olson and Gerald White
Activities for investigating areas of triangles formed when the sides
of an original triangle are subdivided.
(82, 1989) 630 - 636
Illustrating the Euler Line
James M. Rubillo
Finding the coordinates of the points on the line.
80, (1987) 389 - 393.
The Method Of Centroids In Plane Geometry
Aron Pinker
Proofs of classical theorems (Ceva, Steiner-Lehmus, etc.)
73, (1980) 378 - 385.
A Discovery Activity In Geometry
John H. Mathews and William A. Leonard
Division ratios for Cevians.
70, (1977) 126.
Auxiliary Lines and Ratios
Donald W. Stoves
Use in obtaining geometric results. Lines meeting inside a triangle.
60, (1967) 109 - 114.
An Illustration Of The Use Of Vector Methods In Geometry
Herbert E. Vaughan
Some theorems about Cevians.
58, (1965) 696 - 701.
A New Look At Medians
Israel Koral
Proof of a division ratio result.
51, (1958) 123.
On Certain Cases Of Congruence Of Triangles
Victor Thebault
Congruence theorems related to division ratios.
48, (1955) 341 - 343.
A Farewell (?) To Redians, Nedians, Cevians
Merten T. Goodrich
Figures determined by Cevians.
45, (1952) 44 - 46.
Applications
Sheldon S. Myers
Use of Ceva's theorem in proportional variation.
45, (1952) 276 - 278.
The Nedians Of A Plane Triangle
John Satterly
Concurrence of Cevians drawn to 1/n division points.
44, (1951) 46 - 48.
The Centroid Demonstrator
Mathematics Laboratory (Monroe H.S.)
A device for demonstrating the concurrence of Cevians.
44, (1951) 138 - 139.
More About Nedians
Norman Anning
Generalizations concerning 1/n division points.
44, (1951) 310 - 312.
A Harmonic Divider
Emil J. Berger
Construction and use.
44, (1951) 417.
Cevians, Nedians and Redians
Alan Wayna
An area ratio approach to the theorems of Menelaus and Ceva.
44, (1951) 496 - 497.
Some Nedian Details
Adrian Struyk
Another approach to Cevians associated with 1/n division points.
44, (1951) 498 - 500.
Still More About Nedians
Marilyn R. Taig
Applications to quadrilaterals.
44, (1951) 559 - 560.
Centroids
H. v. Baravalle
Constructions. Experiments for locating.
40, (1947) 241 - 249.
CONIC SECTIONS
Folded Paper, Dynamic Geometry, and Proof: A Three-Tier Approach to the Conics
Daniel P. Scher
Folding conics and constructing Sketchpad models.
(889, 1996) 188 - 193
A Direct Derivation of the Equations of the Conic Sections
Duane DeTemple
Deriving the equations by direct appeal to the geometry of a sliced
cone.
(83, 1990) 190 - 193
Constructing Ellipses
Margaret S. Butler
Sharing Teaching Ideas. A discussion of the Trammel method.
(81, 1988) 189 - 190
Spheres in a Cone; or, Proving the Conic Sections
David Atkinson
Using Dandelin's spheres to prove that the conics are indeed
sections of a cone.
80, (1987) 182 - 184.
Halley's Comet in the Classroom
Peter Broughton
Activities involved with the motion of the comet. Construction
of a model showing the relation between the comet's orbit and the
orbit of the earth.
79, (1986) 85 - 89. (see note Sept. 1986, p. 485)
An Alternate Perspective on the Optical Property of Ellipses
Kenzo Seo
A proof of the property.
79, (1986) 656 - 657.
Parabella
Alfinio Flores
A conic parody of Cinderella.
78, (1985) 30 - 33.
The Geometry of Microwave Antennas
William R. Parzynski
Reflective properties of parabolas and hyperbolas. An analytic approach.
77, (1984) 294 - 296.
Constructing The Parabola Without Calculus
Maxim Bruckheimer and Rina Herschkowitz
Three methods.
70, (1977) 658 - 662.
Do Similar Figures Always Have The Same Shape
Paul G. Kumpel, Jr.
Transformational geometry applied to conics with a hint about cubics.
68, (1975) 626 - 628.
The Golden Ratio and Conic Sections
G. Ralph Verno
The golden ratio related to the intersection of conics.
67, (1974) 361 - 363.
Some Methods For Constructing The Parabola
Joseph E. Ciotti
Four methods for sketching parabolas.
67, (1974) 428 - 430.
New Conic Graph Paper
Kenneth Rose
A technique for drawing families of conics.
67, (1974) 604 - 606.
The Limits Of Parabolas
James M. Sconyers
What happens when the distance between the focus and the
directrix varies?
67, (1974) 652 - 653.
Conics From Straight Lines and Circles
Evan M. Maletsky
Activities leading to the construction of conics.
66, (1973) 243 - 246.
Conic Sections In Relation To Physics and Astronomy
Herman v. Baravalle
Models, diagrams, applications.
63, (1970) 101 - 109.
Quadrarcs, St. Peter's and The Colloseum
N.T. Gridgeman
How does one distinguish between an ellipse and an oval?
63, (1970) 209 - 215.
Elliptic Parallels
N.T. Gridgeman
Curves which are everywhere equidistant from a given ellipse.
63, (1970) 481 - 485.
A Psychedelic Approach To Conic Sections
William A. Miller
Generating conics with overhead transparencies (Moire patterns).
63, (1970) 657 - 659.
Why Not Relate The Conic Sections To The Cone?
W. K. Viertel
Developing the usual sum of distances property for an ellipse by
use of a cone.
62, (1969) 13 - 15.
Classroom Inquiry Into The Conic Sections
Arthur Coxford
Activities involving constructions and discovery of properties.
60, (1967) 315 - 322.
A Geometric Approach To The Conic Sections
Sister Maurice Marie Byrne, O.S.U.
Constructions.
59, (1966) 348 - 350.
A Compass-Ruler Method For Constructing Ellipses On Graph Paper
Samuel Kaner
Title tells all.
58, (1965) 260 - 261.
Deductive Proof Of Compass-Ruler Method For Constructing Ellipses
Henry D. Snyder
Proof that the method given in the article by Kaner
(see immediately above) works.
58, (1965) 261.
Conic Sections and Their Constructions
Sister M. Annunciata Burbach, C.P.P.S.
Equations and construction techniques.
56, (1963) 632 - 635.
Johan de Witt's Kinematical Constructions Of The Conics
Joy B. Easton
History and techniques.
56, (1963) 632 - 635.
Trammel Method Construction Of The Ellipse
C.I. Lubin and D. Mazekewitsch
Also includes some theory.
54, (1961) 609 - 612.
The Names "Ellipse", "Parabola" and "Hyperbola"
Howard Eves
History.
53, (1960) 280 - 281.
Simple Paper Models Of The Conic Sections
Ethel Saupe
Methods for construction.
48, (1955) 42 - 44.
Theme Paper, A Ruler, and The Hyperbola
Adrian Struyk
A construction.
47, (1954) 29 - 30.
The Quadrature Of The Parabola: An Ancient Theorem In Modern Form
Carl Boyer
Uses determinants and the method of exhaustion. Some history.
47, (1954) 36 - 37.
Theme Paper, A Ruler, and The Central Conics
Adrian Struyk
Constructions.
47, (1954) 189 - 193.
Tangent Circles and Conic Sections
William Gilbert Miller
A conic as the locus of centers of circles tangent to two given circles.
46, (1953) 78 - 81.
An Optical Method For Demonstrating Conic Sections
Leland D. Hemenway
A device for producing a conical beam of light.
46, (1953) 428 - 429.
Theme Paper, A Ruler, and The Parabola
Adrian Struyk
A construction.
46, (1953) 588 - 590.
Demonstration Of Conic Sections and Skew Curves With String Models
H. v. Baravalle
The construction and uses of such devices.
39, (1946) 284 - 287.
The Hyperbolic Analogues Of Three Theorems On The Circle
Joseph B. Reynolds
The circle theorems are those which concern intersecting lines
which meet a circle in two points.
37, (1944) 301 - 303.
A Lesson On The Parabola, With Emphasis On Its Importance In Modern Life
Chester B. Camp
Analytic approach. Applications.
35, (1942) 59 - 63.
Conic Sections Formed By Some Elements Of A Plane Triangle
Aaron Bakst
Locus problems leading to lines and conics.
24, (1931) 28 - 31.
CONNECTIONS
Illustrating Mathematical Connections: A Geometric Proof of Euler's Theorem
Erin K. Fry and Peter L. Glidden
Using the sum of the measures of the face angles.
(889, 1996) 62 - 65
Technology and Reasoning in Algebra and Geometry
Daniel B. Hirschhorn and Denisse R. Thompson
Explorations to foster reasoning in mathematics. The geometry portion utilizes
dynamic software.
(889, 1996) 138 - 142
Making Connections: Spatial Skills and Engineering Drawings
Beverly G. Baartmans and Sheryl A. Sorby
Orthographic drawings and isometric drawings.
(889, 1996) 348 - 357
Where Are We?
Charles Wavaris and Timothy V. Craine
Activities for exploring longitude and latitude. Construction of a gnomon. Time
zones.
(889, 1996) 524 - 534
Multiple Connections
Rose Mary Zbiek
Width-length-perimeter graphs and width-length-area graphs.
(889, 1996) 628 - 634
Geometry, Iteration, and Finance
A. Landy Godbold, Jr.
Relation of calculation of balances to transformations on the number line.
(889, 1996) 646 - 651
Match Geometric Figures with Trigonometric Identities
Guanshen Ren
Connections between geometric configurations and trigonometric identities.
(88, 1995) 24 - 25
Connecting Geometry and Algebra: Geometric Interpretations of Distance
Terry W. Crites
Primarily as areas under curves.
(88, 1995) 292 - 297
A Geometric Approach to the Discriminant
R. Daniel Hurwitz
Characterizing the number of real solutions to a quadratic equation by investigating
the intersections of a parabola and a line.
(88, 1995) 323 - 325
Guidelines for Teaching Plane Isometries In Secondary School
Adela Jaime and Angel Gutiérrez
Connecting Research to Teaching. Isometries as a link for different branches of
mathematics or for mathematics and other sciences.
(88, 1995) 591 - 597
Geometry in English Wheatfields
The geometry and diatonic ratios of crop circles.
(88, 1995) 802
Making Connections by Using Molecular Models in Geometry
Robert Pacyga
Implementing the Curriculum and Evaluation Standards. Relating models to
compounds found in chemistry. Connecting mathematics, science, and English.
(87, 1994) 43 - 46
Geometry and Poetry
Betty B. Thompson
Sharing Teaching Ideas. Reading poems to find one which conjure up geometric
images and then illustrating the idea graphically.
(87, 1994) 88
Albrecht Durer's Renaissance Connections between Mathematics and Art
Karen Doyle Walton
Some of Durer's geometric work is discussed.
(87, 1994) 278 - 282
Word Roots in Geometry
Margaret E. McIntosh
Suggestions for a unit on word study in geometry.
(87, 1994) 510 - 515
The Functions of a Toy Balloon
Loring Coes III
Activities. Connections between algebra and geometry.
(87, 1994) 619 - 622, 627 - 629
Mathematical Ties That Bind
Peggy A. House
Questions about neckties. Many are geometrical in nature.
(87, 1994) 682 - 689
CONSTRUCTIONS
Two Egyptian Construction Tools
John F. Lamb Jr.
A level and a plumb level.
(86, 1993) 166 - 167
Constructions with Obstructions Involving Arcs
Dick A. Wood
Five constructions (with solutions).
(86, 1993) 360 - 363
Geographic Constructions
Art Johnson and Laurie Boswell
Integrating geography and constructions.
(85, 1992) 184 - 187
The Toothpick Problem and Beyond
Charalampos Toumasis
Activities involving building geometric figures with toothpicks.
(85, 1992) 543 - 545, 555 - 556
Geometric Patterns for Exponents
Frances M. Thompson
Construction of a series of shapes leading to meaning for exponents.
(85, 1992) 746 - 749
Inscribing an "Approximate" Nonagon in a Circle
John F. Lamb, Jr., Farhad Aslan, Ramona Chance, and Jerry D. Lowe
A method discovered by an industrial designer.
(84, 1991) 396 - 398
Two Geometry Applications
Jan List Boal
Problems which arise in the construction of a shuttle returner
for a loom.
(83, 1990) 655 - 658
Equilateral Triangles on an Isometric Grid
Mark A. Spikell
How many equilateral triangles of different sizes can be constructed
on an isometric grid?
(83, 1990) 740 - 743
Simple Constructions for the Regular Pentagon and Heptadecagon
Duane W. DeTemple
Two new constructions.
(82, 1989) 361 - 365
Napoleon's Waterloo Wasn't Mathematics
Jacquelyn Maynard
Solutions for some of Bonaparte's favorite construction problems.
(82, 1989) 648 - 653
Trisecting an Angle - Almost
John F. Lamb, Jr.
A discussion of the method of d'Ocagne.
(81, 1988) 220 - 222
Dropping Perpendiculars the Easy Way
Lindsay Anne Tartre
An alternative technique for obtaining the perpendicular from a
point to a line.
80, (1987) 30 - 31.
Tape Constructions
Lisa Evered
Using tape to do standard ruler-and-compass constructions.
80, (1987) 353 - 356.
Some Challenging Constructions
Joseph V. Roberti
Nine triangle construction problems.
79, (1986) 283 - 287.
Geometric Constructions Using Hinged Mirrors
Jack M. Robertson
Seven constructions which can be accomplished using a hinged mirror.
79, (1986) 380 - 386.
Star Trek: A Construction Problem Using Compass and Straightedge
Bee Ellington
Spock is lost! Perform the indicated constructions in order
to find him.
76, (1983) 329 - 332.
Some Quick Constructions
William M. Waters, Jr.
Given angle ABC, construct a family of angles whose measures
are one-half that of ABC.
75, (1982) 286 - 287.
A New Angle For Constructing Pentagons
John Benson and Debra Berkowitz
Three problems leading to the construction of a regular pentagon.
75, (1982) 288 - 290.
Constructions With An Unmarked Protractor
Joe Dan Austin
Six problems leading to the construction of segment AB given points
A and B.
75, (1982) 291 - 295.
Giving Geometry Students An Added Edge In Constructions
Allan A. Gibb
Ten tasks using an unmarked straightedge with parallel edges.
75, (1982) 296 - 301.
An Improvement Of A Historic Construction
Kim Iles and Lester J. Wilson
Five means (geometric, arithmetic, etc.) included in one figure.
73, (1980) 32 - 34.
Beyond The Usual Constructions
Melfried Olson
Activities leading to the Fermat point, Simpson line, etc.
73, (1980) 361 - 364.
Duplicating The Cube With A Mira
George E. Martin
A method for solving the Delian problem with a Mira and a proof that
it works.
72, (1979) 204 - 208.
Constructing and Trisecting Angles With Integer Angle Measures
Joe Dan Austin and Kathleen Ann Austin
Which angles having integer measures can be constructed? Which of them
can be trisected? Construction of regular polygons.
72, (1979) 290 - 293.
Squaring The Circle - For Fun and Profit
Arthur E. Hallerberg
Eight problems leading to approximations of pi.
71, (1978) 247 - 255.
From Polygons To Pi
James E. Sconyers
Activities for approximating pi.
71, (1978) 514.
Completing The Problem Of Constructing A Unit Segment From SQR(x)
Joe Dan Austin
The final step in the solution of the problem.
71, (1978) 664 - 666.
Using The Compass and The Carpenter's Square: Construct the Cube Root of 2
Jack R. Westwood
Method and proof.
71, (1978) 763 - 764.
Anyone Can Trisect An Angle
Hardy C. Ryerson
Using the trisectrix or the cissoid.
70, (1977) 319 - 321.
There Are More Ways Than One To Bisect An Angle
Allan A. Gibb
Six methods for angle bisection.
70, (1977) 390 - 393.
What Can Be Done With A Mira?
Johnny W, Lott
Euclidean constructions with a Mira.
70, (1977) 394 - 399.
Constructions With Obstructions
Shmuel Avital and Larry Sowder
Eight familiar constructions with constraints.
70, (1977) 584 - 588.
Given A Length SQR(x), Construct The Unit Segment -
An Unfinished Problem For Geometry Students
Edward J. Davis and Thomas Smith
Compass and straightedge techniques. Suggestions for further research.
69, (1976) 15 - 17.
Given A Length SQR(x), Construct The Unit Segment - A Response
The collected results of many submissions to the Editor. Solutions to
some aspects of the problem.
69, (1976) 485 - 490.
Of Shoes - and Ships - and Sealing Wax - Of Barber Poles and Things
Ernest R. Ranucci
Construction and uses of helical designs.
68, (1975) 261 - 264.
Geometric Generalizations
Leslie H. Miller and Bert K. Waite
Given the midpoints of the sides to construct a polygon, generalized
to a situation in which points dividing the sides in certain ratios
are given. One transformational proof.
67, (1974) 676 - 681.
A Student's Construction
Donald W. Stover
Construction of the parallel through a point.
66, (1973) 172.
The Shoemaker's Knife
Brother L. Raphael, F.S.C.
Properties of an arbelos.
66, (1973) 319 - 323.
A Note Concerning A Common Angle "Trisection"
Donald R. Byrkit and William M. Waters, Jr.
"Trisection" by trisecting the base of an isosceles triangle.
65, (1972) 523 - 524.
Mission - Construction
Charles E. Allen
Activities for a unit on construction.
65, (1972) 631 - 634.
Geometric Construction: The Double Straightedge
William Wernick
Euclidean constructions using a two-edged straightedge.
64, (1971) 697 - 704.
The Five-Pointed Star
Lee E. Boyer
Construction of the figure.
61, (1968) 276 - 277.
A New Approach To The Teaching Of Construction
Zalman Usiskin
A postulational development.
61, (1968) 749 - 757.
Geometrical Solutions Of A Quadratic Equation
Amos Nannini
Some classical constructions involved.
59, (1966) 647 - 649.
Introducing Number Theory In High School Algebra and Geometry
Part 2, Geometry
I. A. Barnett
Pythagorean triangles, constructions, unsolvable problems.
58, (1965) 89 - 101.
On Solutions Of Geometrical Constructions Utilizing The Compasses Alone
Jerry P. Becker
A demonstration that the Euclidean constructions can be accomplished
using compasses alone.
57, (1964) 398 - 403.
Trisection Of An Angle By Optical Means
A. E. Hochstein
A device which utilizes a semi-transparent mirror.
56, (1963) 522 - 524.
A Triangle Construction
N. C. Scholomiti and R. C. Hill
Given the lengths of the perpendicular bisectors of the sides,
construct the triangle.
56, (1963) 323 - 324.
Trammel Method Construction Of The Ellipse
C.I. Lubin and D. Mazkewitsch
Method and theory.
54, (1961) 609 - 612.
A Problem With Touching Circles
John Satterly
Construction of sets of tangent circles.
53, (1960) 90 - 95.
George Mohr and Euclides Curiosi
Arthur E. Hallerberg
History and some fixed compass constructions.
53, (1960) 127 - 132.
Graphing Pictures
Frances Gross
Sets of equations and inequalities to produce figures.
53, (1960) 295 - 296.
Right Triangle Construction
Nelson S. Gray
Pythagorean triangles.
53, (1960) 533 - 536.
Graphical Construction Of A Circle Tangent To Two Given Lines and A Circle
D. Mazkewitsch
Title tells all.
52, (1959) 119 - 120.
A Heart For Valentines Day
Mae Howell Kieber
Straightedge and compass construction.
52, (1959) 132.
The Geometry Of The Fixed Compass
Arthur E. Hallerberg
History and constructions.
52, (1959) 230 - 244.
Trisecting Any Angle
Alex J. Mock
A central angle of a circle cannot be trisected by trisecting the arc.
52, (1959) 245 - 246.
Angle Trisection - An Example Of "Undepartmentalized" Mathematics
Rev. Brother Leo, O.S.F.
A method for angle trisection.
52, (1959) 354 - 355.
Trisecting An Angle
C. Carl Robusto
Several methods.
52, (1959) 358 - 360.
Similar Polygons and A Puzzle
Don Wallin
Construction problems and similar polygons.
52, (1959) 372 - 373.
Trisecting An Angle
Hale Pickett
Trisecting an arc does not trisect the angle.
51, (1958) 12 - 13.
Mascheroni Constructions
N. A. Court
History and bibliography.
51, (1958) 370 - 372.
Squaring A Circle
Juan E. Sornito
A method.
50, (1957) 51 - 52.
Mascheroni Constructions
Julius H. Hlavaty
An approach to compass alone constructions.
50, (1957) 482 - 487.
The Tomahawk
Bertram S. Sachman
An angle trisection device.
49, (1956) 280 - 281.
Curves Of Constant Breadth
William J. Hazard
Constructions based on an equilateral triangle and a regular pentagon.
48, (1955) 89 - 90.
Involution Operated Geometrically
Juan E. Sornito
Constructing a segment of length a to the nth.
48, (1955) 243 - 244.
An Individual Laboratory Kit For The Mathematics Student
Nona Mae Allard
The construction of an angle bisector and an angle trisector.
47, (1954) 100 - 101.
Euclidean Constructions
Robert C. Yates
Four compass and straightedge constructions.
47, (1954) 231 - 233.
Golden Section Compasses
Margaret Joseph
Construction of a device for the construction of the golden ratio.
47, (1954) 338 - 339.
Tangible Arithmetic II: The Sector Compasses
Florence Wood
Uses for a scaled compass.
47, (1954) 535 - 542.
Inscribing A Square In A Triangle
Martin Hirsch
Construction and proof.
46, (1953) 107 - 108.
Can We Outdo Mascheroni?
Wm. Fitch Cheney, Jr.
Compass only constructions.
46, (1953) 152 - 156.
A New Solution To An Old Problem
William H. Kruse
Inscribing a square in a semi-circle.
46, (1953) 189 - 190.
Trisection
H. F. Jamison
A discussion of two approximate trisections.
46, (1953) 342 - 344.
Swale's Construction
Adrian Struyk
Finding the center and the radius of a circle.
46, (1953) 507 - 508, 524.
A Novel Linear Trisection
Adrian Struyk
Segment trisection method.
46, (1953) 524.
A Trisection Device Based On The Instrument Of Pascal
The Mathematics Laboratory (Monroe High School)
Construction and proof.
45, (1952) 287, 293.
The Number pi
H. v. Baravalle
Contains some material on squaring the circle.
45, (1952) 340 - 348.
Drawing A Circle With A Carpenter's Square
Sheldon S. Myers
How to accomplish the construction.
45, (1952) 367.
A Method For Constructing A Triangle When The Three Medians Are Given
John Satterly
Title tells all.
45, (1952) 602 - 605.
A Trisection Device
Emil J. Berger
An adaptation of the tomahawk.
44, (1951) 34.
Euclidean Constructions With Well-Defined Intersections
Howard Eves and Vern Hogatt
A point of intersection of two loci is well-defined if the angle of
intersection is larger than some specified angle. Four constructions,
and their relations to Euclidean constructions are given.
44, (1951) 261 - 263.
A Simple Trisection Device
Emil J. Berger
Construction and proof.
44, (1951) 319 - 320.
An Angle Bisector Device
Emil J. Berger
Construction and proof.
44, (1951) 415.
Let's Teach Angle Trisection
Bruce E. Meserve
Some approaches to the problem.
44, (1951) 547 - 550.
Trisecting Any Angle
Werner S. Todd
A technique.
43, (1950) 278 - 279.
A Graphimeter
Howard Eves
A locus problem and the uses of the resulting curve in constructions.
41, (1948) 311 - 313.
A General Method For The Construction Of A Mechanical Inversor
M. H. Ahrendt
Peaucellier cells.
37, (1944) 75 - 80.
The Trisector Of Amadori
Marian E. Daniells
An instrument for angle trisection.
33, (1940) 80 - 81.
Laboratory Work In Geometry
R. M. McDill
Using square, protractor, compass, rule, scissors, etc.
24, (1931) 14 - 21.
Why It Is Impossible To Trisect An Angle Or To Construct
A Regular Polygon Of 7 or 9 Sides By Ruler and Compass
Leonard Eugene Dickson
Relation of the constructions to the solutions of cubic equations.
14, (1921) 217 - 223.
Approximate Values Of pi
Wilfred H. Sherk
Six approaches.
2, (1909-1910) 87 - 93.)
Interesting Work Of Young Geometers
J. T. Rorer
Three triangle theorems and an approximate trisection.
1, (1908-1909) 147 - 149.
DISSECTION PROBLEMS
Mathematical Iteration through Computer Programming
Mary Kay Prichard
Some of the problems involved are geometry related.
Cutting figures, diagonals of a polygon, figurate numbers.
(86, 1993) 150 - 156
Picture Play Leads to Algebraic Patterns
Millie J. Johnson
Sharing Teaching Ideas. Dissection of squares and cubes
to picture algebraic identities.
(86, 1993) 382 - 383
Symmetries of Irregular Polygons
Thomas W. Shilgalis
Investigating bilateral symmetry in irregular convex polygons.
(85, 1992) 342 - 344
The Rug-cutting Puzzle
John F. Lamb, Jr.
Comments on a familiar dissection paradox.
80, (1987) 12 - 14.
Geometric Proofs Of Algebraic Identities
Virginia M. Horak and Willis J. Horak
Most of the proofs are accomplished using dissections.
74, (1981) 212 - 216.
A Different Look At pi r*r
William D. Jamski
Dividing a circle into n congruent sectors, then reassembling
them to form a "quadrilateral".
71, (1978) 273 - 274.
Tetrahexes
Raymond E. Spaulding
Activities involving congruence and symmetry.
71, (1978) 598 - 602.
Tangram Mathematics
Activities involving area relationships.
70, (1977) 143 - 146.
Problem Number 10
George Lenchner
Finding the area of a quadrilateral derived from a right triangle.
67, (1974) 608 - 609.
More About Triangles With The Same Area and The Same Perimeter
Donavan R. Lichtenberg
A method for decomposing a triangle having a given perimeter and
area into another having the same perimeter and area.
67, (1974) 659 - 660.
The Classical Cake Problem
Norman N. Nelson and Forest N. Fisch
Slicing a cake so that each piece contains the same volume of
cake and of frosting.
66, (1973) 659 - 661.
Applications Of The Theorem Of Pythagoras In The Figure-Cutting Problem
Frank Piwnicki
Dissection of squares and rectangles.
55, (1962) 44 - 51.
A Further Note On Dissecting A Square Into An Equilateral Triangle
Chester A. Hawley
Using only three cuts.
53, (1960) 119 - 123.
Four More Exercises In Cutting Figures
Mathematics Staff - University of Chicago
Four dissection problems and their solutions.
51, (1958) 96 - 104.
An Observation On Dissecting The Square
Chester W. Hawley
A classroom use for a dissection.
51, (1958) 120.
New Exercises In Plane Geometry
Mathematics Staff - University of Chicago
Dissection problems.
50, (1957) 125 - 135.
More New Exercises In Plane Geometry
Mathematics Staff - University of Chicago
Dissections.
50, (1957) 330 - 339.
A Problem On The Cutting Of Squares
Mathematics Staff - University of Chicago
Two dissection problems.
49, (1956) 332 - 343.
More On The Cutting Of Squares
Mathematics Staff - University of Chicago
Four dissection problems.
49, (1956) 442 - 454.
Still More On The Cutting Of A Square
Mathematics Staff - University of Chicago
Any convex polygon is equivalent to a square.
49, (1956) 585 - 596.
ENRICHMENT
The Case of Trapezoidal Numbers
Carol Feinberg-McBrian
Activities for pattern investigations.
(889, 1996) 16 - 24
Starting A Euclid Club
Jeremiah J. Brodkey
A student-faculty group discusses the Elements.
(889, 1996) 386 - 388
Spiral Through Recursion
Jeffrey M. Choppin
Finding areas and perimeters of spirals created through recursive processes.
(87, 1994) 504 - 508
Tournaments and Geometric Sequences
Vincent P. Schielack, Jr.
Relating the number of games in a tournament to the sum
of a geometric sequence.
(86, 1993) 127 - 129
Gary O's Fence Question
David S. Daniels
Ninth, tenth, eleventh, and twelfth-grade solutions for the
problem of finding the amount of fence required for a baseball field.
(86, 1993) 252 - 254
Mathematics in Baseball
Michael T. Battista
One section involves the geometry of baseball.
(86, 1993) 336 - 342
The Shape of a Baseball Field
Milton P. Eisner
Determining the shape of an outfield fence utilizing conic sections,
trigonometric functions, and polar coordinates.
(86, 1993) 366 - 371
The Golden Ratio: A Golden Opportunity to Investigate Multiple
Representations of a Problem
Edwin M. Dickey
Several ways of finding the value.
(86, 1993) 554 - 557
Drilling Square Holes
Scott G. Smith
Using a Reuleaux triangle.
(86, 1993) 579 - 583
Inflections on the Bedroom Floor
Jack L. Weiner and G. R. Chapman
Using the path of a folding door to illustrate the concept of a point
of inflection. (This article would more appropriately be included
in a calculus bibliography - however the end-of-year listing
includes it under geometry.)
(86, 1993) 598 - 601
The Silver Ratio: A Vehicle for Generalization
Donald B. Coleman
A discussion of a generalization of the golden ratio.
(82, 1989) 54 - 59
Visualizing the Geometric Series
Albert B. Bennett, Jr.
Using regions in the plane to represent finite and infinite geometric
series. (82, 1989) 130 - 136
The Peelle Triangle
Alan Lipp
Information which can be deduced from the triangle about points,
lines, segments, squares, and cubes. A relation to Pascal's triangle.
80, (1987) 56 - 60.
Periodic Pictures
Ray S. Nowak
Activities involving graphical symmetries produced by periodic
decimals. BASIC program provided.
80, (1987) 126 - 137.
Spheres in a Cone; or, Proving the Conic Sections
David Atkinson
Using Dandelin's spheres to prove that the conics are indeed
sections of a cone.
80, (1987) 182 - 184.
Finding the Area of Regular Polygons
William M. Waters, Jr.
Finding the ratio of the area of one regular polygon to that
of another when they are inscribed in the same circle.
80, (1987) 278 - 280
Geometrical Adventures in Functionland
Rina Hershkowitz, Abraham Arcavi, and Theodore Eisenberg
Determining the change in area produced by making a change in
some property of a particular figure.
80, (1987) 346 - 352.
Tape Constructions
Lisa Evered
Using tape to do standard ruler-and-compass constructions.
80, (1987) 353 - 356.
Crystals: Through the Looking Glass with Planes, Points, and Rotational
Symmetries
Carole J. Reesink
Three-dimensional symmetry related to crystallographic analysis.
Nets for constructing eight three-dimensional models are provided.
80, (1987) 377 - 389.
Illustrating the Euler Line
James M. Rubillo
Finding the coordinates of the points on the line.
80, (1987) 389 - 393.
Some Theorems Involving the Lengths of Segments in a Triangle
Donald R. Byrkit and Timothy L. Dixon
Proof of a theorem concerning the length of an internal angle
bisector in a triangle. Other related results are included.
80, (1987) 576 - 579.
Problem Solving in Geometry--a Sequence of Reuleaux Triangles
James R. Smart
Investigation of area relations for a sequence of Reuleaux
triangles associated with an equilateral triangle and a sequence
of medial triangles.
79, (1986) 11 - 14.
Halley's Comet in the Classroom
Peter Broughton
Activities involved with the motion of the comet. Construction of
a model showing the relation between the comet's orbit and the orbit
of the earth.
79, (1986) 85 - 89. (see note Sept. 1986, p. 485)
Reflection Patterns for Patchwork Quilts
Duane DeTemple
Forming patchwork quilt patterns by reflecting a single square back
and forth between inner and outer rectangles. Investigating the
periodic patterns formed. BASIC program included.
79, (1986) 138 - 143.
Dirichlet Polygons--An Example of Geometry in Geography
Thomas O'Shea
Applications of Dirichlet polygons, including homestead boundaries
and rainfall measurement.
79, (1986) 170 - 173.
A Geometric Figure Relating the Golden Ratio and Pi
Donald T. Seitz
The ratio of a golden cuboid to that of the sphere which
circumscribes it.
79, (1986) 340 - 341.
An Interesting Solid
Louis Shahin
Can the sum of the edges, the surface, and the volume of a
three-dimensional object be numerically equal?
79, (1986) 378 - 379.
The Bank Shot
Dan Byrne
Geometry of similar triangles and reflections applied to pool.
79, (1986) 429 - 430, 487.
Where Is the Ball Going?
Jack A. Ott and Anthony Contento
Examination of ball paths on a pool table. BASIC routine included.
79, (1986) 456 - 460.
High Resolution Plots of Trigonometric Functions
Marvin E. Stick and Michael J. Stick
Some of the plots were part of a "mathematics in art" project in a
high school geometry class. BASIC routines included.
78, (1985) 632 - 636.
Chamelonic Cubes
Gary Chartrand, Ratko Tosic, Vojislav Petrovic
Cube coloring related to Instant Insanity and to Rubik's Cube.
76, (1983) 23 - 26.
Enrichment Activities for Geometry
Zalman Usiskin
Four facets, 16 activities.
76, (1983) 264 - 266.
The Teddy Bear That Stays Stranded
Vernon Thomas Sarver, Jr.
Given two boards try to retrieve a teddy bear from a circular island
in a circular lake.
76, (1983) 496 - 497.
A Student Run Geometry Contest
Charles G. Ames
Description and sample problems.
75, (1982) 142 - 143, 178.
1979 National Middle School Mathematics Olympiads In
The People's Republic of China
Jerry P. Becker
There are some geometry problems provided.
75, (1982) 161 - 169.
Some Applications Of The Circumference Formula
Eugene F. Krause
Looks at distances around various types of tracks and the effect of
lane positions, finally comes to a consideration of the construction
of train wheels.
75, (1982) 369 - 377.
Geomegy or Geolotry: What Happens When Geology Visits Geometry Class?
Carole J. Reesink
Crystallography, axes, symmetry, activities, examples.
75, (1982) 454 - 461.
Repeating Decimals, Geometric Patterns and Open-Ended Questions
Robert L. McGinty and William Mutch
Deals with geometric patterns derived using chords of a circle obtained
utilizing the repeating decimal block for 1/p where p is a prime number.
75, (1982) 600 - 602.
Some Strategy Games Using Desargues Theorem
Andrew J. Salisbury
Tic Tac Toe on a grid derived from the Desargues configuration.
75, (1982) 652 - 653.
The Geometry Of Tennis
Jay Graening
The development of strategy (primarily ball placement) using
triangle geometry.
75, (1982) 658 - 663.
The Golden Ratio In Geometry
Susan Martin Peeples
Activities exploring Fibonacci numbers and the golden ratio.
75, (1982) 672 - 676, 685.
Geometric Probability - A Source Of Interesting and Significant
Applications Of High School Mathematics
Richard Dahlke and Robert Fakler
Probabilities related to area ratios.
75, (1982) 736 - 745.
Mathematical Olympiad Competitions In The People's Republic of China
Jerry P. Becker and Kathy C. Hsi
There are several geometry problems presented and solved.
74, (1981) 421 - 433.
Activities From "Activities": An Annotated Bibliography
Christian A. Hirsch
A list of articles from the "Activities" section. Geometry is
on pages 47 - 49.
73, (1980) 46 - 50.
Unsolved Problems In Geometry
Lynn Arthur Steen
A reprint from Science News. Lists and discusses several problems.
73, (1980) 366 - 369.
A Student Presented Mathematics Club Program - Non-Euclidean Geometries
Suggested program topics.
73, (1980) 451 - 452.
Geometric Transformations and Music Composition
Thomas O'Shea
Relations between musical procedures (transposition, inversion, etc.)
and transformations of the plane.
72, (1979) 523 - 528.
Geometry Word Search
Margaret M. Conway
Word search game.
71, (1978) 269.
Geodesic Domes In The Classroom
Charles Lund
Classroom activities related to the structure of geodesic domes.
71, (1978) 578 - 581.
Geodesic Domes By Euclidean Construction
M.J. Wenninger, O.S.B.
The use of Euclidean constructions to determine chord factors, etc.
71, (1978) 582 - 587.
Curve-Stitching The Cardioid and Related Curves
Peter Catranides
Some theory and instructions.
71, (1978) 726 - 732.
A Mathematics Club Project From Omar Khyyam
Beatrice Lumpkin
Conics and a cubic equation.
71, (1978) 740 - 744.
Finding Chord Factors Of Geodesic Domes
Fred Blaisdell and Art Indelicato
Some of the mathematics encountered in building a dome.
70, (1977) 117 - 124.
The Orthotetrakaidecahedron - A Cell Model For Biology Classes
M. Stroessel Wahl
An application of geometry to biology.
70, (1977) 244 - 247.
Maps: Geometry in Geography
Thomas W. Shilgalis
Projections from a sphere to a plane.
70, (1977) 400 - 404.
Student Projects In Geometry
Andrew A. Zucker
Eighteen suggestions and a bibliography.
70, (1977) 567 - 700.
Dual Concepts - Graphing With Lines (Points)
Deloyd E. Steretz and Joseph D. Teeters
An exhibition of duality.
70, (1977) 726 - 731.
Discovery In One, Two, and Three Dimensions
Lyle R. Smith
Relationships involving segments, squares, and cubes.
70, (1977) 733 - 738.
The Nine-Point Circle On A Geoboard
Robert L. Jones
Locating the nine points and the center.
69, (1976) 141 - 142.
Minimal Surfaces Rediscovered
Sister Rita M. Ehrmann
Soap bubble experiments for Plateau's problem (find the surface of
smallest area with a given boundary.) Soap film experiments for
Steiner's problem (minimal linear linkage of points in a plane.)
69, (1976) 146 - 152.
Coordinates For Lines: An Enrichment Activity
Alan R. Osbourne
Developing a system of coordinates for lines in a plane.
69, (1976) 264 - 267.
Circles, Chords, Secants, Tangents, and Quadratic Equations
Alton T. Olson
Using geometric techniques to solve quadratic equations.
69, (1976) 641 - 645.
The Design, Proof, and Placement Of An Inclined Gnomon Sundial Accurate For Your Locality
Charles T. Wolf
Title tells all.
68, (1975) 438 - 441.
Paper Folds and Proofs
Joan E. Fehlen
Geometric results by paper folding.
68, (1975) 608 - 611.
Rolling Curves
Stanley A. Smith
Activities involving curves of constant width.
67, (1974) 239 - 242.
How To Draw Tessellations Of The Escher Type
Joseph L. Teeters
Methods for students to use in the creation of tessellations.
67, (1974) 307 - 310.
Spirolaterals
Frank C. Odds
Figures derived from a logically constructed set of rules.
66, (1973) 121 - 124.
On The Occasional Incompatibility Of Algebra and Geometry
Margaret A. Farrell and Ernest R. Ranucci
Situations in which geometric analysis indicates that an initial
algebraic solution is incomplete.
66, (1973) 491 - 497.
Fun With Flips
Evan M. Maletsky
Activities for introducing the concept of a locus as the path of
a point moving under certain conditions.
66, (1973) 531 - 534.
The Wheel Of Aristotle
David W. Ballew
A look at mathematical paradoxes.
65, (1972) 507 - 509.
What? A Roller With Corners?
John A. Dossey
Closed curves of constant width.
65, (1972) 720 - 724.
Mathematics On A Pool Table
Nicholas Grant
The use of geometric techniques for predicting into which pocket
a ball will fall.
64, (1971) 255 -257.
A Construction Of and Physical Model For Finite Euclidean and Projective
Geometries
William A. Miller
Models utilizing squares and tori. Some development of theory.
63, (1970) 301 - 306.
The Crossnumber Puzzle Solves A Teaching Problem
Sheila Moskowitz
A crossnumber puzzle involving geometric concepts.
62, (1969) 200 - 204.
Modern Mathematics Or Traditional Mathematics
Werner E. Buker
Fagnano's problem and Dandelin's ellipse.
62, (1969) 665 - 669.
In The Name Of Geometry
Thomas P. Hillman and Barbara Sirois
A crossword puzzle involving puns.
61, (1968) 264 - 265.
Six Nontrivial Equivalent Problems
Zalman Usiskin
Two of the problems are geometric in nature.
61, (1968) 388 - 390.
A Christmas Tree For 1968
Lucille Groenke
An exercise in graphing.
61, (1968) 764.
A Christmas Puzzle
Sister Anne Agnes von Steger, C.S.J.
Geometrically based.
60, (1967) 848 - 849.
The Relation Between Distance and Sight Area
Chew Chi-Ming
The apparent length of an object related to its distance
from the viewer.
58, (1965) 298 - 302.
What To Do In A Mathematics Club
Dolores Granito
Some of the activities could be used for geometric enrichment.
57, (1964) 35 - 39.
Approximating An Angle Division By A Sequence of Bisections
Lyle E. Pursell
Utilizes binary fractions.
57, (1964) 529 - 532.
A Christmas Graph
John D. Holcomb
Graphing a snowman.
57, (1964) 560 - 561.
Enrichment: A Geometry Laboratory
Peter Dunn-Rankin and Raymond Sweet
A discussion of possible activities.
56, (1963) 134 - 140.
Christmas At Palm Beach High School - "The Geome Tree"
Josephine M. Chaney
Polyhedral tree ornaments.
55, (1962) 600 - 602.
Construction and Evaluation Of Trigonometric Functions Of Some Special Angles
James D. Bristol
Applied geometry.
54, (1961) 4 - 7.
The Cardioid
Robert C. Yates
Properties.
52, (1959) 10 - 14.
Review Tests Can Be Different
Louise Hazzard
A crossnumber puzzle review test on area.
52, (1959) 133.
Mobile Geometric Figures
Alvin E. Ross
Construction of mobiles to demonstrate geometric principles.
51, (1958) 375 - 376.
Another Approach To The Nine-Point Circle
John Satterly
Also includes a proof of Feuerbach's theorem.
50, (1957) 53 - 54.
An Unusual Application Of A Simple Geometric Principle
Laura Guggenbuhl
The law of cosines and plastic surgery.
50, (1957) 322 - 324.
Fun With Graphs
Paul S. Jorgensen
Pictures by graphing.
50, (1957) 524 - 525.
A Geometric Approach To Field-Goal Kicking
Gerald R. Rosing
On taking a five-yard penalty to obtain a "better angle".
47, (1954) 463 - 466.
A Method Of Exhibiting The Theorem Of Pappus In The Classroom
Norman Anning
The construction of a device.
46, (1953) 50.
Applications
Sheldon S. Myers
The height of a room, the law of lenses, the inverse squares
law for light.
44, (1951) 141 - 143.
Projects For Plane Geometry
Marie L. Bauer
Suggested projects for dealing with applications.
44, (1951) 235 - 239.
Flying Saucers - A Project In Circles
Nina Oliver
Using geometric techniques and principles to decorate paper plates.
44, (1951) 355 - 357.
Mathematics and Art
William L. Schaff
A bibliography which contains many entries which might be of use
to geometry teachers.
43, (1950) 423 - 426.
A Lesson In Appreciation: The Nine-Point Circle
Robert E. Pingry
A construction approach.
41, (1948) 314 - 316.
The Mathematical Foundations Of Architecture
Mary E. Craver
Applications, constructions, ratios, examples.
32, (1939) 147 - 155.
Art In Geometry
Lorella Ahern
Geometric enrichment through art applications.
32, (1939) 156 - 162.
Paper Folding In Plane Geometry
Sarah Louise Britton
Finding the perpendicular bisector of a segment.
32, (1939) 227 - 228.
Calculus Versus Geometry
Claire Fisher Adler
Geometric and calculus solutions of three extremum problems.
31, (1938) 19 - 23.
The Mathematics Of The Sundial
LaVergne Wood and Frances M. Lewis
Applications of geometric principles.
29, (1936) 295 - 303.
The Incommensurables Of Geometry
E. T. Browne
Irrational numbers and geometry.
27, (1934) 181 - 189.
Constructing A Transit As A Project In Geometry
T. L. Engle
How to do it.
24, (1931) 444 - 447.
Sources Of Program Material and Some Types Of Program Work Which
Might Be Undertaken By High School Mathematics Clubs
Ruth Hoag
Suggested topics and bibliography. (Geometry 495 - 497.)
24, (1931) 492 - 502.
Recreations For The Mathematics Club
Byron Bently
Contains some interesting geometric puzzles and fallacies.
23, (1930) 95 - 103.
Geometric Proofs For Trigonometric Formulas
Arthur Haas
Functions of the sum and difference of angles.
23, (1930) 321 - 326.
Geometry Humanized
Erma Scott
A play in one act.
21, (1928) 92 - 101.
Applications Of Indeterminate Equations To Geometry
M.O. Tripp
Methods for finding integer sides for polygons.
21, (1928) 268 - 272.
Stewart's Theorem, With Applications
Richard Morris
Three proofs. Applications.
21, (1928) 465 - 478.
Note On The Fallacy
Walter H. Carnahan
Part of the segment equals the whole.
19, (1926) 496 - 498.
Magic Circles
Vera Sanford
An example of 1920's Japanese mathematics.
16, (1923) 348 - 349.
Japanese Problems
Shige Hiyama
From an 1818 manuscript.
16, (1923) 359 - 365.
FINITE GEOMETRIES
Projective Space Walk For Kirkman's Schoolgirls
Sr. Rita Ehrmann
Among other things it relates the classical problem to finite
projective geometries.
68, (1975) 64 - 69.
General Finite Geometries
Steven H. Heath
Finite systems in which parallelism is not unique.
64, (1971) 541 - 545.
Developing A Finite Geometry
Charles M. Bundrick, Robert C. Frazier, and Homer C. Gerber
Details of the development of a model for a finite affine plane.
63, (1970) 487 - 492.
A Coordinate Approach To The 25-Point Miniature Geometry
Martha Heidlage
Coordinatizing a 25-point affine plane.
58, (1965) 109 - 113.
Geometric Diversions: A 25-Point Geometry
Arthur F. Coxford, Jr.
Some development of the geometry of the 25-point affine plane
57, (1964) 561 - 564.
Applications Of Finite Arithmetic, III
Roy Dubisch
Lines in a finite plane.
55, (1962) 162 - 164.
Finite Planes For The High School
A. A. Albert
Suggestions for presenting material on finite projective planes.
55, (1962) 165 - 169.
Finite Planes and Latin Squares
Truman Botts
Developments in finite geometry.
54, (1961) 300 - 306.
Miniature Geometries
Burton W. Jones
Finite projective planes.
52, (1959) 66 - 71.
FOUNDATIONS OF GEOMETRY
Starting A Euclid Club
Jeremiah J. Brodkey
A student-faculty group discusses the Elements.
(889, 1996) 386 - 388
Mathematical Structures: Answering the "Why" Questions
Doug Jones and William S. Bush
Axiomatic structures. Suggestions for teaching mathematical structure appropriate
for the secondary school.
(889, 1996) 716 - 722
What Is a Quadrilateral?
Lionel Pereira-Mendoza
An activity designed to develop an understanding of the role of
definitions in mathematics.
(86, 1993) 774 - 776
Formal Axiomatic Systems and Computer Generated Theorems
Michael T. Battista
Using a microcomputer to develop an axiomatic system.
75, (1982) 215 - 220.
Changing Postulates Can Provide Variety and Meaningful Learning
Donald Mahaffey
Proving the uniqueness of parallel lines as a consequence of an
S.A.S. similarity postulate.
75, (1982) 677 - 679.
Developing Mathematics On A Pool Table
Thomas Ray Hamel and Ernest Woodward
A mathematical system on a pool table, axioms, theorems and proofs.
70, (1977) 154 - 163.
The Meaning Of Euclidean Geometry In School Mathematics
Edwin E. Moise
Remarks by a geometry educator.
68, (1975) 472 - 477.
Independence Of The Incidence Postulates
David C. Huffman
A study of a set of incidence postulates.
62, (1969) 269 - 277.
Mathematical Definition and Teaching
Henri Poincare
A discussion of the role of definitions in mathematics.
62, (1969) 295 - 304.
The "New Mathematics" In Historical Perspective
F. Lynwood Wren
Definition 23 and postulates 1 - 5 of Book I of Euclid.
62, (1969) 579 - 584.
A Proof Of The Space-Separation Postulate
Charles A. McComas
Utilizing plane separation and plane intersection.
61, (1968) 472 - 474.
Euclidean and Other Geometries
Bruce E. Meserve
Euclidean, hyperbolic, spherical, and elliptic.
60, (1967) 2 - 11.
On The Geometry Of Euclid
M. C. Gemignani
Primarily concerned with Euclid's attempts to define point and line.
60, (1967) 160 - 164.
Equivalent Forms Of The Parallel Postulate
Lucas N. H. Hunt
Reprint from Euclides. Equivalences and proofs.
60, (1967) 641 - 652.
Aba Daba Daba
Betty Plunkett
Independence of a postulate.
59, (1966) 236 - 239.
Reflexive, Symmetric and Transitive Properties Of Relations
Dorothy H. Hoy
Examples using lines in a plane.
58, (1965) 201 - 210.
Mathematics From The Modern Viewpoint
Truman Botts and Leonard Pikaart
Axiomatic development.
54, (1961) 498 - 504.
Another View Of The Process Of Definition
Robert S. Fouch
The importance of understanding definitions.
48, (1955) 178, 186.
The Meaning Of Mathematics
C. E. Springer
A discussion of the postulational method.
48, (1955) 453 - 459.
Just What Is Mathematics
William L. Schaff
A bibliography of materials dealing with the nature and meaning
of mathematics.
46, (1953) 515 - 516.
Superposition
Philip S. Jones
A letter discussing the problems involved in the use of superposition.
45, (1952) 232 - 234.
An Interpretation and Comparison Of Three Schools Of Thought
In The Foundations Of Mathematics
E. Russell Stabler
Postulational, logical, and formalist approaches.
28, (1935) 5 - 35.
To Postulate Or Not To Postulate
Nelson A. Jackson
How many first principles (which could be proved) should
be postulated in a beginning course?
23, (1930) 194 - 196.
Applications and Proofs
E. Russell Stabler
Use of postulates.
21, (1928) 46 - 48.
Geometry Notes
M. M. S. Moriarty
Urges clearer statements of some postulates and
more consistent treatment of others.
21, (1928) 280 - 291.
Rigor Versus Expediency In The Proof Of Locus Originals
Elmer B. Bowker
Postulate freely and do not worry about redundancies.
20, (1927) 82 - 90.
Postulates and Sequences In Euclid
George W. Evans
Some analysis of the Elements.
20, (1927) 310 - 320.
Certain Undefined Elements and Tacit Assumptions In The First Book Of Euclid's Elements
Harrison E. Webb
Perceived aims in Euclid and a discussion of their attainment.
12, (1919-1920) 41 - 60.
THE FOUR COLOR PROBLEM
Some Colorful Mathematics
Duane W. DeTemple and Dean A. Walker
Activities involving the coloration of geometric objects.
(889, 1996) 307 - 312, 318 - 320
A Map-Coloring Algorithm
David Keeports
A discussion of the four-color problem and an algorithm for four-
coloring a large class of maps.
(84, 1991) 759 - 763
Creativity With Colors
Christian R. Hirsch
Map-coloring activities.
69, (1976) 215 - 218.
Map Coloring
Norman K. Roth
Suggestions for classroom activities in map coloring.
68, (1975) 647 - 653.
A Topological Problem For The Ninth-Grade Mathematics Laboratory
Jerome A. Auclair and Thomas P. Hillman
Map coloring and a related exercise on the geoboard.
61, (1968) 503 - 507.
The Four-Color Map Problem, 1840 - 1890
H.S.M. Coxeter
History.
52, (1959) 283 - 289.
Coloring Maps
Mathematics Staff-University of Chicago
Introducing the four color problem.
50, (1957) 546 - 550.
FRACTALS AND CHAOS
Some Pleasures and Perils of Iteration
Lawrence O. Cannon and Joe Elich
Solving equations by iteration. Relations to chaos theory
and sensitivity to initial conditions.
(86, 1993) 233 - 239
Building Fractal Models with Manipulatives
Loring Coes, III
Using tiles and interlocking cubes to build two and three
dimensional models of self-similar objects. Discusses the
self-similar dimension.
(86, 1993) 646 - 651
The Mandelbrot Set in the Classroom
Manny Frantz and Sylvia Lazarnick
Introducing the Mandelbrot set in second-year-algebra and precalculus
classes.
(84, 1991) 173 - 177
Fractals and Transformations
Thomas J. Bannon
Self-similar fractals and iterated function systems.
(84, 1991) 178 - 185
A Fractal Excursion
Dane R. Camp
Area and perimeter results for the Koch curve and surface area and
volume results for three-dimensional analogs.
(84, 1991) 265 - 275
Exploring Fractals - A Problem-solving Adventure Using Mathematics
an Logo
Jane F. Kern and Cherry C. Mauk
Using Logo procedures to generate self-similar figures.
(83, 1990) 179 - 185, 244
Chaos and Fractals
Ray Barton
A discussion of the chaos game and iterated function systems.
(83, 1990) 524 - 529
The Sierpinski Triangle: Deterministic versus Random Models
Margaret Cibes
Two methods for the formation of a Sierpinski triangle.
(83, 1990) 617 - 621
Supersolids: Solids Having Finite Volume and Infinite Surfaces
William P. Love
Forming solids of the indicated type. Some relation
to fractal geometry.
(82, 1989) 60 - 65
An Interesting Introduction to Sequences and Series
John C. Egsgard
Using the Koch snowflake curve.
(81, 1988) 108 - 111
GEOBOARD
Analyzing Teaching and Learning: The Art of Listening
Bridget Arnold, Pamela Turner, and Thomas J. Cooney
The relation to geometry is slight. The editors included it in the geometry section in
the end-of-year index. A small amount of work with a geoboard.
(889, 1996) 326 - 329
Multiple Solutions Involving Geoboard Problems
Lyle R. Smith
Finding areas and perimeters of polygons formed on a geoboard.
(86, 1992) 25 - 29
Problem Solving on Geoboards
Joe Kennedy
A conjecture about the number of triangles which can be formed
on an n x n geoboard.
(86, 1993) 82
If Pythagoras Had a Geoboard
Bishnu Naraine
Activities for discovering the relationship among the areas of the
four triangles determined by the squares constructed on the sides
of a given triangle.
(86, 1993) 137 - 140, 145 - 148
Start the Year Right - Discover Pick's Theorem
Douglas Wilcock
Motivating the theorem by asking for the area of a complicated polygon.
(85, 1992) 424 - 425
Pick's Theorem Extended and Generalized
Christopher Polis
The extension is to lattices other than square lattices. The author
was an eighth-grade student at the time the article was written.
(84, 1991) 399 - 401
How Many Triangles?
James M. Moses
.... can be formed on a five by five geoboard?
78, (1985) 598 - 604.
Triangles On A Grid
Bob Willcutt
Finding right triangles on a grid. Suggested related problems.
78, (1985) 608 - 614.
Sum Squares On A Geoboard Revisited
James E. L'Heureux
More about the number of different squares on a geoboard.
75, (1982) 686 - 692.
Perimeters Of Polygons On The Geoboard
Lyle R. Smith
Is it always possible to find a polygon with a given perimeter?
73, (1980) 127 - 130.
Fractions On The Geoboard
Ann E. Watkins and William Watkins
Associating rational numbers with lattice points.
73, (1980) 133 - 139.
The Pythagorean Theorem On An Isometric Geoboard
James J. Hirstein and Sidney L. Rachlin
Using area measures to establish the theorem of Pythagoras.
73, (1980) 141 - 144.
Geoboard Geometry: A Minicourse For A Middle School Classroom
John E. Feeney
Lines, angles, polygons. A 30 day schedule is provided.
73, (1980) 675 - 678.
Right Isosceles Triangles On The Geoboard
Joe Dan Austin
An exploration of number patterns (sum of integers, etc.).
72, (1979) 24 - 27.
Extremal Problems On A Geoboard
Johnny A. Lott and Hien Q. Nguyen
Investigates the minimal number of interior diagonals of an n-gon.
72, (1979) 28 - 29.
Square Roots and Geoboards
Alice Mae Gucken
A method for introducing the concept of a square root.
72, (1979) 354 - 355.
The Surveyor and The Geoboard
Ronald R. Steffani
A surveyors method for determining area related to the geoboard.
70, (1977) 147 - 149.
Sum Squares On A Geoboard
James J. Camella and James D. Watson
The number of different squares on a geoboard and their areas.
70, (1977) 150 - 153.
The Nine-Point Circle On A Geoboard
Robert L. Jones
Locating the nine points and the center.
69, (1976) 141 - 142.
From The Geoboard To Number Theory To Complex Numbers
Donavan R. Lichtenberg
Relating geometry and some aspects of number theory.
68, (1975) 370 - 375.
A Non-Simply Connected Geoboard - Based On The "What If Not" Idea
Philip A. Schmidt
Geometry on a geoboard with one square missing.
68, (1975) 384 - 388.
The Circular Geoboard - A Promising Teaching Device
James W. Hutchison
Activities on a circular geoboard.
68, (1975) 395 - 398.
The Equivalence Of Euler's and Pick's Theorems
Duane de Temple and Jack M. Robertson
Proof of the equivalence and some suggestions for the use of the
geoboard when dealing with the problem.
67, (1974) 222 - 226.
"Thought Starters" For The Circular Geoboard
Stanley M. Jenks and Donald M. Peck
A sequence of investigations leading to results about angles
and arcs of circles.
67, (1974) 228 - 233.
An Open-Ended Problem On The Geoboard
William J. Masalski
How many squares of different sizes can be formed on a 6x6 geoboard?
67, (1974) 264 - 268.
If Pythagoras Had A Geoboard
William A. Ewbank
The theorem and some variations on a geoboard.
66, (1973) 215 - 221.
The Limit Concept On The Geoboard
J.B. Harkin
Pick's formula, generalized Pick's formula, applications to simple
closed curves.
65, (1972) 13 - 17.
A Topological Problem For The Ninth-Grade Mathematics Laboratory
Jerome A. Auclair and Thomas P. Hillman
Map coloring and a related exercise on the geoboard.
61, (1968) 503 - 507.
A Multi-Model Demonstration Board
Donovan A. Johnson
A pegboard as a teaching aid. (Is this the first geoboard?)
49, (1956) 121 - 122.
GEOMETRY AND ALGEBRA
Connecting Geometry and Algebra: Geometric Interpretations of Distance
Terry W. Crites
Primarily as areas under curves.
(88, 1995) 292 - 297
The Functions of a Toy Balloon
Loring Coes III
Activities. Connections between algebra and geometry.
(87, 1994) 619 - 622, 627 - 629
Exhibiting Connections between Algebra and Geometry
David R. Laing and Arthur T. White
Situations in which the expression 2n/(n - 2) arises.
(84, 1991) 703 - 705
The Peelle Triangle
Alan Lipp
Information which can be deduced from the triangle about points, lines,
segments, squares, and cubes. A relation to Pascal's triangle.
80, (1987) 56 - 60.
Periodic Pictures
Ray S. Nowak
Activities involving graphical symmetries produced by periodic decimals.
BASIC program provided.
80, (1987) 126 - 137.
Geometrical Adventures in Functionland
Rina Hershkowitz, Abraham Arcavi, and Theodore Eisenberg
Determining the change in area produced by making a change in some
property of a particular figure.
80, (1987) 346 - 352.
Nearly Isosceles Pythagorean Triples--Once More
Hermann Hering
A proof that every NIPT can be generated by the formula provided.
79, (1986) 724 - 725.
Geometric Proof Of Algebraic Identities
Virginia M. Horak and Willis J. Horak
The proofs are primarily accomplished by dissections.
74, (1981) 212 - 216.
Measure For Measure
Harold Trimble
Geometric views of several algebraic problems.
72, (1979) 217 - 220.
Completing The Cube
Barbara Turner
Geometric models for summation formulas.
70, (1977) 67 - 70.
The "Piling Up Of Squares" In Ancient China
Frank Swetz
History. Geometric solutions to algebraic problems.
70, (1977) 72 - 78.
The Algebra and Geometry Of Polyhedra
Joseph A. Troccolo
Algebraic and geometric approaches to construction of polyhedra.
69, (1976) 220 - 224.
Circles, Chords, Secants, Tangents, and Quadratic Equations
Alton T. Olson
Using geometric techniques to solve quadratic equations.
69, (1976) 641 - 645.
Elementary Linear Algebra and Geometry via Linear Equations
Thomas J. Brieski
Relationship of the set of solutions of a homogeneous linear equation,
the coordinate plane, and the set of transformations of the plane.
68, (1975) 378 - 383.
On The Occasional Incompatibility Of Algebra and Geometry
Margaret A. Farrell and Ernest R. Ranucci
Situations in which geometric analysis indicates that an initial
algebraic solution is incomplete.
66, (1973) 491 - 497.
Geometric Solutions To Quadratic and Cubic Equations
Harley B. Henning
Geometric analogs of solutions of algebraic equations.
65, (1972) 113 - 119.
Permutation Patterns
Ernest R. Ranucci
Geometric interpretations of permutations.
65, (1972) 333 - 338.
Another Geometric Introduction To Mathematical Generalization
H. L. Kung
A geometric approach to the formula for the sum of the first n
positive integers.
65, (1972) 375 - 376.
On Proofs Of The Irrationality of SQR(2)
V. C. Harris
Contains one geometric proof.
64, (1971) 19 - 21.
Abstract Algebra From Axiomatic Geometry
J.D. MacDonald
The derivation of an abstract algebraic structure from a
projective geometry.
59, (1966) 98 - 106.
Geometric Solutions Of A Quadratic Equation
Amos Nannini
Some classical constructions are involved.
59, (1966) 647 - 649.
Vectors In Algebra and Geometry
A. M. Glicksman
Geometric results obtained by considering vectors
and linear equations.
58, (1965) 327 - 332.
Using Geometry In Algebra
John H. White
Similar triangles and navigation.
38, (1945) 58 - 63.
Use Of Figures In Solving Problems In Algebra and Geometry
Offa Neal
Applied problems interpreted geometrically.
33, (1940) 210 - 212.
GEOMETRY AND COMPUTERS
Technology and Reasoning in Algebra and Geometry
Daniel B. Hirschhorn and Denisse R. Thompson
Explorations to foster reasoning in mathematics. The geometry portion utilizes
dynamic software.
(889, 1996) 138 - 142
Folded Paper, Dynamic Geometry, and Proof: A Three-Tier Approach to the Conics
Daniel P. Scher
Folding conics and constructing Sketchpad models.
(889, 1996) 188 - 193
Theorems in Motion: Using Dynamic Geometry to Gain Fresh Insights
Daniel P. Scher
Construction of a constant-perimeter rectangle; a constant area rectangle.
(889, 1996) 330 - 332
Using Interactive-Geometry Software for Right-Angle Trigonometry
Charles Vonder Embse and Arne Englebretsen
Directions for the exploration utilizing The Geometer's Sketchpad, Cabri Geometry
II, and TI-92 Geometry.
(889, 1996) 602 - 605
Geometry and Proof
Michael T. Battista and Douglas H. Clements
Connecting Research to Teaching. Discussion of research and instructional
possibilities. Includes comments on computer programs and classroom
recommendations.
(88, 1995) 48 - 54
From Drawing to Construction with The Geometer's Sketchpad
William F. Finzer and Dan S. Bennett
Understanding the difference between a drawing and a construction.
(88, 1995) 428 - 431
Conjectures in Geometry and The Geometer's Sketchpad
Claudia Giamati
Exploration as a foundation on which to base proof.
(88, 1995) 456 - 458
Network Neighbors
William F. Finzer
An experiment in network collaboration using The Geometer's Sketchpad.
(88, 1995) 475 - 477
Technology in Perspective
Albert A. Cuoco, E. Paul Goldenberg, and Jane Mark
Technology Tips. Constructions and investigations with dynamic geometry
software.
(87, 1994) 450 - 452
Teaching Relationships between Area and Perimeter with The Geometer's Sketchpad
Michael E. Stone
For all n-gons with the same perimeter, what shape will have the greatest area?
Sketchpad investigations of the problem.
(87, 1994) 590 - 594
Dynamic Geometry Environments: What's the Point?
Celia Hoyles and Richard Noss
Technology Tips. Constructions in Cabri Geometry.
(87, 1994) 716 - 717
Mathematical Iteration through Computer Programming
Mary Kay Prichard
Some of the problems involved are geometry related.
Cutting figures, diagonals of a polygon, figurate numbers.
(86, 1993) 150 - 156
The Geometry Proof Tutor: An "Intelligent" Computer-based Tutor
in the Classroom
Richard Wertheimer
A description of classroom experiences with the GPTutor.
(83, 1990) 308 - 317
Students' Microcomputer-aided Exploration in Geometry
Daniel Chazan
Using the Geometric Supposers.
(83, 1990) 628 - 635
Let the Computer Draw the Tessellations That You Design
Jimmy C. Woods
Gives BASIC routines to save time in the drawing of tessellations.
(81, 1988) 138 - 141
Using Logo Pseudoprimitives for Geometric Investigations,
Michael T. Battista and Douglas H. Clements
A set of Logo procedures to allow the investigation of traditional
geometric topics.
(81, 1988) 166 - 174
Estimating Pi by Microcomputer
Richard J. Donahoe
Four BASIC programs using different techniques.
(81, 1988) 203 - 206
Integrating Spreadsheets into the Mathematics Classroom
Janet L. McDonald
Some of the spreadsheets presented involve geometric investigations.
(81, 1988) 615 - 622
Periodic Pictures
Ray S. Nowak
Activities involving graphical symmetries produced by periodic
decimals. BASIC program provided.
80, (1987) 126 - 137.
Lessons Learned While Approximating Pi
James E. Beamer
Approximations of pi. BASIC, FORTRAN, and TI55-II programs provided.
80, (1987) 154 - 159.
Turtle Graphics and Mathematical Induction
Frederick S. Klotz
Revising the FD command in Logo. Links to inductive proofs.
80, (1987) 636 - 639, 654.
Reflection Patterns for Patchwork Quilts
Duane DeTemple
Forming patchwork quilt patterns by reflecting a single square back
and forth between inner and outer rectangles. Investigating the
periodic patterns formed. BASIC program included.
79, (1986) 138 - 143.
Logo and the Closed-Path Theorem
Alton T. Olson
Investigation of some plane geometry theorems utilizing Logo and
the Closed-Path Theorem. Logo procedure included.
79, (1986) 250 - 255
The Geometric Supposer: Promoting Thinking and Learning
Michal Yerushalmy and Richard A. Houde
A description of classroom use of the Supposer.
79, (1986) 418 - 422.
Logo in the Mathematics Curriculum
Tom Addicks
Using Logo to produce bar graphs and pie charts.
79, (1986) 424 - 428.
Where Is the Ball Going?
Examination of ball paths on a pool table. BASIC routine included.
79, (1986) 456 - 460.
Circles and Star Polygons
Clark Kimberling
BASIC programs for producing the shapes.
78, (1985) 46 - 51.
Investigating Shapes, Formulas, and Properties With LOGO
Daniel S. Yates
LOGO activities leading to results on areas and triangle geometry.
78, (1985) 355 - 360. (See correction p. 472.)
Measuring the Areas of Golf Greens and Other Irregular Regions
W. Gary Martin and Joao Ponto
Divide the region into triangles having a common vertex at an
interior point. BASIC program provided.
78, (1985) 385 - 389.
A Piagetian Approach to Transformation Geometry via Microworlds
Patrick W. Thompson
The use of a computerized microworld called Motions to allow students
to work with transformation geometry.
78, (1985) 465 - 471.
Microworlds: Options for Learning and Teaching Geometry
Joseph F. Aieta
Using Logo in order to study relations in families of figures.
Logo procedures provided.
78, (1985) 473 - 480.
High Resolution Plots of Trigonometric Functions
Marvin E. Stick and Michael J. Stick
Some of the plots were part of a "mathematics in art" project in a
high school geometry class. BASIC routines provided.
78, (1985) 632 - 636.
A Square Share: Problem Solving with Squares
Some geometry and work with Logo.
77, (1984) 414 - 420.
Shipboard Weather Observation
Richard J. Palmaccio
Vector geometry applied to determining wind velocity from a moving
ship. BASIC programs provided.
76, (1983) 165 - 169.
Geometric Transformations On A Microcomputer
Thomas W. Shilgalis
Microcomputer programs for use in demonstrating motions and
similarities.
75, (1982) 16 - 19.
Formal Axiomatic Systems and Computer Generated Theorems
Michael T. Battista
The use of a microcomputer in the development of an abstract system.
75, (1982) 215 - 220.
Visualization, Estimation, Computation
Evan M. Maletsky
Activities for investigating the manner in which the dimensions
of a cone change as its shape changes. BASIC program provided.
75, (1982) 759 - 764.
Using The Computer To Help Prove Theorems
Louise Hay
Using a computer in an attempt to generate possible counterexamples
can be an aid toward finding a proof for the theorem.
74, (1981) 132 - 138.
Computer Classification Of Triangles and Quadrilaterals - A Challenging Application
J. Richard Dennis
Computer application, uses coordinates of vertices.
71, (1978) 452 - 458.
An Investigation Of Integral 60 degree and 120 degree Triangles
Richard C. Muller
Law of cosines investigation. Computer related.
70, (1977) 315 - 318.
GRAPH THEORY
Network Neighbors
William F. Finzer
An experiment in network collaboration using The Geometer's Sketchpad.
(88, 1995) 475 - 477
Games, Graphs, and Generalizations
Christian R. Hirsch
Activities for some problems associated with geometry and graph theory.
(81, 1988) 741 - 745
You Can't Get There From Here--An Algorithmic Approach to Eulerian and
Hamiltonian Circuits
Joan H. Shyers
Graph theory discussion.
80, (1987) 95 - 98, 148.
Charting A Classroom Cold Epidemic
Catherine Folio
An application of graph theory.
80, (1987) 204 - 206.
Graphs and Games
Christian R. Hirsch
Activities for graph theory problems.
68, (1975) 125 - 132.
Network Theory - An Enrichment Topic
Charles A Reeves
Euler's formula in the plane and in three-space.
67, (1974) 175 - 178.
Garbage Collection, Sunday Strolls, and Soldering Problems
Walter Meyer
Some work with graph theory.
65, (1972) 307 - 308.
Try Graph Theory For A Change
Jon M. Laible
The usual problems. (See correction 64, (1971) 138.)
63, (1970) 557 - 562.
Jungle - Gym Geometry
Ernest R. Ranucci
Vertices in rectangular networks.
61, (1968) 25 - 28.
GEOMETRIES OF DIMENSION GREATER THAN TWO
Making Connections: Spatial Skills and Engineering Drawings
Beverly G. Baartmans and Sheryl A. Sorby
Orthographic drawings and isometric drawings.
(889, 1996) 348 - 357
The Volume of a Sphere: A Chinese Derivation
Frank J. Swetz
A history of the development of the formula.
(88, 1995) 142 - 145
Exploring Three- and Four-Dimensional Space
Charlotte Williams Mack
Activities. Building a model for a cube and representations of a hypercube.
(88, 1995) 572 - 578, 587 - 590
Nested Platonic Solids: A Class Project in Solid Geometry
Ronald B. Hopley
Using solid models and nets. Calculating edge lengths.
(87, 1994) 312 - 318
Practical Geometry Problems: The Case of the Ritzville Pyramids
Donald Nowlin
Volumes and surface areas of cones.
(86, 1993) 198 - 200
The Method of Archimedes
John del Grande
Finding the volumes of various geometrical objects.
(86, 1993) 240 - 243
The Excitement of Learning with Our Students -- an Escalator
of Mathematical Knowledge
Alan H. Hoffer
Some of the discussion involves nets for the construction
of polyhedra.
(86, 1993) 315 - 319
The Volume of a Cone
Boris Lavric
Sharing Teaching Ideas. A method for demonstrating a
development of the formula for the volume of a cone.
(86, 1993) 384 - 385
Cube Challenge
Judy Bippert
Activities for promoting logical thinking skills in a spatial context.
(86, 1993) 386 - 390, 395 - 398
Looking at Sum k and Sum k*k Geometrically
Eric Hegblom
Using squares and determining area, using cubes and
determining volume.
(86, 1993) 584 - 587
Illustrating Mathematical Connections: Two Proofs That
Only Five Regular Polyhedra Exist
Peter L. Glidden and Erin K. Fry
A geometric proof and a graph-theoretic proof.
(86, 1993) 657 - 661
Graphing a Solid: A Classroom Activity
George Marino
Sharing Teaching Ideas. Using three-dimensional coordinates
and a distance formula to generate models of solids which
students can build.
(86, 1993) 734 - 737
Making Connections: Beyond the Surface
Dan Brutlag and Carole Maples
Dealing with scaling-surface area-volume relationships.
(85, 1992) 230 - 235
Problem Solving with Cubes
Christine A. Browning and Dwayne E. Channell
Activities for developing spatial-reasoning skills.
(85, 1992) 447 - 450, 458 - 460
Playing with Blocks: Visualizing Functions
Miriam A. Leiva, Joan Ferrini-Mundy, and Loren P. Johnson
Activities which could be used to develop spatial visualization.
(85, 1992) 641 - 646, 652 - 654
A Fractal Excursion
Dane R. Camp
Area and perimeter results for the Koch curve and surface area and
volume results for three-dimensional analogs.
(84, 1991) 265 - 275
Calculating Surface Area
Ray A. Krenek
Sharing Teaching Ideas. Calculating the area of a rectangular solid
and a cylinder.
(84, 1991) 367 - 369
Estimating the Volumes of Solid Figures with Curved Surfaces
Donald Cohen
Gives examples of solid figures that students can use to develop
estimating skills.
(84, 1991) 392 - 395
The Circle and Sphere as Great Equalizers
Steven Schwartzman
Relations between parts of figures and inscribed figures.
(84, 1991) 666 - 672
Some Discoveries with Right-Rectangular Prisms
Robert E. Reys
Activities for problem-solving experiences with area and volume.
(82, 1989) 118 - 123
Interdimensional Relationships
Joseph V. Roberti.
A look at relationships suggested by the fact that the derivative of
the area of a circle yields the circumference and the derivative of
the volume of a sphere yields the surface area.
(81, 1988) 96 - 100
Pyramids, Prisms, Antiprisms, and Deltahedra
Donovan R. Lichtenberg
A description of, and patterns for, some polyhedra which have faces
that are regular polygons.
(81, 1988) 261 - 265
Discovery With Cubes
Robert E. Reys
Activities for pattern investigation with cubes.
(81, 1988) 377 - 381
Puzzles That Section Regular Solids
William A. Miller
Activities for developing a recognition of the surface formed when a
solid is cut by a plane.
(81, 1988) 463 - 468
Dodecagon of Fortune
Dane R. Camp
Sharing Teaching Ideas. A game for use during reviews.
(81, 1988) 734 - 735
Discoveries with Rectangles and Rectangular Solids
Lyle R. Smith
Differentiating between area and perimeter for rectangles and
between volume and surface area for rectangular solids.
80, (1987) 274 - 276.
Crystals: Through the Looking Glass with Planes, Points, and Rotational
Symmetries
Carole J. Reesink
Three-dimensional symmetry related to crystallographic analysis.
Nets for constructing eight three-dimensional models are provided.
80, (1987) 377 - 389.
A Geometric Figure Relating the Golden Ratio and Pi
Donald T. Seitz
The ratio of a golden cuboid to that of the sphere which
circumscribes it.
79, (1986) 340 - 341.
An Interesting Solid
Louis Shahin
Can the sum of the edges, the surface, and the volume of a
three-dimensional object be numerically equal?
79, (1986) 378 - 379.
The Spider and the Fly: A Geometric Encounter in Three Dimensions
Rick N. Blake
Eight problems involving a minimum path.
78, (1985) 98 - 104.
Making Boxes
Steve Gill
Activities for measurement skills. Developing spatial relationships
from two-dimensional patterns.
77, (1984) 526 - 530.
Spatial Visualization
Glenda Lappus, Elizabeth A. Phillips, and Mary Jean Winter
Activities involving three-dimensional figures. Building shapes
from cubes.
77, (1984) 618 - 625.
Generating Solids
Evan J. Maletsky
Activities involving solids of revolution generated by polygons.
76, (1983) 499 - 500, 504 - 507.
An Easy Dodecahedron
Jean M. Shaw
Construction of a model.
75, (1982) 380 - 382.
Semiregular Polyhedra
Rick N. Blake and Charles Verhille
Activities for use in searching for patterns involved in the
structure of polyhedra.
75, (1982) 577 - 581.
Visualization, Estimation, Computation
Evan M. Maletsky
Activities for investigating the manner in which the dimensions of
a cone change as the shape changes. BASIC program provided.
75, (1982) 759 - 764.
A New Look Pythagoras
Carol A. Thornton
A 3-space extension of the theorem.
74, (1981) 98 - 100.
Some Circular Reasoning
Scott G. Smith
Formulas for lateral areas.
74, (1981) 191 - 194.
Spherical Geodesics
William D. Jamski
Finding the shortest distance between two points on a sphere.
74, (1981) 227 - 228, 236.
A Model Of Three Space
Jane Keller and Robert Anderson
Description of a student developed model.
74, (1981) 350 - 353.
Pythagoras On Pyramids
Aggie Azzolino
Activities involving the use of the theorem of Pythagoras to find
the altitudes of pyramids.
74, (1981) 537 - 541.
The Second National Assessment In Mathematics: Area and Volume
James J. Hirstein
A discussion of student results on these concepts.
74, (1981) 704 - 708.
Sectioning A Regular Tetrahedron
Edward J. Davis and Don Thompson
Activities for the development of generalizations about sections
of a tetrahedron.
73, (1980) 121 - 125.
Applying The Technique Of Archimedes To The "Birdcage" Problem
W. A. Stannard
Finding the volume common to two intersecting cylinders.
72, (1979) 58 - 60.
Facts Of A Cube
Ruth Butler and Robert W. Clark
Activities for the development of spatial visualization.
72, (1979) 199 - 202.
Rectangular Solids With Integral Sides
Robert W. Prielipp, John A. Aman and Norbert J. Kuenzi
What happens geometrically if all side lengths are relatively prime?
72, (1979) 368 - 370.
On Archimedean Solids
Tom Boag, Charles Boberg and Lyn Hughes
Junior high explorations using vertex sequences.
72, (1979) 371 - 376.
Polyhedra Planar Projection
Geraldine Daunis
Activities for developing geometric perception.
72, (1979) 438 - 443.
Painting Polyhedra
Christian R. Hirsch
Activities involving polyhedra. Euler's formula.
71, (1978) 119 - 122.
A Recursive Approach To The Construction Of The Deltahedra
William E. McGowan
A guide for constructing polyhedra.
71, (1978) 204 - 210.
An Easy-To-Paste Model Of The Rhombic Dodecahedron
M. Stroessel Wahl
Instructions for construction.
71, (1978) 589 - 593.
Polycubes
William J. Masalski
Activities involving cubes.
70, (1977) 46 - 50.
Polyhedra From Cardboard and Elastics
John Woolaver
Activities for construction.
70, (1977) 335 - 338.
Hypercubes, Hyperwindows and Hyperstars
Dean B. Priest
Some n-dimensional geometry.
70, (1977) 606 - 609.
Three Dimensional Geometry
Gordon D. Pritchett
Polyhedra construction. Platonic solids. Euler's formula.
69, (1976) 5 - 10.
The Algebra and Geometry Of Polyhedra
Joseph A. Troccolo
Algebraic and geometric approaches to the building of polyhedra.
69, (1976) 220 - 224.
A General Intersection Formula For Subspaces Of n-Dimension
J. Taylor Hollist
Generalizing to higher dimensions.
68, (1975) 153.
Discovery With Cubes
Robert E. Reys
Activities for visualizing three dimensional figures. Looking
for patterns.
67, (1974) 47 - 50.
An Application Of Volume and Surface Area
Robert W. Mercaldi
A game for dealing with the concepts.
67, (1974) 71 - 73.
The Fourth Dimension and Beyond ... With A Surprise Ending!
Boyd Henry
Patterns for familiar figures are extended to higher dimensions.
67, (1974) 274 - 279.
Tetrahedral Frameworks
Charles W. Trigg
A model for the analysis of tetrahedral frameworks.
67, (1974) 415 - 418.
The Volume Of The Regular Octahedron
Charles W. Trigg
Five methods of computation.
67, (1974) 644 - 646.
Collapsible Models Of Isosceles Tetrahedrons
Charles W. Trigg
How to build them from envelopes and strips of triangles.
66, (1973) 109 - 112.
Some Investigations Of N-dimensional Geometries
Sallie W. Abbas
Bounds and cross sections of n-dimensional figures.
66, (1973) 126 - 130.
Soma Cubes
George S. Carson
Possible and impossible configurations. How to show that a design
is impossible.
66, (1973) 583 - 592.
Patterns and Positions
Evan M. Maletsky
Activities for visualizing a cube using two-dimensional patterns.
66, (1973) 723 - 726.
The Total Angular Deficiency Of Polyhedra
William L. Lepowsky
Investigates the angles at the vertices of a polyhedron.
66, (1973) 748 - 752.
Collapsible Models Of The Regular Octahedron
Charles W. Trigg
How to make them.
65, (1972) 530 - 533.
Total Surface Area Of Boxes
L. Carey Bolster
Activities for investigation.
65, (1972) 535 - 538.
A Look At Regular and Semiregular Polyhedra
Carol E. Stengel
History, interrelationships and properties.
65, (1972) 713 - 719.
Viewing Diagrams In Four Dimensions
Adrien L. Hess
Representations of results in four-dimensional geometry.
64, (1971) 247 - 248.
On Skewed Regular Polygons
Ernest R. Ranucci
Polygons whose elements are not coplanar.
64, (1971) 219 - 222.
A Geometry Capsule Concerning The Five Platonic Solids
Howard Eves
History and occurrence in nature.
62, (1969) 42 - 44.
What Points Are Equidistant From Two Skew Lines?
Alexandra Forsythe
Analytic approach.
62, (1969) 97 - 101.
A Study Of The Ability Of Secondary School Pupils To Perceive The Plane
Sections Of Selected Solid Figures
Barbara L. Roe
The title explains the content.
61, (1968) 415 - 421.
Can Space Be Overtwisted?
Douglas A. Engel
Twisting chains of links of geometric figures.
61, (1968) 571 - 574.
The World Of Polyhedra
Rev. Magnus Wenninger
History and theory.
58, (1965) 244 - 248.
The History Of The Dodecahedron
J. P. Phillips
Applications also.
58, (1965) 248 - 250.
The Mathematics Of The Honeycomb
David F. Siemans, Jr.
An explanation of the shapes in which bees build.
58, (1965) 334 - 337.
Remarks On Some Elementary Volume Relations Between Familiar Solids
A. L. Loeb
The relation of volume to diagonal length.
58, (1965) 417 - 419.
The Volume Of A Truncated Pyramid In Ancient Egyptian Papyri
R. J. Gillings
History and formulae.
57, (1964) 552 - 555.
Stellated Rhombic Dodecahedron Puzzle
Rev. M. Wenninger, O.S.B.
Cardboard model.
56, (1963) 148 - 150.
Interest In The Tetrahedron
John J. Keough
Some properties.
56, (1963) 446 - 448.
The Construction Of Skeletal Polyhedra
John McClellan
Models and topological properties.
55, (1962) 106 - 111.
Stalking Solid Geometry With Knife and Clay
Jack Price
Constructing clay models.
54, (1961) 47.
The Wiequahic Configuration
E. R. Ranucci
Visualization in three space.
53, (1960) 124 - 126.
A Historical Puzzle
N. A. Court
The altitudes of a tetrahedron.
52, (1959) 31 - 32.
On Teaching Dihedral Angle and Steradian
Howard Fehr
Extension of the definition of angle in a plane.
51, (1958) 272 - 275.
On Teaching Trihedral Angle and Solid Angle
Howard Fehr
Solid geometry methods suggestions.
51, (1958) 358 - 361.
The "Steinmetz Problem" and School Arithmetic
Richard M. Sutton
The volume contained by the intersection of two cylinders.
50, (1957) 434 - 435.
A Paper Model For Solid Geometry
Ethel Saupe
Prisms.
49, (1956) 185 - 186.
Three Folding Models Of Polyhedra
Adrian Struyk
How to make them.
49, (1956) 286 - 288.
Casting Geometric Models In Plaster-of-Paris
Wallace L. Hainlin
Model constructions.
48, (1955) 329.
Fishline and Sinker
Emil J. Berger
A model for a polyhedral angle.
48, (1955) 408.
A Model For Giving Meaning To Superposition In Solid Geometry
Emil J. Berger
Construction of teaching aids.
47, (1954) 33 - 35.
Eureka
Emil J. Berger
The ratio of the surface area of a sphere to the lateral area of
a circumscribed cylinder.
47, (1954) 105.
A Tetrahedron With Planes Bisecting Three Dihedral Angles
Emil J. Berger
Construction of a model.
47, (1954) 186 - 188.
Parallelogram and Parallelepiped
Victor Thebault
Theorems about diagonals.
47, (1954) 266 - 267.
A Problem From Solid Geometry
Emil J. Berger
A sphere and a trihedral angle.
46, (1953) 505 - 506.
Some Notes On The Prismoidal Formula
B.E. Meserve and R.E. Pingry
Volume formulas.
45, (1952) 257 - 263.
Leonardo da Vinci and The Center Of Gravity Of A Tetrahedron
John Satterly
History and a proof.
45, (1952) 576 - 577.
Models For Certain Pyramids
Joseph A Nyberg
Construction.
39, (1946) 84 - 85.
Continuous Transformations Of Regular Solids
H. v. Baravalle
Relations between cube and tetrahedron, etc.
39, (1946) 147 - 154.
Demonstration Of Conic Sections and Skew Curves With String Models
H. v. Baravalle
Construction and uses of models.
39, (1946) 284 - 287.
Models Of The Regular Polyhedrons
R. F. Graesser
Construction.
38, (1945) 368 - 369.
Teaching Solid Geometry
Nancy C. Wylie
Suggestions.
36, (1943) 126 - 127.
Models In Solid Geometry
Miles C. Hartley
Models and theorems which they can be used to illustrate.
35, (1942) 5 - 7.
Looking At Solid Geometry Through Perspective
Ethel Spearman
Using perspective drawings to deal with solid geometric concepts.
34, (1941) 147 - 150.
A Helpful Technique In Teaching Solid Geometry
James V. Bernardo
Use of models.
33, (1940) 39 - 40.
The Efficiency Of Certain Shapes In Nature and Technology
May Hickey
A suggested unit of instruction in intuitive solid geometry.
32, (1939) 129 - 133.
The Dandelin Spheres
Lee Emerson Boyer
History and comments.
31, (1938) 124 - 125.
The Teaching Of Solid Geometry At The University of Vermont
G. H. Nicholson
Approaches, objectives, techniques.
30, (1937) 326 - 330.
The Tetrahedron and Its Circumscribed Parallelepiped
N.A. Court
Construction of the parallelepiped, some of its geometry and some
geometry of the tetrahedron.
26, (1933) 46 - 52.
Drawing For Teachers Of Solid Geometry
John W. Bradshaw
Part Four. Drawing solids bounded by the right circular cylinder
and the sphere.
26, (1933) 140 - 145.
Part Three. Techniques for drawing prisms.
19, (1926) 401 - 407.
Part Two. Representing positions of points in space.
18, (1925) 37 - 45.
Part One. Some beginning techniques.
17, (1924) 475 - 481.
The Fourth Dimension
Anice Seybold
General discussion.
24, (1931) 41 - 45.
The Fourth Dimension and Hyperspace
Theresa Tremp
A discussion of their nature.
19, (1926) 140 - 146.
A Course In Solid Geometry
William A. Austin
Description, methods and content.
19, (1926) 349 - 361.
Some Applications Of Algebra To Theorems In Solid Geometry
Joseph B. Reynolds
Volumes of solids.
18, (1925) 1 - 9.
Reflections On Fourth Dimension
A. N. Altieri
A 1920's student view.
18, (1925) 490 - 495.
The Extension Of Concepts In Mathematics
Aubrey W. Kempner
Infinite elements in geometry, non-Euclidean geometry,
four-dimensional geometry.
16, (1923) 1 - 23.
A Study Of The Cultivation Of Space Imagery In Solid Geometry Through
The Use Of Models
Edwin W. Schreiber
Construction and use of models.
16, (1923) 103 - 111.
The Volume Of A Sphere
Proof of the formula.
15, (1922) 90 - 93.
A Simple Method Of Constructing A Hyperbolic Paraboloid
E.J. Guy
A model.
12, (1919-1920) 28 - 29.
A Geometric Representation
E. D. Roe, Jr.
The surface on which a family of spirals lies. Analytic approach.
11, (1918-1919) 9 - 25.
A Geometric Representation
E. D. Roe, Jr.
Analytic geometry in space.
10, (1917-1918) 205 - 210.
Geometric Stereograms - A Device For Making Solid Geometry
Tangible To The Average Student
Walter Francis Shenton
The use of colored glasses and special drawings to produce 3-D effects.
8, (1915-1916) 124 - 131.
Geometry Of Four Dimensions
Henry P. Manning
Results which are presented in more detail in the author's book which
has the same title.
7, (1914-1915) 49 - 58.
The Five Platonic Solids
James H. Weaver
Some of their properties.
7, (1914-1915) 86 - 88.
The Way To Begin Solid Geometry
Howard F. Hart
Teaching methods.
4, (1911-1912) 54 - 57.
Solid Geometry
Howard F. Hart
Some geometry on a sphere.
3, (1910-1911) 24 - 26.
HISTORY OF GEOMETRY
The Volume of a Sphere: A Chinese Derivation
Frank J. Swetz
A history of the development of the formula.
(88, 1995) 142 - 145
Albrecht Durer's Renaissance Connections between Mathematics and Art
Karen Doyle Walton
Some of Durer's geometric work is discussed.
(87, 1994) 278 - 282
Word Roots in Geometry
Margaret E. McIntosh
Suggestions for a unit on word study in geometry.
(87, 1994) 510 - 515
Humanize Your Classroom with the History of Mathematics
James K. Bidwell
Some of the suggestions apply to the geometry classroom.
(86, 1993) 461 - 464
A Chain of Influence in the Development of Geometry
James E. Lightner
A look at some early geometers and their influence on the next
generation of geometers.
(84, 1991) 15 - 19
Euclid and Descartes: A Partnership
Dorothy Hoy Wasdovich
Integrating coordinate and synthetic geometry.
(84, 1991) 706 - 709
Using Problems from the History of Mathematics in Classroom Instruction
Frank J. Swetz
Some of the examples presented are geometric.
(82, 1989) 370 - 377
When Did Euclid Live? An Answer Plus a Short History of Geometry
Gail H. Adele
A chronological table of geometric events.
(82, 1989) 460 - 463
Did Gauss Discover That, Too?
Richard L. Francis
Is Gauss given proper credit (positive or negative) for various
mathematical developments?
79, (1986) 288 - 293.
Mathematical Firsts--Who Done It?
Richard H. Williams and Roy D. Mazzagatti
Historical comments relating names of objects and theorems to their
actual discoverers. Includes the theorem of Pythagoras, Euler's
polyhedral theorem, Mascheroni constructions, and Playfair's axiom.
79, (1986) 387 - 391.
The Contributions of Karaji--Successor to al-Khwarizmi
Hormoz Pazwash and Gus Mavrigian
History. Some geometric ideas involved.
79, (1986) 538 - 541.
An Astounding Revelation on the History of Pi
Alfred S. Posamentier and Noam Gorden
A reinterpretation of the biblical value of pi.
77, (1984) 52.
Seeking Relevance? Try the History of Mathematics
Frank J. Swetz
Suggestions for incorporating historical material into secondary
classroom presentations. Several geometrical aspects are included.
77, (1984) 54 - 62.
The World of Buckminster Fuller
Ernest R. Ranucci
History.
71, (1978) 568 - 577.
The "Piling Up of Squares" in Ancient China
Frank Swetz
History. Geometric solutions for algebraic problems.
70, (1977) 72 - 78.
The Artist As Mathematician
Norman Slawsky
Explores the creative process in mathematics from the viewpoint of
the history and development of geometry.
70, (1977) 298 - 308.
President Garfield and The Pythagorean Theorem
Robert Schloming
History and Garfield's proof.
69, (1976) 686 - 687.
Master of Tessellations: M.C. Escher, 1898-1972
Ernest R. Ranucci
An account of Escher's contributions to geometry.
67, (1974) 299 - 306.
Thabit ibn Qurra and The Pythagorean Theorem
Robert Schloming
History.
63, (1970) 519 - 528.
Guido Fubini
Clayton W. Dodge
History. Some exercises on projection.
62, (1969) 45 - 46.
The "New Mathematics" in Historical Perspective
F. Lynwood Wren
Definition 23 and postulates 1-5 of Book I of Euclid.
62, (1969) 579 - 584.
A Medieval Proof Of Heron's Formula
Yusef Id and E.S. Kennedy
A proof by Al-Shanni.
62, (1969) 585 - 587.
The Parallel Postulate
Raymond H. Rolwing and Maita Levine
Notes on attempts at proofs.
62, (1969) 665 - 669.
The Position of Thomas Carlyle in the History of Mathematics
Peter A. Wursthorn
Contains some of his geometrical work.
59, (1966) 755 - 770.
How Ptolemy Constructed Trigonometric Tables
Brother T. Brendan
Contains some geometry of the circle.
58, (1965) 141 - 149.
Gaspard Monge and Descriptive Geometry
Leo Gaffney, S.J.
Some of the geometric work of Monge.
58, (1965) 338 - 343.
Recent Evidences Of Primeval Mathematics
Daniel B. Lloyd
Geometry on the Tel Harmal tablets (c. 1800 B.C.).
58, (1965) 720 - 723.
The Dawn Of Demonstrative Geometry
Nathan Altshiller Court
History.
57, (1965) 163 - 166.
The Volume Of A Truncated Pyramid In Ancient Egyptian Papyri
R.J. Gillings
History and formulae.
57, (1964) 552 - 555.
Johan de Witt's Kinematical Constructions Of The Conics
Joy B. Easton
History and techniques.
56, (1963) 632 - 635.
Al-Biruni On Determining The Meridian
E.S. Kennedy
History and techniques.
56, (1963) 635 - 637.
Notes On Inversion
N.A. Court
History.
55, (1962) 655 - 657.
George Mohr and Euclides Curiosi
Arthur E. Hallerberg
History and some fixed compass constructions.
53, (1960) 127 - 132.
The Names "Ellipse", "Parabola", and "Hyperbola"
Howard Eves
History.
53, (1960) 280 - 281.
Why and How Should We Correct The Mistakes Of Euclid
Paul H. Daus
History and foundational comments.
53, (1960) 576 - 581.
Omar Khayyam - Mathematician
D. J. Struik
History with some comments on the parallel postulate.
51, (1958) 280 - 285.
Omar Khayyam's Solution Of Cubic Equations
Howard Eves
History with geometrical applications.
51, (1958) 285 - 286.
Helmholtz and The Nature Of Geometrical Axioms:
A Segment In The History Of Mathematics
Morton R. Kenner
Geometry and the work of Helmholtz.
50, (1957) 98 - 104.
Curiosity and Culture
F. Lynwood Wren
Contains some material on the development of geometries.
50, (1957) 361 - 371.
The Evolution Of Geometry
Bruce E. Meserve
History.
49, (1956) 372 - 382.
Archytas' Duplication Of The Cube
R. F. Graesser
History.
49, (1956) 393 - 395.
A New Ballad Of Sir Patrick Spens
Phillip S. Jones
Historical, a parody of an old ballad, dealing with the first
propositions of Book I of Euclid.
48, (1955) 30 - 32.
Tangible Arithmetic III: The Proportional Divider
Lucille Pinetti
History, uses, and proofs.
48, (1955) 91 - 95.
Leonardo da Vinci and The Center Of Gravity Of A Tetrahedron
John Satterly
History and a proof.
45, (1952) 576 - 577.
Early American Geometry
Phillip S. Jones
History.
37, (1944) 3 - 11.
Some Of Euclid's Algebra
George W. Evans
Algebraic results in the Elements.
20, (1927) 127 - 141.
Some Lovers Of The Conic Sections
Margaret L. Chapin
History.
19, (1926) 36 - 45.
HOW SHOULD GEOMETRY BE TAUGHT?
Concept Worksheet: An Important Tool for Learning
Charalampos Toumasis
The example presented is geometric in nature, it deals with the characterization of a
parallelogram.
(88, 1995) 98 - 100
Bringing Pythagoras to Life
Donna Ericksen, John Stasiuk, and Martha Frank
Sharing Teaching Ideas. A pursuit game with path a right triangle. The questions
are related to the theorem of Pythagoras.
(88, 1995) 744 - 747
Making Connections by Using Molecular Models in Geometry
Robert Pacyga
Implementing the Curriculum and Evaluation Standards. Relating models to
compounds found in chemistry. Connecting mathematics, science, and English.
(87, 1994) 43 - 46
Pi Day
Bruce C. Waldner
Mathematically related contests held on March 14 (i.e. 3/14).
(87, 1994) 86 - 87
Geometry and Poetry
Betty B. Thompson
Sharing Teaching Ideas. Reading poems to find one which conjure up geometric
images and then illustrating the idea graphically.
(87, 1994) 88
Exploratory Geometry - Let the Students Write the Text
Virginia Stallings-Roberts
A description of a course.
(87, 1994) 403 - 408
Technology in Perspective
Albert A. Cuoco, E. Paul Goldenberg, and Jane Mark
Technology Tips. Constructions and investigations with dynamic geometry
software.
(87, 1994) 450 - 452
Word Roots in Geometry
Margaret E. McIntosh
Suggestions for a unit on word study in geometry.
(87, 1994) 510 - 515
Animating Geometry Discussions with Flexigons
Ruth McClintock
A flexigon is created by stringing together plastic straws of varying lengths in a
closed loop. These tools are then used to investigate the geometry of polygons.
(87, 1994) 602 - 606
An Active Approach to Geometry
Arthur A. Hiatt and William E. Allen
Sharing Teaching Ideas. A variation on the problem of finding a minimum path
from A to B if you required to go through C.
(87, 1994) 702 - 703
A Core Curriculum in Geometry
Martha Tietze
The use of hands-on activities in the third year of an integrated
sequence for the non-college bound.
(85, 1992) 300 - 303
Problem Solving with Cubes
Christine A. Browning and Dwayne E. Channell
Activities for developing spatial-reasoning skills.
(85, 1992) 447 - 450, 458 - 460
Folding Perpendiculars and Counting Slope
Ann Blomquist
Sharing Teaching Ideas. Folding activities to discover relations
between slopes of perpendicular lines.
(85, 1992) 538 - 539
Playing with Blocks: Visualizing Functions
Miriam A. Leiva, Joan Ferrini-Mundy, and Loren P. Johnson
Activities which could be used to develop spatial visualization.
(85, 1992) 641 - 646, 652 - 654
Integrating Transformation Geometry into Traditional High School Geometry
Steve Okolica and Georgette Macrina
Moving transformation geometry ahead of deductive geometry.
(85, 1992) 716 - 719
Van Hiele Levels of Geometric Thought Revisited
Anne Teppo
Relating the van Hiele theory to the Standards.
(84, 1991) 210 - 221
Communicating Mathematics
Mary M. Hatfield and Gary G. Bitter
Generating patterns and making conjectures.
(84, 1991) 615 - 621
Make Your Own Problems - and Then Solve Them
Robert L. Kimball
Activities for solving a maximum problem.
(84, 1991) 647 - 655
STAR Experimental Geometry: Working with Mathematically Gifted
Middle School Students
Gary Talsma and Jim Hersberger
A description of a course for mathematically gifted middle
school students.
(83, 1990) 351 - 357
High School Geometry Should be a Laboratory Course
Ernest Woodward
Encourages the use of a laboratory format in geometry teaching.
(83, 1990) 4 - 5
Students' Microcomputer-aided Exploration in Geometry
Daniel Chazan
Using the Geometric Supposers.
(83, 1990) 628 - 635
An Interactive Approach to Problem Solving: The Relay Format
Viji K. Sundar
A game for review purposes. Some geometry problems are included.
(82, 1989) 168 - 172
"Figuring" Out A Jigsaw Puzzle
Ken Irby
Sharing Teaching Ideas. Analyzing a puzzle using geometric techniques.
(82, 1989) 260 - 263
Games, Geometry, and Teaching
George W. Bright and John G. Harvey
Games for teaching content and developing problem solving skills.
(81, 1988) 250 - 259
Let ABC Be Any Triangle
Baruch Schwartz and Maxim Bruckheimer
Drawing a triangle that does not look special.
(81, 1988) 640 - 642
Dodecagon of Fortune
Dane R. Camp
Sharing Teaching Ideas. A game for use during reviews.
(81, 1988) 734 - 735
The Indirect Method
Joseph V. Roberti
Examples of indirect proofs and suggested further problems for
investigation.
80, (1987) 41 - 43.
Guessing Geometric Shapes
Gloria J. Bledsoe
A guessing game designed to help students to become familiar with
properties of various geometric figures, applications to both two
and three dimensions.
80, (1987) 178 - 180.
Sometimes Students' Errors Are Our Fault
Nitsa Movshovitz-Hadar, Shlomo Inbar, and Orit Zaslavsky
Examples of student errors in written tests which can be attributed
to editorial factors. Three of four problems examined are geometric
in nature.
80, (1987) 191 - 194.
Discoveries with Rectangles and Rectangular Solids
Lyle R. Smith
Differentiating between area and perimeter for rectangles and between
volume and surface area for rectangular solids.
80, (1987) 274 - 276.
Stuck! Don't Give Up! Subgoal-Generation Strategies in Problem Solving
Robert J. Jensen
Managing the problem solution process. Subgoals and strategies.
80, (1987) 614 - 621, 634.
Place Your Geometry Class in "Geopardy"
Hal M. Saunders
A Jeopardy-like game for teaching and reviewing geometric facts.
80, (1987) 722 - 725.
Teaching the Elimination Strategy
Daniel T. Dolan and James Williamson
Activities for developing the problem solving skill elimination.
79, (1986) 34 - 36, 41 - 47.
Logo and the Closed-Path Theorem
Alton T. Olson
Investigation of some plane geometry theorems utilizing Logo and
the Closed-Path Theorem. Logo procedure included.
79, (1986) 250 - 255
Teaching Students How to Study Mathematics: A Classroom Approach
Marcia Birken
Not specifically geometry oriented, but still quite useful. Eight
procedures involved.
79, (1986) 410 - 413.
The Geometric Supposer: Promoting Thinking and Learning
Michal Yerushalmy and Richard A. Houde
A description of classroom use of the Supposer.
79, (1986) 418 - 422.
Logo in the Mathematics Curriculum
Tom Addicks
Using Logo to produce bar graphs and pie charts.
79, (1986) 424 - 428.
Math Trivia
Jim Kuhlmann
An activity dealing with a Trivial Pursuit approach to mathematics
learning. There are some geometry questions involved.
79, (1986) 446 - 454.
Using Writing to Learn Mathematics
Cynthia L. Nahrgang and Bruce T. Peterson
Not specifically geometry oriented but the journal writing concept
which is discussed here could be applied in a geometry class.
79, (1986) 461 - 465.
The Looking-back Step in Problem Solving
Larry Sowder
Looking-back after the completion of the solution to a problem to search
for other problems. The technique is applied to one geometry problem.
79, (1986) 511 - 513.
Chomp--an Introduction to Definitions, Conjectures, and Theorems
Robert J. Keeley
A game designed to introduce students to the concepts of conjecture,
theorem, and proof.
79, (1986) 516 - 519.
A Lab Approach for Teaching Basic Geometry
Joan L. Lennie
Construction of a device for measuring angles and its use to make
indirect measurements.
79, (1986) 523 - 524.
Informal Geometry - More is Needed
Philip L. Cox
Sound-off feature urging the teaching of more informal geometry at the
secondary level.
78, (1985) 404 - 405.
Spadework Prior to Deductive Geometry
J. Michael Shaughnessy and William F. Burger
A discussion of van Hiele levels and their applications to methods of
preparing students for deductive geometry.
78, (1985) 419 - 428.
How Well Do Students Write Geometry Proofs?
Sharon L. Senk
The results of some testing regarding proof writing ability developed
by secondary geometry students. Data from the CDASSG project.
78, (1985) 448 - 456.
Microworlds: Options For Learning and Teaching Geometry
Joseph F. Aieta
Using Logo to study relations in families of figures. Logo procedures
provided.
78, (1985) 473 - 480.
The Shape of Instruction in Geometry: Some Highlights from Research
Marilyn N. Suydam
"Why, what, when, and how is geometry taught most effectively."
Research findings on these questions.
78, (1985) 481 - 486.
Seeking Relevance? Try the History of Mathematics
Frank J. Swetz
Suggestions for incorporating historical material into secondary
classroom presentations. Several geometrical aspects are included.
77, (1984) 54 - 62.
Adding Dimension to Flatland: A Novel Approach to Geometry
Donald H. Esbenshade, Jr.
Adding a cultural dimension to a secondary geometry course by
requiring the reading of Abbott's Flatland.
76, (1983) 120 - 123.
Learning By Example
Thomas Butts
Some geometry problems are involved in the discussion.
75, (1982) 109 - 113.
Is Your Mind In A Rut?
Glenn D. Allingen
Negative mind sets (visual perception, Einstellung effect,
functional fixedness) encountered in the mathematics classroom.
Geometrical examples.
75, (1982) 357 - 361, 428.
Understanding Area and Area Formulas
Michael Battista
A sequence of lessons to discourage some common misunderstandings
about area.
75, (1982) 362 - 368, 387.
Making Geometry A Personal and Inventive Experience
Richard G. Brown
Using a discover-it-yourself approach to the teaching of geometry.
75, (1982) 442 - 446.
Motivating Students To Make Conjectures and Proofs In Secondary School
Geometry
Lynn H. Brown
Guided discovery with worksheets.
75, (1982) 447 - 451.
Activities From "Activities": An Annotated Bibliography
Christian A. Hirsch
Articles from the "Activities" section. Geometry (47 - 49).
73, (1980) 46 - 50.
Help For The Slower Geometry Student
Diane Bohannon
Analysis of proofs (worksheet).
73, (1980) 594 - 596.
A Theorem Named Fred
Lloyd A. Jerrold
Developing an often used procedure into a theorem.
73, (1980) 596 - 597.
To Prove Or Not To Prove - That Is The Question
Thomas E. Inman
Suggested procedure for teaching the art of geometric proof.
72, (1979) 668 - 669.
Geometry: A Group Participation Game Of Definitions
Linda C. Barkey
A game for definition learning.
71, (1978) 117 - 118.
Teacher-Made Cassette Tapes - Geometry
Brendan Brown and Dorothy Dow
Discusses the use of audio tapes in geometry instruction.
69, (1976) 375 - 376.
Grading and Class Management In Geometry
Jane Broadbooks
Individualized instruction in geometry.
69, (1976) 376 - 377.
Chess In The Geometry Classroom
Nancy C. Whitman
Using chess to introduce the study of geometry.
68, (1975) 71 - 72.
Results and Implications of the NAEP Mathematics Assessment: Secondary School
Thomas P. Carpenter, Terrence G. Coburn, Robert E. Reys, and James W. Wilson
Title tells all. (Geometry on 465 - 467.)
68, (1975) 453 - 470.
A Geometry Game
James B. Caballero
Designed to develop precise mathematical modes of expression.
67, (1974) 127 - 128.
The Converses Of A Familiar Isosceles Triangle Theorem
F. Nicholson Moore and Donald R. Byrkit
Converses, difference between necessary and sufficient conditions,
use of counterexamples.
67, (1974) 167 - 170.
A System To Analyze Geometry Teacher's Questions
Morton Friedman
Suggestions for analyzing teaching.
67, (1974) 709 - 713.
In Search Of The Perfect Scalene Triangle
Bro. L. Raphael, F.S.C.
Drawing a triangle which is noticeably not isosceles nor right.
66, (1973) 57 - 60.
Geometry and Other Science Fiction
Jerry Lenz
Bibliography (including some science fiction) chosen for its
geometrical content.
66, (1973) 529.
Revolution, Rigor and Rigor Mortis
Stephen S. Willoughby
Appropriateness of various degrees of rigor in the teaching of
mathematics.
60, (1967) 105 - 108.
A Model For Teaching Mathematical Concepts
Kenneth B. Henderson
Primarily concerned with definitions.
60, (1967) 573 - 577.
A Comparative Study Of Methods Of Teaching Plane Geometry
James L. Jordy
Programmed material, conventional lectures, etc.
57, (1964) 472 - 478.
The First Days Of Geometry
Edward Davis
Introduction to deductive reasoning.
56, (1963) 645 - 646.
Using The Overhead Projector In Teaching Geometry
Harmon Unkrich
Suggested slides and procedures.
55, (1962) 502 - 505.
High School Geometry via Ruler-and-Protractor Axioms - Report On A
Classroom Trial
Max S. Bell
Use of the Birkhoff-Beatley approach.
54, (1961) 353 - 360.
The Game of Euclid
A. Henry Albaugh
Geometry via a card game.
54, (1961) 436 - 439.
When I Teach Geometry
Hope H. Chipman
Suggestions for teaching.
53, (1960) 140 - 142.
Teaching The Etymology Of Mathematical Terms
T.F. Mulcrone, S.J.
Making use of word origins and meanings in the teaching of mathematics.
51, (1958)
What Is Wrong With Euclid?
A.E. Meder, Jr.
Should the methods of Euclid be used in the teaching of high school
geometry?
51, (1958) 578 - 584.
A Logical Beginning For High School Geometry
John D. Wiseman, Jr.
Introducing students to geometry
51, (1958) 462 - 463.
An Electric Matching Device
Clarence Clander
A Teaching aid.
49, (1956) 278 - 279.
Prove As Much As You Can
Robert R. Halley
Assignment suggestions.
49, (1956) 491 - 492.
Mathematics - A Language
George R. Seidel
Training students to reason clearly.
48, (1955) 214 - 217.
The Use Of Puzzles In Teaching Mathematics
Jean Parker
Examples, several geometrical.
48, (1955) 218 - 227.
Mathematics As A Creative Art
Julia Wells Bower
Uses the works of Euclid to consider creation in mathematics.
47, (1954) 2 - 7.
The Angle-Mirror - A Teaching Device for Plane Geometry
Lauren G. Woodby
How to use it.
47, (1954) 71 - 72.
A Simple Multiple Purpose Dynamic Device
Frances Ek
A teaching aid for demonstrating angles, parallels, etc.
47, (1954) 184 - 185.
Models Of Loci
John F. Schacht
The construction of devices satisfying loci expressions.
47, (1954) 546 - 549.
Blackboard Locus Drawing Device
Mathematics Laboratory (Monroe High School)
How to construct one.
46, (1953) 88 - 89.
The Case For Syllogism In Plane Geometry
James F. Ulrich
Use the form of logic but avoid the rigors in teaching high school
geometry.
46, (1953) 311- 315, 323.
Random Notes On Modern Geometry
William C. Schaff
Bibliography.
46, (1953) 355 - 357.
The Carpenter's Rule: An Aid In Teaching Geometry
Ethel L. Moore
Suggestions for use.
46, (1953) 478.
The Multi-Converse Concept In Geometry
Frank B. Allen
Variations on theorems.
45, (1952) 582 - 583.
A Multiple Purpose Device
Louise B. Eddy
Construction of and uses for work with triangle, quadrilateral and
locus theorems.
44, (1951) 320 - 322.
Teaching For Generalization In Geometry
Frank B. Allen
So that transfer of learning will be possible. Examples, topics and
techniques.
43, (1950) 245 - 251.
A New Technique In Plane Geometry
D. A. Zarlengo
The use of color-coded figures in proofs.
41, (1948) 189 - 190.
Linkages As Visual Aids
Bruce E. Meserve
Use as demonstration devices.
39, (1946) 372 - 379.
A Guiding Philosophy For Teaching Demonstrative Geometry
Morris Hertzig
Motivating the study of synthetic geometry.
38, (1945) 112 - 115.
How To Develop Critical Thinking About Inter-Group Relations In The
Geometry Classroom
Paul E. Cantonwine
Logical reasoning applied to social, economic and moral problems.
42, (1949) 247 - 251.
How Shall Geometry Be Taught?
M. Van Waynen
Suggested techniques.
37, (1944) 64 - 67.
The Place Of Experimentation In Plane Geometry
Harry Sitomer
Using manipulatives to investigate geometric conjectures.
37, (1944) 122 - 124.
Developing Mental Perspective and Unity Of Principle In Geometry
Peter Drohan
Coordinating geometric knowledge by grouping it about certain figures.
37, (1944) 209 - 211.
Enriching Plane Geometry With Air Navigation
Harry Schor
Visualization of geometric principles by use of some principles of
navigation.
37, (1944) 254 - 257.
Developing The Principle Of Continuity In The Teaching Of Euclidean Geometry
Daniel B. Lloyd
Introducing the concept of continuity into the teaching of geometry.
37, (1944) 258 - 262.
The Use Of Models In The Teaching Of Plane Geometry
F. M. Burns
Methods and reasons for use.
37, (1944) 272 - 277.
Developing Reflective Thinking Through Geometry
Inez M. Cook
Course organization and material. Results of an experiment.
36, (1943) 79 - 82.
Teaching Solid Geometry
Nancy C. Wylie
Suggested methods.
36, (1943) 126 - 127.
Teaching A Unit In Logical Reasoning In The Tenth Grade
Daniel B. Lloyd
Objectives, content, bibliography.
36, (1943) 226 - 229.
A New Technique In Handling The Congruence Theorems In Plane Geometry
Ralph C. Miller
Using constructions.
36, (1943) 237 - 239.
Geometry For Everyone
Kenneth S. Davis
Objects occurring in everyday life which can be used to illustrate
geometric principles.
35, (1942) 64 - 67.
Individual Differences and Course Revision In Plane Geometry
James M. Lynch
Dealing with the problem of the increase in the numbers of
non-college-bound students.
35, (1942) 122 - 126.
You Can Make Them
Clara O. Larson
The construction of geometric models and tools. (Angle bisector,
parallel rulers, etc.)
35, (1942) 182 - 183.
The War On Euclid
Charles Salkind
Comments on attempts to modify methods and content in plane geometry.
35, (1942) 205 - 207.
Geometry For All Laymen
Harold Fawcett
Using a course in geometry to develop reflective thinking.
35, (1942) 269 - 274.
Vocabulary In Plane Geometry
Earl R. Keesler
Research assignments for determining word origins in plane geometry.
35, (1942) 331.
A Reorganization Of Geometry For Carryover
Harold D. Alten
Changing the geometry course so as to have the students apply the
type of geometric reasoning required in non-geometric situations.
34, (1941) 151 - 154.
A Helpful Technique In Teaching Solid Geometry
James V. Bernardo
The use of models.
33, (1940) 39 - 40.
Vitalizing Geometry With Visual Aids
R. Drake and D. Johnson
Activities, objectives, supplies and equipment.
33, (1940) 56 - 59
Three Major Difficulties In The Learning Of Demonstrative Geometry
Rolland R. Smith
Part I - Analysis of Errors.
Particular errors and data on the numbers of students committing them.
33, (1940) 99 - 134.
Three Major Difficulties In The Learning Of Demonstrative Geometry
Rolland R. Smith
Part II - Description and Evaluation Of Methods Used To Remedy Errors
The title tells it all.
33, (1940) 150 - 178.
The Teaching Of "Flexible" Geometry
Daniel B. Lloyd
The use of linkages (pantographs, etc.) in the teaching of geometry.
32, (1939) 321 - 323.
The Educational Value Of Logical Geometry
J.H. Blackhurst
Suggestions for improving the teaching of geometry.
32, (1939) 163 - 165.
Inverted Geometry
Daniel Luzen Morris
Teaching geometry by beginning with solids and planes, then proceeding
to points and lines.
31, (1938) 78 - 80.
The Nature and Place Of Objectives In Teaching Geometry
E. R. Breslich
Suggested methods and materials for teaching geometry.
31, (1938) 307 - 315.
Linkages
Joseph Hilsenrath
Types, uses, theory, history.
30, (1937) 277 - 284.
Generalization As A Method In Teaching Mathematics
R.M. Winger
A generalization of the theory of Pythagoras.
29, (1936) 241 - 250.
The Use Of Original Exercises In Geometry
Mabel Syles
Suggestions for the assigning of exercises from geometry texts.
28, (1935) 36 - 42.
Visualizing Geometry Through Illustrative Material
Idella Waters
Using models to demonstrate geometric principles.
28, (1935) 101 - 110.
A Psychological Analysis Of Student's Reasons For Specific Errors On Drill
Materials In Plane Geometry
Lyle K. Henry
Errors, reasons, recommendations.
28, (1935) 482 - 488.
Analysis Is Not Enough
Alma M. Fabricius
Teaching geometry in the light of Gestalt Psychology. Developing
analysis and synthesis.
27, (1934) 257 - 264.
"Locus Makes A Plea"
D. McLoed
The use of locus problems in the teaching of geometry.
27, (1934) 336 - 339.
Teaching The Locus Concept In Plane Geometry
E. B. Woodford
Techniques and tools for drawing loci.
26, (1933) 105 - 106.
An Attempt To Apply The Principles Of Progressive Education To The
Teaching Of Geometry
Leroy H. Schnell
Objectives, preliminary steps, one unit of material.
26, (1933) 163 - 175.
Book Propositions In Teaching Geometry
Aaron Horn
Present original problems on examinations rather than results from
the text.
25, (1925) 76 - 78.
Laboratory Work In Geometry
R. M. McDill
Using square, protractor, compass, rule, scissors, etc.
24, (1931) 14 - 21.
The Fusion Of Plane and Solid Geometry
Joseph B. Orleans
Teaching a combined course.
24, (1931) 151 - 159.
A Combined Course In Plane and Solid Geometry?
Charles A. Stone
Opinions, questionnaires, results of experimental courses.
24, (1931) 160 - 165.
Individual Work In Plane Geometry
James H. Zant
The use of work sheets in teaching geometry.
23, (1930) 155 - 160.
Geometry In The Junior High School
Marie Gugle
What should be taught? How should it be taught? Course outline
included.
23, (1930) 209 - 226.
Geometry Measures Land
W. R. Ransom
Geometry has become too much an exercise in pure logic.
23, (1930) 243 - 251.
Grouping In Geometry Classes
H. Weissman
Discussion, different materials and examinations for different ability
levels within the same classroom.
22, (1929) 93 - 108.
Concerning Orientation and Application In Geometry
D.G. Ziegler
Using intuition and applications in the teaching of geometry.
22, (1929) 109 - 116.
Two Methods Of Teaching Geometry: Syllabus vs Textbook
James D. Ryan
Teaching without a text is superior.
21, (1928) 31 - 36.
Techniques and Devices Conducive To Better Teaching Of Geometry
Laura Blank
Outline of suggested steps for studying geometry. Examples. Comments.
21, (1928) 171 - 181.
The Teaching Of Properties In Plane Geometry
Warren R. Good and Hope H. Chipman
Literature review, textbook analysis, proposed course changes.
21, (1928) 454 - 464.
A Different Beginning For Plane Geometry
H.C. Christofferson
Beginning with construction of triangles and congruence by SSS.
21, (1928) 479 - 482.
Analysis Versus Synthesis
Alma M. Wuest
Using analytical thinking in a geometry class.
20, (1927) 46 - 49.
A Number Of Things For Beginners In Geometry
Vesta A. Richmond
Some facts of which beginning geometry students should be made aware.
20, (1927) 142 - 149.
The Laboratory Method In Teaching Of Geometry
C. A. Austin
Geometry as an experimental science.
20, (1927) 286 - 294.
Teaching Plane Geometry Without A Textbook
Theodore Strong
Comments on methods and results.
19, (1926) 115 - 119.
Heresy and Orthodoxy In Geometry
George W. Evans
How should geometry be taught?
19, (1926) 195 - 201.
Suggestions On Conducting The Recitation In Geometry
J.O. Hassler
Methods of class presentation.
19, (1926) 411 - 418.
Adapting Plane Geometry To Pupils Of Limited Ability
Martha Hildebrandt
How to deal with the slow and the reluctant learner.
18, (1925) 102 - 110.
Purpose, Method and Mode Of Demonstrative Geometry
W.W. Hart
Why and how demonstrative geometry should be taught.
17, (1924) 170 - 177.
The Slide Rule In Plane Geometry
W.W. Gorsline
Uses.
17, (1924) 385 - 403.
A Study Of The Cultivation Of Space Imagery In Solid Geometry Through
The Use Of Models
Edwin W. Schreiber
Classroom models and their construction.
16, (1923) 103 - 111.
Experimental Geometry
G. A. Harper
Experiments followed by formal proof. Examples and suggested exercises.
15, (1922) 157 - 163.
The Teaching Of Beginning Geometry
A. J. Schwartz
Historical beginnings, some suggested topics and approaches.
15, (1922) 265 - 282.
First Lessons In Demonstrative Geometry
M. J. Neweel and G. A. Harper
Introducing principles of demonstrative geometry.
14, (1921) 42 - 45.
Geometry Detected By Sherlock Holmes
Blanche B. Hedges
Holmesian crime detection methods applied to geometric analysis.
14, (1921) 128 - 136.
Teaching Incommensurables
Vera Sanford
Some geometric examples included.
14, (1921) 147 - 150.
The Teaching Of Locus Problems In Elementary Geometry
Fred D. Aldrich
Suggestions and examples.
14, (1921) 200 - 205.
Comments On The Teaching Of Geometry
Frank C. Touten
Suggested teaching methods.
14, (1921) 246 - 251.
Geometric Stereograms - A Device For Making Solid Geometry Tangible
To The Average Student
Walter Francis Shinton
Use of colored glasses and special drawings to produce 3-D effects.
8, (1915-1916) 124 - 131.
Some Ideas On The Study Of Geometry
Charles R. Schultz
A discussion of a movement to bring about better teaching of geometry.
6, (1913-1914) 1 - 9.
Originals In Geometry
Harry B. Marsh
Teaching problem solving in geometry.
6, (1913-1914) 17 - 21.
Some Suggestions On Decreasing The Mortality In Our Geometry Classes
William R. Lasher
Special classes for slow learners.
4, (1911-1912) 26 - 31.
The Way To Begin Solid Geometry
Howard F. Hart
Some teaching methods.
4, (1911-1912) 98 - 103.
Special Devices In Teaching Geometry
Paul Noble Peck
Some suggested methods.
3, (1910,1911) 49 - 55.
Intuition and Logic In Geometry
W. Betz
The use of intuition in the teaching of geometry. The school
cannot take the attitude of the rigorous mathematician.
2, (1909-1910) 3 - 31.
Some Suggestions In The Teaching Of Geometry
Isaac J. Schwatt
A detailed discussion of many topics.
2, (1909-1910) 94 - 115.
The Aims Of Studying Plane Geometry and How To Attain Them
E. P. Sisson
How can a teacher be most effective?
1, (1908-1909) 44 - 47.
Teaching Classes In Plane Geometry To Solve Original Exercises
Fletcher Durell
Steps in problem solving. Comments on classroom use.
1, (1908-1909) 123 - 135.
The Syllabus Method Of Teaching Plane Geometry
Eugene R. Smith
Comments on then current teaching methods. Argues for the use of
the syllabus method.
1, (1908-1909) 135 - 147.
GEOMETRIC INEQUALITIES AND OPTIMIZATION
Network Neighbors
William F. Finzer
An experiment in network collaboration using The Geometer's Sketchpad.
(88, 1995) 475 - 477
An Isoperimetric Problem Revisited
Scott J. Beslin and Laurette L. Simmons
Finding a simple closed curve with fixed perimeter which bounds
a maximum area.
(86, 1993) 207 - 210
Area and Perimeter Connections
Jane B. Kennedy
Activities for investigating maximum area rectangles
with fixed perimeter.
(86, 1993) 218 - 221, 231 - 232
The Bug on the Box
William Wallace
Looking for a shortest path.
(85, 1992) 474 - 475
Largest Quadrilaterals
J. N. Boyd and P. N. Raychowdhury
Given three fixed segments how should a fourth segment be chosen so
as to produce a quadrilateral of maximum area?
(85, 1992) 750 - 751
Dissecting a Circle by Chords Through n Points
A. V. Boyd and M. J. Glencross
Finding the maximum number of regions into which a circular region
can be divided by chords. (84, 1991) 318 - 319
Make Your Own Problems - and Then Solve Them
Robert L. Kimball
Activities for solving a maximum problem.
(84, 1991) 647 - 655
Geometrical Inequalities via Bisectors
Larry Hoehn
Alternatives to the usual proofs of inequalities in triangles.
(82, 1989) 96 - 99
A Constructive Proof of a Common Inequality
Richard C. Ritter
Sharing Teaching Ideas. The arithmetic mean - geometric mean
inequality.
(82, 1989) 531 - 532
A Geometric Solution to a Problem of Minimization
Li Changming
Rowing and walking to get from a boat to a lighthouse.
(81, 1988) 61 - 64
Solving Extreme-Value Problems without Calculus
David I. Spanagel and Gerald Wildenberg
Some of the examples utilize geometric techniques.
(81, 1988) 574 - 576
The Shortest Route
J. Andrew Archer
Finding the shortest possible route when mowing a rectangular lawn.
80, (1987) 88 - 93, 142.
A Matter of Disks
William E. Ewbank
In what manner should disks be cut from a piece of posterboard in
order to minimize wastage?
79, (1986) 96 - 97, 146.
Reflective Paths to Minimum-Distance Solutions
Joan H. Shyers
The uses of reflections in order to find paths of minimum length.
79, (1986) 174 - 177, 203
Problem-solving Techniques with Microcomputers
William E. Haigh
Finding the dimensions for a rectangle which will yield a sub-rectangle
having maximum area. BASIC program included.
79, (1986) 598 - 601, 655
The Spider and the Fly: A Geometric Encounter in Three Dimensions
Rick N. Blake
Eight problems involving a minimum path.
78, (1985) 98 - 104.
A Geometric View of the Geometric Series
Steven R. Lay
A "sharing teaching idea." Diagrams to illustrate the convergence of
the geometric series.
78, (1985) 434 - 435.
Geometry For Pie Lovers
William Fisher
Finding a line through a given point O of a convex region which
produces a subregion of maximum area.
75, (1982) 416 - 419.
Spherical Geodesics
William D. Jamski
Find the shortest distance between two points on a globe.
74, (1981) 227 - 228, 236.
The Isoperimetric Theorem
Ann E. Watkins
Activities to aid in the discovery of the fact that for a given
perimeter the circle encloses the greatest area.
72, (1979) 118 - 122.
An Optimization Problem and Model
Deane Arganbright
A minimum path problem and a device for exhibiting it.
71, (1978) 769 - 773.
Minimal Surfaces Rediscovered
Sister Rita M. Ehrmann
Soap bubble experiments for Plateau's problem (find the surface of
smallest area having a given boundary), soap film experiments for
Steiner's problem (minimal linear linkage of points in a plane.)
69, (1976) 146 - 152.
Experiments Leading To Figures Of Maximum Area
J. Paul Moulton
Thirteen results concerning polygons having maximum area under given
conditions.
68, (1975) 356 - 363.
Maximum Rectangle Inscribed In A Triangle
M. T. Bird
A characterization.
64, (1971) 759 - 760.
Exploring Geometric Maxima and Minima
J. Garfunkel
Paths, areas, perimeters, chords.
62, (1970) 85 - 90.
Maxima and Minima By Elementary Methods
Amer Nannina
Geometric solutions.
60, (1967) 31 - 32.
On Some Geometric Inequalities
Murray S. Klamkin
Geometric maximum and minimum problems.
60, (1967) 323 - 328.
Using Geometry To Prove Algebraic Inequalities
J. Garfunkel and B. Plotkin
Synthetic and analytic techniques applied to ten problems.
59, (1966) 730 - 734.
Geometric Intuition and SQR(ab) < (a + b)/2
E. M. Harais
Using surfaces in 3-space.
57, (1964) 84 - 85.
Going Somewhere?
Oystein Ore
Paths of minimum length.
53, (1960) 180 - 182.
Out Of The Mouths Of Babes
Paul C. Clifford
Maximum and minimum problems solved geometrically.
47, (1954) 115.
The "Attack" In Propositions On Inequality Of Lines
Arthur Haas
Teaching propositions on inequalities.
19, (1926) 228 - 234.
JOINING POINTS AND DETERMINING REGIONS
Symmetries of Irregular Polygons
Thomas W. Shilgalis
Investigating bilateral symmetry in irregular convex polygons.
(85, 1992) 342 - 344
Periodic Pictures
Ray S. Nowak
Activities involving graphical symmetries produced by periodic
decimals. BASIC program provided.
80, (1987) 126 - 137.
Learning To Count In Geometry
George W. Bright
The number of regions determined by overlapping circles and by
overlapping squares.
70, (1977) 15 - 19.
Visualizing Mathematics With Rectangles and Rectangular Solids
John F. Sharlow
Subdividing a rectangle into congruent rectangles and then
counting them.
70, (1977) 60 - 63.
Trisection Triangle Problems
Marjorie Bicknell
Connecting vertices and n-section points.
69, (1976) 129 - 134
The Vertex Connection
Christian R. Hirsch
Activities for the investigation of the number of diagonals of
a polygon.
69, (1976) 579 - 582.
Partitioning The Plane By Lines
Nathan Hoffman
Looks at the maximum number of regions determined by n lines in a plane.
68, (1975) 196 - 197.
Spaces, Functions, Polygons and Pascal's Triangle
L.C. Johnson
Relation of Pascal's triangle to the number of lines determined by
points, regions determined by lines, n-gons determined by points.
66, (1973) 71 - 77.
Paths On A Grid
Robert Willcutt
Looks at the number of paths determined by two points on a grid.
66, (1973) 303 - 307.
The Classical Cake Problem
Norman N. Nelson and Forest N. Fisch
How may a cake be sliced so that each piece contains the same volume
of cake and frosting.
66, (1973) 659 - 661.
Induction: Fallible But Valuable
Jay Graening
Regions determined by chords of a circle.
64, (1971) 127 - 131.
A Mathematician's Progress
Brother U. Alfred
Regions determined by lines in a plane and planes in space.
59, (1966) 722 - 727.
Application Of Combinations and Mathematical Induction To A Geometry Lesson
Adril Lindsay Wright
Planes determined by points.
56, (1963) 325 - 328.
Complex Figures In Geometry
John D. Wiseman, Jr.
Figures having overlapping parts.
52, (1959) 91 - 94.
Isosceles (to the power) n
Ernest R. Ranucci
Conditions under which an isosceles triangle can be separated into
other non-congruent, non-overlapping isosceles triangles.
69, (1976) 289 - 294.
LINES, ANGLES, MEASUREMENT
Pixy Stix Segments and the Midpoint Connection
Ruth McClintock
Several activities for finding the midpoint of a model of a
line segment.
(86, 1993) 668 - 675
An Abundance of Solutions
Donald Barry
Solutions to the problem of finding the angle between segments drawn
from a vertex of a square to the midpoints of the opposite sides.
(85, 1992) 384 - 387
The Railroad-Track Problem
Maxine Bridger
How high above the ground is the midpoint of a buckling section
of track?
(85, 1992) 439 - 441
Where is My Reference Angle?
Joanne Staulonis
A manipulative for demonstrating the concept of a reference angle.
(85, 1992) 537
Trisecting an Angle - Almost, Part 2
John F. Lamb, Jr.
Looks at the method of Karajordanoff.
(84, 1991) 20 - 23
The Artist's View of Points and Lines
Richard S. Millman and Ramona R. Speranza
Art can be used to present early concepts in geometry.
(84, 1991) 133 - 138
Angle Hunt
Cheryl Reger
Sharing Teaching Ideas. An activity which allows students to
estimate angle measures and measure angles.
(83, 1990) 282 - 283
Understanding Angles: Wedges to Degrees
Patricia S. Wilson
Activities for measuring angles with standard and non-standard
units of measurement.
(83, 1990) 294 - 300
"Metes and Bounds" Descriptions: An Application of Geometry and Measurement
Mary Kim Prichard
Activities for drawing the boundaries of a plot of land using the
legal description of the property.
(83, 1990) 462 - 468
Dropping Perpendiculars the Easy Way
Lindsay Anne Tartre
An alternative technique for obtaining the perpendicular from a
point to a line.
80, (1987) 30 - 31.
A Lab Approach for Teaching Basic Geometry
Joan L. Lennie
Construction of a device for measuring angles and its use to
make indirect measurements.
79, (1986) 523 - 524.
An Improvement of the Congruent Angles Theorem
Shraga Yeshurun
A theorem relating lengths of segments formed by pairs of
intersecting lines.
78, (1985) 53 - 54.
Sighting The Value Of Pi
P. K. Srinivasan
Using parallel lines to find the value of pi.
74, (1981) 380 - 384.
Taxi Distance
Stanley A. Smith
Activities for taxicab geometry.
70, (1977) 431 - 434.
Taxicab Geometry
Eugene F. Krause
Geometry on a grid. Comparison to Euclidean Geometry.
66, (1973) 695 - 706.
A Metric World
H. W. Stanley
The consequences of redefining distance.
66, (1973) 713 - 721.
A Non-Euclidean Distance
Stanley R. Clemens
A metric on RxR (different from the usual) which yields
unique parallels.
64, (1971) 595 - 600.
How Shall We Define Angle?
Harry Sitomer and Howard F. Fehr
Asks for a reconsideration of the definition.
60, (1967) 18 - 19.
What Are Perpendicular Lines?
C. R. Wylie, Jr.
Perpendicularity relations and coordinate systems.
60, (1967) 24 - 30.
The SMSG Angle Is A Good One
Frank Wright
Defends the definition.
60, (1967) 856 - 857.
Angles, Arcs and Archimedes
Carl B. Allendoerfer
What is an angle?
58, (1965) 82 - 88.
How Far Is It From Here To There?
Irene Fischer
Development of systems of measurement.
58, (1965) 123 - 140.
An Introduction To The Angle Measurement Theorems In Plane Geometry
Harry Schor
The use of a circular protractor to introduce angle measure in circles.
56, (1963) 107 - 108.
Square Circles
Francis Scheid
A metric on lattice points.
54, (1961) 307 - 312.
What Is A Geometric Tangent?
Richard V. Andree
A definition and discussion.
50, (1957) 498 - 501.
On Teaching Angle and Angle Measure
Howard F. Fehr
Definition and measurement of angles.
50, (1957) 551 - 556.
The Construction and Measurement Of Angles With A Steel Tape:
Surveyor's Method
Richard W. Shoemaker
Description and proof that the method works.
49, (1956) 550.
Angle Comparison Device
Hope H. Chipman
Construction method.
48, (1955) 554.
Construct Any Angle With A Steel Tape
Edwin Eagle.
Method.
48, (1955) 563 - 564.
An Angle Device
Sister Mary Donald, I.H.M.
A tool for demonstrating some angle concepts.
46, (1953) 429 - 430.
LOGIC
A Visual Approach to Deductive Reasoning
Frances Van Dyke
Activities. Using Venn diagrams rather than truth tables to examine the validity of
arguments.
(88, 1995) 481 - 486, 492 - 494
Geometry Proof Writing: A Problem-Solving Approach à la Pólya
Jean M. McGivney and Thomas C. DeFranco
Proof writing is problem solving.
(88, 1995) 552 - 555
What Is a Quadrilateral?
Lionel Pereira-Mendoza
An activity designed to develop an understanding of the role of
definitions in mathematics.
(86, 1993) 774 - 776
Teaching Logic with Logic Boxes
Walter J. Sanders and Richard L. Antes
Using boxes to represent concepts of logic.
(81, 1988) 643 - 647
Intuition and Logic
Patrick J. O'Regan
Capitalizing on students' ways of thinking to lead them to a greater
understanding of logical relationships.
(81, 1988) 664 - 668
Two Views of Oz
John Pancari and John P. Pace
Using the Scarecrow's Pythagorean-like utterance to define the
fundamental isosceles triangle of Oz.
80, (1987) 100 - 101.
Teaching Modeling and Axiomatization with Boolean Algebra
Michael D. DeVilliers
Proofs of Boolean Algebra statements, analysis of the proofs, and
the development of a suitable axiomatic basis.
80, (1987) 528 - 532.
Did the Scarecrow Really Get A Brain?
Lowell Leake
An analysis of the Scarecrow's Pythagoras-like statement in The
Wizard of Oz.
79, (1986) 438 - 439.
Deductive and Analytical Thinking
Robert L. McGinty and John G. Van Buynen
Activities for enhancing deductive reasoning abilities.
78, (1985) 188 - 194.
The Relativity of Mathematics
Israel Kleiner and Schmuel Avital
Logic. Truth and validity.
77, (1984) 554 - 558.
Star Trek Logic
John Lamb, Jr.
An analysis of events in "Amok Time". (Spock's wedding.)
72, (1979) 342 - 343.
Why "False -> False" Is True - A Discovery Explanation
Jack Bookman
Activities in logic.
71, (1978) 675 - 676.
The Converses Of A Familiar Isosceles Triangle Theorem,
F. Nicholson Moore and Donald R. Byrkit
Converses, the difference between necessary and sufficient
conditions, use of counterexamples.
67, (1974) 167 - 170.
Variation - A Process Of Discovery In Geometry
Clarence H. Heinke
Changing the elements of a theorem to produce a new theorem.
50, (1957) 146 - 150.
Quod Erat Demonstrandum
Harold P. Fawcett
A discussion of proof and logic.
49, (1956) 2 - 6.
What Do We Mean?
Robert E. K. Rourke and Myron F. Rosskopf
An examination of the meanings of some mathematical terms.
49, (1956) 597 - 604.
Some Concepts Of Logic and Their Application In Elementary Mathematics
Myron F. Rosskopf and Robert M. Evans
Discusses some aspects of geometric logic and proof.
48, (1955) 290 - 298.
The Logic Of The Indirect Proof In Geometry
Nathan Lazar
Analysis, criticism, and recommendations.
40, (1947) 225 - 240.
Teaching A Unit In Logical Reasoning In The Tenth Grade
Daniel B. Lloyd
Objectives, contents, and bibliography.
36, (1943) 226 - 229.
The Importance Of Certain Concepts and Laws Of Logic For The
Study and Teaching Of Geometry
Nathan Lazar
Detailed examinations of the materials with examples.
31, (1938).
Chapter I, The Converse. 99 - 113.
Chapter II, The Inverse. 156 - 162.
Chapter III, The Contrapositive. 162 - 174.
Chapter IV, An Extension of the Concept and the
Law of Contraposition. 216 - 225.
Chapter V, The Law of Converses. 226 - 240.
Geometry, A Way Of Thinking
H. C. Christofferson
Logic and deductive thinking.
31, (1938) 147 - 155.
Applying Geometric Methods Of Thinking To Life Situations
Elizabeth Loetzer Hall
The application of classroom methods of thinking to real
life situations.
31, (1938) 379 - 384.
Geometry and Life
Kenneth B. Leisenring
Geometry and deductive thinking. The value of learning geometry.
30, (1937) 331 - 335.
Elementary Logic As A Basis For Plane Geometry
Eugene R. Smith
Report on a teaching experiment.
1, (1908-1909) 6 - 14.
NON-EUCLIDEAN GEOMETRIES
Using a Surface Triangle to Explore Curvature
James Casey
Investigating triangle angle sums on various surfaces, e.g., bananas, soap bottles,
watermelons, etc.
(87, 1994) 69 - 77
Bringing Non-Euclidean Geometry Down to Earth
Catherine Folio
A "sharing teaching idea." Drawing triangles on a styrofoam ball.
78, (1985) 430 - 431.
An Improvement on SSA Congruence for Geometry and Trigonometry
Shraga Yushurum and David C. Kay
Conditions under which SSA yields congruence. A result for
non-Euclidean geometry is also presented.
76, (1983) 364 - 367.
A Student Presented Mathematics Club Program - Non-Euclidean Geometries
Leroy C. Dalton
Suggested program topics.
73, (1980) 451 - 452.
Neutral and Non-Euclidean Geometry - A High School Course
Peter A. Krause and Steven L. Okolica
Content of a classroom tested introduction to non-Euclidean geometries.
70, (1977) 319 - 324.
Taxicab Geometry
Eugene F. Krause
Geometry on a grid, comparison to Euclidean geometry.
66, (1973) 695 - 706.
Taxicab Geometry - A Non-Euclidean Geometry Of Lattice Points
Donald R. Byrkit
An axiomatic presentation of a geometry of lattice points.
64, (1971) 418 - 422.
A Non-Euclidean Distance
Stanley R. Clemens
A metric on RxR (different from the usual) which yields unique parallels.
64, (1971) 595 - 600.
The Parallel Postulate
Raymond H. Rolwing and Maita Levine
Historical notes on attempts at proof.
62, (1969) 665 - 669.
Equivalent Forms Of The Parallel Axiom
Lucas N. H. Bunt
Reprint from Euclides. Equivalences and proofs.
60, (1967) 641 - 652.
Saccheri, Forerunner Of Non-Euclidean Geometry
Sister Mary of Mercy Fitzpatrick
History and some examples.
57, (1964) 323 - 331.
Introduction To Non-Euclidean Geometry
Wesley W. Maiers
Directional parallels, quadrilaterals, triangles, some exercises.
57, (1964) 457 - 461.
The Saccheri Quadrilateral
Louis O. Kattsoff
An introduction to non-Euclidean geometries.
55, (1962) 630 - 636.
Problems In Presenting Non-Euclidean Geometries To High School Teachers
Louis O. Katsoff
Nature and uses of non-Euclidean geometries.
53, (1960) 559 - 563.
Polar Maps
John Kinsella and A. Day Bradley
Some spherical geometry.
42, (1949) 219 - 225.
The Lessons Non-Euclidean Geometry Can Teach
Kenneth B. Henderson
Riemannian and hyperbolic geometries involved.
33, (1940) 73 - 79.
The Extension Of Concepts In Mathematics
Aubrey W. Kemper
Infinite elements in geometry, non-Euclidean geometries,
four-dimensional geometry.
16, (1923) 1 - 23.
Some Varieties Of Space
Emilie N. Martin
Non-Euclidean geometries discussed.
16, (1923) 470 - 480.
"Steradians" and Spherical Excess
George W. Evans
Some geometry on a sphere.
15, (1922) 429 - 433.
Non-Euclidean Geometry
W. H. Bussey
History. Some results in hyperbolic and elliptic geometry.
15, (1922) 445 - 459.
Philosophy and Non-Euclidean Geometry
F.A. Foraker
The philosophical implications of non-Euclidean geometries.
11, (1918-1919) 196 - 198.
Solid Geometry
Howard F. Hart
Some geometry on a sphere.
3, (1910-1911) 24 - 26.
Some Thoughts On Space
E. D. Roe, Jr.
With reference to the philosophy of Kant.
2, (1909-1910) 31 - 38.
POLYGONS HAVING MORE THAN FOUR SIDES
The Pentagon Problem: Geometric Reasoning with Technology
Rose Mary Zbiek
Area ratios for a pentagon inscribed in a pentagon inscribed in a pentagon.
(889, 1996) 86 - 90
Perimeters, Patterns, and Pi
Sue Barnes
Areas and perimeters of inscribed and circumscribed regular polygons.
(889, 1996) 284 - 288
Morgan's Theorem
Tad Watanabe, Robert Hanson, and Frank D. Nowosielski
Investigating the area of a hexagon formed in the interior of a triangle by certain n- sectors of the angle.
(889, 1996) 420 - 423
Pentagrams and Spirals
Lew Douglas
Activities eventually leading to the Golden Ratio.
(889, 1996) 680 - 687
Golden Triangles, Pentagons, and Pentagrams
William A. Miller and Robert G. Clason
Informal investigations of recursion. The golden ratio, Fibonnaci sequence, regular
polygons, and pentagrams.
(87, 1994) 338 - 344, 350 - 353
Counting Embedded Figures
Timothy V. Craine
Activities. How many triangles, squares, rectangles, etc., are there in a given
figure?
(87, 1994) 524 - 528, 538 - 541
Animating Geometry Discussions with Flexigons
Ruth McClintock
A flexigon is created by stringing together plastic straws of varying lengths in a
closed loop. These tools are then used to investigate the geometry of polygons.
(87, 1994) 602 - 606
Folding n-pointed Stars and Snowflakes
Steven I. Dutch
Methods for accomplishing the task.
(87, 1994) 630 - 637
Starring in Mathematics
Donald M. Fairbairn
Activities for studying n-grams.
(84, 1991) 463 - 470
Octagons at Monticello
Peggy Wielenberg
Geometry of octagons. Jefferson's construction of three sides of an
octagon on a segment of fixed length.
(83, 1990) 58 - 61
Polygonal Numbers and Recursion
William A. Miller
Activities for studying recursion utilizing polygonal numbers.
(83, 1990) 555 - 562
Polygons Made to Order
Joseph A. Troccolo
Activities for producing accurate regular polygons with specified
side lengths.
80, (1987) 44 - 50.
Finding the Area of Regular Polygons
William M. Waters, Jr.
Finding the ratio of the area of one regular polygon to that of
another when they are inscribed in the same circle.
80, (1987) 278 - 280
Revisiting the Interior Angles of Polygons
Herbert Wills III
Several approaches to calculating the sum of the interior angles
of a polygon.
80, (1987) 632 - 634.
Dirichlet Polygons - An Example of Geometry in Geography
Thomas O'Shea
Applications of Dirichlet polygons, including homestead boundaries
and rainfall measurement.
79, (1986) 170 - 173.
The Twelve Days of Christmas and the Number of Diagonals in a Polygon
Adrian McMaster
Notes a relation between the number of gifts received on a particular
day and the diagonals in a polygon.
79, (1986) 700 - 702.
Regular Polygons and Geometric Series
Areas and inscribed regular polygons.
75, (1982) 258 - 261.
Area and Cost Per Unit: An Application
Jan J. Vandever
Activities for use in practice with area formulas.
73, (1980) 281 - 284, 287.
Getting The Most Out Of A Circle
Joe Donegan and Jack Pricken
Polygons determined by six equally spaced points on a circle.
73, (1980) 355 - 358.
Graphing - Perimeter - Area
Merrill H. Meneley
Activities concerned with the perimeter and area of polygons.
Uses a coordinate system.
73, (1980) 441 - 444.
Some Properties Of Regular Polygons
William Jamski
Activities involving angle sums of polygons. Some work with diagonals.
68, (1975) 213 - 220.
Area Ratios In Convex Polygons
Gerald Kulm
Area ratios when one regular n-gon is derived from another using
division points of sides.
67, (1974) 466 - 467.
Some Whimsical Geometry
Jean Pederson
Polygon construction by paper folding.
65, (1972) 513 - 521.
An Intuitive Approach To Pierced Polygons
Donald E. Jennings
Polygons which have certain sides coincident.
63, (1970) 311 - 312.
Polygon Sequences
John E. Mann
Polygons formed from the midpoints of sides of polygons.
63, (1970) 421 - 428.
Pierced Polygons
Charles E. Moore
Regions formed when a polygonal region is cut from the interior
of another polygonal region. Some angle relations.
61, (1968) 31 - 35.
Conditions Governing Numerical Equality Of Perimeter, Area and Volume
Leander W. Smith
Triangles, general polygons, polyhedra.
58, (1965) 303 - 307.
Concave Polygons
Roslyn M. Berman and Martin Berman
Finding angle sums.
56, (1963) 403 - 406.
Regular Polygons
Robert C. Yates
Complex numbers and regular polygons.
55, (1962) 112 - 116.
Teaching The Concept Of Perimeter Through The Use Of Manipulative Aids
Jen Jenkins
Title tells all.
50, (1957) 309 - 310.
The Pentagon and Betsy Ross
Phillip S. Jones
Folding a five pointed star.
46, (1953) 341 - 342.
The Sum Of The Exterior Angles Of Any Polygon Is 360 degrees
George R. Anderson
A demonstration device.
45, (1952) 284 - 285.
The Geometry Of The Pentagon and The Golden Section
H. v. Baravalle
Synthetic and analytic approaches. Some history.
41, (1948) 22 - 31.
Ptolemy's Theorem and Regular Polygons
L. S. Shively
Proof and applications.
39, (1946) 117 - 120.
Linkages As Visual Aids
Bruce E. Meserve
Polygonal models.
39, (1946) 372 - 379.
METHODS AND FORMATS OF PROOF
Learning and Teaching Indirect Proof
Denisse R. Thompson
Discussion of research and teaching implications.
(889, 1996) 474 - 482
Geometry and Proof
Michael T. Battista and Douglas H. Clements
Connecting Research to Teaching. Discussion of research and instructional
possibilities. Includes comments on computer programs and classroom
recommendations.
(88, 1995) 48 - 54
Conjectures in Geometry and The Geometer's Sketchpad
Claudia Giamati
Exploration as a foundation on which to base proof.
(88, 1995) 456 - 458
A Visual Approach to Deductive Reasoning
Frances Van Dyke
Activities. Using Venn diagrams rather than truth tables to examine the validity of
arguments.
(88, 1995) 481 - 486, 492 - 494
Geometry Proof Writing: A Problem-Solving Approach à la Pólya
Jean M. McGivney and Thomas C. DeFranco
Proof writing is problem solving.
(88, 1995) 552 - 555
When Is a Quadrilateral a Parallelogram?
Charalampos Toumasis
Investigations of sets of sufficient conditions.
(87, 1994) 208 - 211
Helping Students write Paragraph Proofs in Geometry
Joseph L. Brandell
Utilizing flowcharts.
(87, 1994) 498 - 502
Communicating Mathematics
Mary M. Hatfield and Gary G. Bitter
Generating patterns and making conjectures.
(84, 1991) 615 - 621
The Big Picture
Maurice J. Burke
Looking at a picture from a large distance, noticing an analogy,
and drawing an informal conclusion.
(83, 1990) 258 - 262
Coordinate Geometry: A Powerful Tool for Solving Problems
Stanley F. Tabak
Contrasting synthetic and analytic proofs for three theorems.
(83, 1990) 264 - 268
The Geometry Proof Tutor: An "Intelligent" Computer-based Tutor
in the Classroom
Richard Wertheimer
A description of classroom experiences with the GPTutor.
(83, 1990) 308 - 317
Inductive and Deductive Reasoning
Phares G. O'Daffer
Activities to encourage students to use both inductive and
deductive reasoning to make conjectures about geometric figures.
(83, 1990) 378 - 384
Indirect Proof: The Tomato Story
Philinda Stern Denson
Sharing Teaching Ideas. A story for illustrating indirect proofs.
(82, 1989) 260
Jigsaw Proofs
Suzanne Goldstein
Sharing Teaching Ideas. A proof teaching technique.
(82, 1989) 186 - 188
Which Method Is Best?
Edward J. Barbeau
Synthetic, transformational, analytic, vector, and complex number
proofs that an angle inscribed in a semicircle is a right angle.
(81, 1988) 87 - 90
The Proof is in the Puzzle
Carl Sparano
Puzzles for developing proof-making strategies.
(81, 1988) 456 - 457
The Indirect Method
Joseph V. Roberti
Examples of indirect proofs and suggested further problems
for investigation.
80, (1987) 41 - 43.
Teaching Modeling and Axiomatization with Boolean Algebra
Michael D. DeVilliers
Proofs of Boolean Algebra statements, analysis of the proofs, and the
development of a suitable axiomatic basis.
80, (1987) 528 - 532.
Stuck! Don't Give Up! Subgoal-Generation Strategies in Problem Solving
Robert J. Jensen
Managing the problem solution process. Subgoals and strategies.
80, (1987) 614 - 621, 634.
Turtle Graphics and Mathematical Induction
Frederick S. Klotz
Revising the FD command in Logo. Links to inductive proofs.
80, (1987) 636 - 639, 654.
The Looking-back Step in Problem Solving
Larry Sowder
Looking-back after the completion of the solution to a problem to search
for other problems. The technique is applied to one geometry problem.
79, (1986) 511 - 513.
Chomp--an Introduction to Definitions, Conjectures, and Theorems
Robert J. Keeley
A game designed to introduce students to the concepts of conjecture,
theorem, and proof.
79, (1986) 516 - 519.
Spadework Prior to Deduction in Geometry
J. Michael Shaughnessy and William F. Burger
A discussion of van Hiele levels and their applications to methods
of preparing students for deductive geometry.
78, (1985) 419 - 428.
Motivating Students To Make Conjectures and Proofs In Secondary
School Geometry
Lynn H. Brown
Guided discovery with worksheets.
75, (1982) 447 - 451.
Mysteries Of Proof
George Marino
Suggested method for introducing proof development.
75, (1982) 559 - 563.
Help For The Slower Geometry Student
Diane Bohannon
Analysis of proofs (worksheet).
73, (1980) 594 - 596.
A Theorem Named Fred
Lloyd A. Jerrold
Turning an often used procedure into a theorem.
73, (1980) 596 - 597.
More On Flow Proofs In Geometry
Dale Basinger
Another format.
72, (1979) 434 - 436.
To Prove Or Not To Prove - That Is The Question
Thomas E. Inman
Suggested procedure for teaching the art of geometric proof.
72, (1979) 668 - 669.
Three Column Proofs
Michael Shields
Suggestions for proof writing formats.
71, (1978) 515 - 516.
Flow Proofs In Geometry
Robert McMurray
Proof writing format.
71, (1978) 592 - 595.
On The Proof-Making Task
Robert B. Kane
Teaching students to develop proofs.
68, (1975) 89 - 94.
Let's Use Trigonometry
John J. Rodgers
The use of trigonometry in proving some theorems of geometry.
68, (1975) 157 - 160.
Auxiliary Lines - A Testing Problem
Bruce J. Alpart
Using helping lines in proofs.
66, (1973) 159 - 160.
A Form Of Proof
Arthur E. Hallerberg
Flow diagrams, examples provided.
64, (1971) 203 - 214.
A Geometrical Introduction To Mathematical Induction
Margaret Wiscamb
Some geometrical problems (lines determined by points, etc.)
which illustrate inductive techniques.
63, (1970) 402 - 404.
Strategies Of Proof In Secondary Mathematics
Henry van Engen
Some geometry involved.
63, (1970) 637 - 645.
Motivating Induction
Harry Sitomer
Some geometry involved.
63, (1970) 661 - 664.
Sight Versus Insight
Harry Sitomer
The use of figures in geometric proofs.
60, (1967) 474 - 478.
Structuring A Proof
Donn L. Klinger
Techniques applied to three geometric theorems.
57, (1964) 200 - 203.
Another Format For Proofs In High School Geometry
Arthur E. Tenney
Suggested outline.
56, (1963) 606 - 607.
Structure Diagrams For Geometry Proofs
Carolyn C. Thorsen
Flow diagrams.
56, (1963) 608 - 609.
A Method Of Proof For High School Geometry
Harold M. Ness, Jr.
Suggested forms for organization.
55, (1962) 567 - 569.
Geometric Proof In The Eighth Grade
Myron F. Rosskopf
Possible approaches.
54, (1961) 402 - 405.
Symbolized Theorems
Maeriam C. Clough.
Stating hypotheses and conclusions in symbolic form.
52, (1959) 107 - 108.
Proofs With A New Format
Emil Berger
Classify each statement as given, assumption, or deduction.
52, (1959) 371.
Chains Of Reasoning In Geometry
John D. Wiseman, Jr.
Chain models of proofs.
52, (1959) 457 - 458.
Proofs With A New Format
W. W. Sawyer
Proof organization.
52, (1959) 480 - 481.
An Aid To Writing Deductive Proofs In Plane Geometry
John F. Schacht
Suggested format.
51, (1958) 303 - 305.
Modern Emphases In The Teaching of Geometry
Myron F. Rosskopf
Strategies of proof and axiomatic structure.
50, (1957) 272 - 279.
The ABC's Of Geometry
John D. Wiseman, Jr.
An aspect of proof.
50, (1957) 327 - 359.
Interpretation Of The Hypotheses In Terms Of The Figure
Helen L. Garstens
Use of figures in proofs, examples.
49, (1956) 562 - 564.
What Does "If" Mean
Kenneth O. May
Discussion of proof methods.
48, (1955) 10 - 12.
A Note On The Statements Of Theorems and Assumptions
Charles H. Butler
A discussion of discrepancies between statements and figures.
48, (1955) 106 - 107.
Helping Students Use Proofs Of Theorems In Geometry
Francis G. Lankford, Jr.
The use of model proofs.
48, (1955) 428 - 430.
A Logical Symbolism For Proof in Elementary Geometry
Wallace Manheimer
Symbols for givens in proofs.
46, (1953) 246 - 252.
Signed Areas Applied To "Recreations of Geometry"
H.C. Trimble
Analytic approach to some triangle geometry. The dangers of
arguing from a figure.
40, (1947) 3 - 7.
The Logic Of Indirect Proofs In Geometry
Nathan Lazar
Analysis, criticism, and recommendations.
40, (1947) 225 - 240.
Random Notes On Geometry Teaching, Note 4 - Superposition
Harry C. Barber
Arguments for the use of superposition.
31, (1938) 31.
The Concept Of Dependence In The teaching Of Plane Geometry
F. L. Wren
An analysis of the interdependence of elements of a figure in order
to discover its complete geometric significance.
31, (1938) 70 - 74.
"If - Then" In Plane Geometry
Harry Sitomer
Proof methods. Use of "if - then" form for statements.
31, (1938) 326 - 329.
A Fallacy In Geometric Reasoning
H. C. Christofferson
A discussion of circular reasoning in the proof of the isosceles
triangle theorem.
23, (1930) 19 - 22.
When Is A Proof Not A Proof
P. Stroup
Comments on proof in geometry.
19, (1926) 499 - 505.
Teaching Classes In Plane Geometry To Solve Original Exercises
Fletcher Daniel
Steps in problem solving. Comments on classroom use.
1, (1908 - 1909) 123 - 135.
QUADRILATERALS
Trap a Surprise in an Isosceles Trapezoid
Margaret M. Housinger
Isosceles trapezoids with integral sides in which a circle can be inscribed.
(889, 1996) 12 - 14
Theorems in Motion: Using Dynamic Geometry to Gain Fresh Insights
Daniel P. Scher
Construction of a constant-perimeter rectangle; a constant area rectangle.
(889, 1996) 330 - 332
Concept Worksheet: An Important Tool for Learning
Charalampos Toumasis
The example presented is geometric in nature, it deals with the characterization of a
parallelogram.
(88, 1995) 98 - 100
When Is a Quadrilateral a Parallelogram?
Charalampos Toumasis
Investigations of sets of sufficient conditions.
(87, 1994) 208 - 211
Creative Teaching Will Produce Creative Students
Stephen Krulik and Jess A. Rudnick
Solving the problem of finding all rectangles with integral dimensions whose area
and perimeter are numerically equal.
(87, 1994) 415 - 418
Counting Embedded Figures
Timothy V. Craine
Activities. How many triangles, squares, rectangles, etc., are there in a given
figure?
(87, 1994) 524 - 528, 538 - 541
A Quadrilateral Hierarchy to Facilitate Learning in Geometry
Timothy V. Craine and Rheta N. Rubenstein
Creating a "family tree" for quadrilaterals to enable generalization
of results. Analytic proofs are also involved.
(86,1993) 30 - 36
Ladders and Saws
Debra Tvrdik and David Blum
An activity for demonstrating many geometric relationships from
angle sums of polygons to properties of parallelograms.
(86, 1993) 510 - 513
Improving Students' Understanding of Geometric Definitions
Jim Hersberger and Gary Talsma
Sharing Teaching Ideas. Activities involving standard convex
quadrilaterals.
(84, 1991) 192 - 194
Area Ratios of Quadrilaterals
David R. Anderson and Michael J. Arcidiacono
Looks at the area of the quadrilateral formed by joining points on
the sides of a given quadrilateral.
(82, 1989) 176 - 184
An Application of the Criteria ASASA for Quadrilaterals
Spencer P. Hurd
A series of results leading to the Theorem of Pythagoras.
(81, 1988) 124 - 126
Discoveries with Rectangles and Rectangular Solids
Lyle R. Smith
Differentiating between area and perimeter for rectangles and between
volume and surface area for rectangular solids.
80, (1987) 274 - 276.
Geometrical Adventures in Functionland
Rina Hershkowitz, Abraham Arcavi, and Theodore Eisenberg
Determining the change in area produced by making a change in some
property of a particular figure.
80, (1987) 346 - 352.
Median of a Trapezoid
Pamela Allison
Using the result about the segment joining the midpoints of the sides
of a triangle in order to find the length of the median of a trapezoid.
79, (1986) 103 - 104.
A Postal Scale Linkage
Andrew A. Zucker
A "Sharing Teaching Idea". Use of physical models. Application to
quadrilaterals.
78, (1985) 431 - 43
The Rhombus Construction Company
Joseph A. Troccolo
Activities for looking at properties of a rhombus.
76, (1983) 37 - 41.
Triangles, Rectangles, and Parallelograms
Melfried Olsen and Judith Olsen
Activities involving the manipulation of models of geometric figures.
76, (1983) 112 - 116.
President Garfield's Configuration
Allan Weiner
Geometric and trigonometric results derived from the trapezoidal
configuration used by Garfield in his proof of the theorem of
Pythagoras.
75, (1982) 567 - 570.
Spirolaterals
Richard Brannan and Scott McFadden
Activities involving figures made up of rectangles on a grid.
74, (1981) 279 - 282, 285.
Measuring Squares To Prepare For Pi
Don E. Ryote
Seven activities leading to a consideration of the ratio of perimeter
to diagonal for a rectangle.
74, (1981) 375 - 379.
Properties Of Quadrilaterals
Stephen Maraldo
Definitions, theorems, and a diagram.
73, (1980) 38 - 39.
Area and Cost Per Unit: An Application
Jan J. Vandever
Activities providing practice with area formulas.
73, (1980) 281 - 284, 287.
Are Circumscribable Quadrilaterals Always Inscribable?
Joseph Shin
A condition under which they will be is developed.
73, (1980) 371 - 372.
Graphing - Perimeter - Area
Merrill H. Murphy
Activities concerning areas and perimeters of polygons. A coordinate
system is used
73, (1980) 441 - 444.
Computer Classification Of Triangles and Quadrilaterals -
A Challenging Application
J. Richard Dennis
Computer application, uses coordinates of vertices.
71, (1978) 452 - 458.
Exploring Skewsquares
Alten T. Olson
Properties of quadrilaterals having congruent, mutually perpendicular
diagonals. (Transformational approach.)
69, (1976) 570 - 573.
Consistent Classification Of Geometric Figures
Joe K. Smith
Suggestions for developing classification systems.
69, (1976) 574 - 576.
Midpoints and Quadrilaterals
W.J. Masalski
Activities for considering what happens when figures are formed from
polygons by using midpoints of segments.
68, (1975) 37 - 44.
The Area Of A Parallelogram Is The Product Of Its Sides
William J. Lepowsky
An experiment concerning the area of a parallelogram.
67, (1974) 419 - 421.
An Absent-Minded Professor Builds A Kite
Norman Gore and Sidney Penner
Can you build a trapezoid having the same side lengths as those
of a kite?
66, (1973) 184 - 185.
Midpoints and Measures
L. Carey Bolster
Activities involving figures formed using midpoints of sides of
triangles and quadrilaterals.
66, (1973) 627 - 630.
Urquhart's Quadrilateral Theorem
Howard Grossman
A proof and a generalization.
66, (1973) 643 - 644.
Problem Solving In Geometry
Arthur A. Hiatt
Quadrilaterals formed by using trisection points of the sides
of a quadrilateral.
65, (1972) 595 - 600.
That Area Problem
Benjamin Greenberg
Finding the area of a quadrilateral formed by using trisection points
of the sides of a quadrilateral.
64, (1971) 79 - 80.
Some Results On Quadrilaterals With Perpendicular Diagonals
Steven Szabo
Characterization of such quadrilaterals, uses vector techniques.
60, (1967) 336 - 338.
The N-Sectors Of The Angles Of A Square
James R. Smart
Extension of the concepts involved in Morley's theorem.
60, (1967) 459 - 463.
What Is A Trapezoid?
David L. Dye
Is a parallelogram a trapezoid?
60, (1967) 727 - 728.
What Is An Isosceles Trapezoid?
Don E. Ryoti
Is a parallelogram an isosceles trapezoid?
60, (1967) 729 - 730.
What Is A Quadrilateral?
Denis Crawforth
Reprint from Mathematics Teaching. Activities concerning four points.
60, (1967) 778 - 781.
What Is A Trapezoid?
M. L. Keedy
A parallelogram should be a trapezoid.
59, (1966) 646.
A Unit In High School Geometry Without The Textbook
Paul W. Avers
Application of discovery methods to the study of quadrilaterals.
57, (1964) 139 - 142.
Discovering The Centroid Of A Quadrilateral By Construction
Samuel Kaner
With a suggestion for generalization.
57, (1964) 484 - 485.
Optional Proofs Of Theorems In Plane Geometry
Francis G. Lankford, Jr.
Parallels, angle sum of a triangle.
48, (1955) 578 - 580.
Parallelogram and Parallelepiped
Victor Thebault
Theorems concerning diagonals.
47, (1954) 266 - 267.
A Skew Quadrilateral
Mathematics Laboratory (Monroe High School)
Construction of a model.
46, (1953) 50 - 51.
A Parallelogram Device
M. H. Ahrendt
The construction and uses of a linkage.
43, (1950) 350 - 351.
Functional Thinking In Geometry
Hale Pickett
Some results concerning the consequences of joining the midpoints of
the sides of a quadrilateral.
33, (1940) 69 - 72.
The Story Of The Parallelogram
Robert C. Yates
Parallelograms and linkages.
33, (1940) 301 - 309.
RIGHT TRIANGLES AND THE THEOREM OF PYTHAGORAS
Using Interactive-Geometry Software for Right-Angle Trigonometry
Charles Vonder Embse and Arne Englebretsen
Directions for the exploration utilizing The Geometer's Sketchpad, Cabri Geometry
II, and TI-92 Geometry.
(889, 1996) 602 - 605
Bringing Pythagoras to Life
Donna Ericksen, John Stasiuk, and Martha Frank
Sharing Teaching Ideas. A pursuit game with path a right triangle. The questions
are related to the theorem of Pythagoras.
(88, 1995) 744 - 747
Using Similarity to Find Length and Area
James T. Sandefur
Similar figures and scaling factors. Constructing spirals in triangles and squares.
Involvement with the theorem of Pythagoras.
(87, 1994) 319 - 325
The Converse of the Pythagorean Theorem
Jerome Rosenthal
Three proofs.
(87, 1994) 692 - 693
If Pythagoras Had a Geoboard
Bishnu Naraine
Activities for discovering the relationship among the areas
of the four triangles determined by the squares constructed
on the sides of a given triangle.
(86, 1993) 137 - 140, 145 - 148
Pythagorean Dissection Puzzles
William A. Miller and Linda Wagner
Activities and puzzles involving a Pythagorean configuration.
(86, 1993) 302 - 308, 313 - 314
A Geometrical Approach to the Six Trigonometric Ratios
Martin V. Bonsangue
Visualizing the trigonometric ratios graphically.
(86, 1993) 496 - 498
A Pythagorean Party
Philinda Stern Denson
Sharing Teaching Ideas. Group presentations of different proofs
of the theorem of Pythagoras.
(85, 1992) 112
Mathematics in Weighting
Richard L. Francis
Using templates to investigate several concepts. Included are
squaring problems and the theorem of Pythagoras.
(85, 1992) 388 - 390
Preparing for Pythagoras
Robert A. Laing
Activities for discovering area relations for figures constructed
on a right triangle.
(82, 1989) 271 - 275
Pythagoras Meets Fibonacci
William Boulger
Pythagorean triples hidden among the Fibonacci numbers.
(82, 1989) 277 - 282
Nearly Nice Right Triangles
Bob Reid
Side length ratios in 22.5-67.5-90, 18-72-90, and 15-75-90 triangles.
(82, 1989) 296 - 298
Using Puzzles to Teach the Pythagorean Theorem
James E. Beamer
Gives some proofs of the Theorem based on puzzles.
(82, 1989) 336 - 341
A Different Approach to Teaching the Midpoint Formula
Beverly A. May
Sharing Teaching Ideas. Using the fact that the midpoint of the
hypotenuse of a right triangle is equidistant from the vertices.
(82, 1989) 344 - 345
Interesting Area Ratios Within A Triangle
Manfried Olson and Gerald White
Activities for investigating areas of triangles formed when the sides
of a original triangle are subdivided.
(82, 1989) 630 - 636
An Application of the Criteria ASASA for Quadrilaterals
Spencer P. Hurd
A series of results leading to the Theorem of Pythagoras.
(81, 1988) 124 - 126
Pythagorean Triples Using Double-angle Identities
Mary Ann Weidl
Any angle in standard position with integral coordinates for points
on its terminal side will generate a Pythagorean triple by doubling
the angle.
(81, 1988) 374 - 375
A Property of Right Triangles and Some Classical Relations
Angelo S. DiDomenico
A Pythagorean triple relation which leads to other results including
Heron's formula and the law of cosines.
79, (1986) 640 - 643.
Nearly Isosceles Pythagorean Triples--Once More
Hermann Hering
A proof that every NIPT can be generated by the formula provided.
79, (1986) 724 - 725.
Proof by Analogy: The Case of the Pythagorean Theorem
Deborah R. Levine
A proof of an area result involving triangles constructed on the sides
of a right triangle.
76, (1983) 44 - 46.
Nearly Isosceles Pythagorean Triples
Robert Ryder
Right triangles in which the lengths of the legs differ by a unit.
76, (1983) 52 - 56.
Right Triangle Proportion
James K. Rowe
Several results obtained using the altitude to the hypotenuse.
74, (1981) 111 - 114.
Pythagoras On Pyramids
Aggie Azzolino
Activities involving the use of the theorem of Pythagoras to find
altitudes of pyramids.
74, (1981) 537 - 541.
On The Radii Of Inscribed and Escribed Circles Of Right Triangles
David W. Hansen
Relations between these radii and the area of a right triangle.
72, (1979) 462 - 464.
Pythagorean Theorem and Transformation Geometry
Medhat H. Rahim
A proof utilizing translations and rotations.
72, (1979) 519 - 522.
Preparing For Pythagoras
Robert A. Laing
Activities preliminary to the theorem of Pythagoras.
72, (1979) 599 - 602.
Problem Posing and Problem Solving: An Illustration Of Their Interdependence
Marion I. Walter and Stephen I. Brown
Given two equilateral triangles find a third equilateral triangle whose
area is the sum of the areas of the given triangles. The Pythagorean
theorem and a generalization.
70, (1977) 4 - 13.
A Two-Square One-Square Puzzle: The Pythagorean Theorem Revisited
Jessie Ann Engle
A puzzle for use in constructing squares.
69, (1976) 112 - 113.
President Garfield and The Pythagorean Theorem
Malcolm Graham
Garfield's proof.
69, (1976) 686 - 687.
Pythagorean Puzzles
Raymond E. Spaulding
Activities for the demonstration of the theorem.
67, (1974) 143 - 146, 159.
Are Triangles That Have The Same Area and The Same Perimeter Congruent?
Robert W. Prielipp
Some theorems about right triangles and a counterexample.
67, (1974) 157 - 159.
If Pythagoras Had A Geoboard
William A. Ewbank
The theorem of Pythagoras and some variations on a geoboard.
66, (1973) 215 - 221.
Helping Students To See The Patterns
J. Edwin Eagle
Some problems related to the theorem of Pythagoras.
64, (1971) 315 - 322.
Two Incorrect Solutions Explored Correctly
Merle C. Allen
Converse of Pythagoras, area of a triangle.
63, (1970) 257 - 258.
The Area Of A Pythagorean Triangle and The Number Six
Robert W. Prielipp
The area of such a triangle is a multiple of six.
62, (1969) 547 - 548.
Introducing Number Theory In High School Algebra and Geometry,
Part 2, Geometry
I. A. Barnett
Pythagorean triangles, constructions, unsolvable problems.
58, (1965) 89 - 101.
Application Of The Theorem Of Pythagoras In The Figure Cutting Problem
Frank Piwnicki
Dissection of squares and triangles.
55, (1962) 44 - 51.
Pythagorean Converse
Martin Hirsch
Six proofs.
54, (1961) 632 - 634.
Right Triangle Construction
Nelson S. Gray
Pythagorean triangles.
53, (1960) 533 - 536.
Primitive Pythagorean Triples
Ben Moshan
Geometric approaches to the problem.
52, (1959) 541 - 545.
Pappus's Extension Of The Pythagorean Theorem
Howard Eves
History and proof.
51, (1958) 544 - 546.
A Model For Visualizing The Pythagorean Theorem
Emil J. Berger
How to construct it.
48, (1955) 246 - 247.
A Model For Visualizing The Pythagorean Theorem
Clarence Clander
How to construct it.
48, (1955) 331.
Note On "Model For Visualizing The Pythagorean Theorem"
E. Eagle
See above. {Berger 48, (1955) 246-247}
48, (1955) 475 - 476.
The Pythagorean Theorem - Proof Number One Thousand
J. C. Eaves
Demonstration devices and a proof.
47, (1954) 346 - 347.
Company For Pythagoras
Adrian Struyk
Seven geometrical situations satisfying a(nth) + b(nth) = c(nth).
47, (1954) 411.
A Third Note On The Pythagorean Theorem
Victor Thebault
3,4,5 right triangles.
46, (1953) 188 - 189.
Note On Pythagoras' Theorem
C. Gattegno
Areas and the theorem.
45, (1952) 6 - 9.
Pythagorean Theorem Model
Isadore Chertoff
How to construct it.
45, (1952) 371 - 372.
A Second Note On The Pythagorean Theorem
Victor Thebault
A proof of the converse which is independent of the theorem.
44, (1951) 396.
Right Triangle Models
Isadore Chertoff
For use in demonstrating five theorems.
44, (1951) 563 - 565.
The Theorem Of Pythagoras
William L. Schaff
A bibliography.
44, (1951) 585 - 588.
The Pythagorean Theorem
Phillip S. Jones
Historical comments.
43, (1950) 162 - 163.
A Note On The Pythagorean Theorem
Victor Thebault
The particular 3,4,5 case.
43, (1950) 278.
Generalization As A Method In Teaching Mathematics
R. M. Winger
Geometrically the article considers generalizations of the theorem
of Pythagoras.
29, (1936) 241 - 250.
Proof Of The Theorem Of Pythagoras
Alvin Knoer
Another.
18, (1925) 496 - 497.
A Proof Of The Theorem Of Pythagoras
George W. Evans
Another.
16, (1923) 440.
Some Angles Of The Right Triangle
Alfred L. Booth
Constructing some special right triangles.
11, (1918-1919) 177 - 181.
Editorial (Proofs Of The Pythagorean Theorem)
Comments on a collection of proofs by Arthur R. Coburn.
4, (1911-1912) 45 - 48.
SIMILARITY
The Pentagon Problem: Geometric Reasoning with Technology
Rose Mary Zbiek
Area ratios for a pentagon inscribed in a pentagon inscribed in a pentagon.
(889, 1996) 86 - 90
The Incredible Three-by-Five Card
Dan Lufkin
Three similar triangles cut from a three-by-five card. Geometric activities for the
triangles.
(889, 1996) 96 - 98
Using Lined Paper to Make Discoveries
Sandra L. Hudson
Sharing Teaching Ideas. Proportional divisions by parallel transversals (the lines
on the paper.)
(87, 1994) 246 - 247
The Sidesplitting Story of the Midpoint Polygon
Y. David Gau and Lindsay A. Tartre
The midline of a triangle theorem. Varignon's theorem. Extensions to pentagons
and other polygons.
(87, 1994) 249 - 256
Using Similarity to Find Length and Area
James T. Sandefur
Similar figures and scaling factors. Constructing spirals in triangles and squares.
Involvement with the theorem of Pythagoras.
(87, 1994) 319 - 325
Multiple Approaches to Geometry: Teaching Similarity
Sharon L. Senk and Daniel B. Hirschhorn
Teaching similarity first at a visual level and then at a
theoretical level.
(83, 1990) 274 - 279
Interpreting Proportional Relationships
Kathleen A. Cramer, Thomas R Post, and Merlyn J. Behr
Activities which include some discussion of surface area and
map scaling.
(82, 1989) 445 - 452
The Bank Shot
Dan Byrne
Geometry of similar triangles and reflections applied to pool.
79, (1986) 429 - 430, 487.
Where Is the Ball Going?
Jack A. Ott and Anthony Contento
Examination of ball paths on a pool table. BASIC routine included.
79, (1986) 456 - 460.
A Few Problems Involving Scale
William D. McKillip and Cynthia Stinnette Kay
Making scale drawings.
78, (1985) 544 - 547.
A Geometry Exercise From National Assessment
Donald R. Kerr, Jr.
Similarity exercises.
74, (1981) 27 - 32.
Tiling
Richard A. Freitag
Activity involving replication of figures. Congruence and similarity.
71, (1978) 199 - 202.
Discovering A Congruence Theorem: A Project Of A Geometry For Teachers Class
Malcolm Smith
Showing that corresponding chords of homothetic circles are parallel.
65, (1972) 750 - 751.
On The Shape Of Plane Curves
W. G. Dotson, Jr.
A study of similarity.
62, (1969) 91 - 94.
The Use Of Elastic For Illustrating Homothetic Figures
Alexander Arcache
A model for demonstrating a homothety.
61, (1968) 54.
Similar Polygons and A Puzzle
Don Wallin
Construction problems and similar polygons.
52, (1959) 372 - 373.
The Definition Of Similarity
George W. Evans
Two figures will be similar if every triangle of one is similar to the
corresponding triangle of the other.
15, (1922) 147 - 151.
TESSELLATIONS
Perimeters, Patterns, and Conjectures.
Charlene Kincaid, Guy R. Mauldin, and Deanna M. Mauldin
Activities. Investigating the number of possible perimeters, maximum and
minimum perimeters for tile arrangements.
(87, 1994) 98 - 101, 107 - 108
Mathematical Connections with a Spirograph
Alfinio Flores
Activities with a spirograph for investigating patterns and symmetry.
(85, 1992) 129 - 137
Let the Computer Draw the Tessellations That You Design
Jimmy C. Woods
Gives BASIC routines to save time in the drawing of tessellations.
(81, 1988) 138 - 141
A Matter of Disks
William E. Ewbank
In what manner should disks be cut from a piece of posterboard in
order to minimize wastage?
79, (1986) 96 - 97, 146.
Reflection Patterns for Patchwork Quilts
Duane DeTemple
Forming patchwork quilt patterns by reflecting a single square back
and forth between inner and outer rectangles. Investigating the
periodic patterns formed. BASIC program included.
79, (1986) 138 - 143.
Dirichlet Polygons--An Example of Geometry in Geography
Thomas O'Shea
Applications of Dirichlet polygons, including homestead boundaries
and rainfall measurement.
79, (1986) 170 - 173.
Honeycomb Geometry: Applied Mathematics in Nature
William J. Roberts
Covering the plane with regular shapes.
77, (1984) 188 - 190.
Perplexed by Hexed
Caroline Hollingsworth
"Tessellation like" problems.
77, (1984) 560 - 562.
Tiling
Richard A Freitag
Activity involving replication of figures. Congruence and similarity.
71, (1978) 199 - 202.
A Strip Of Wallpaper
Joseph A. Troccolo
Symmetries and transformations involving wallpaper patterns.
70, (1977) 55 - 58.
A Pentamino Unit
Phyllis C. Ferrell
Geometric activities with pentaminos.
70, (1977) 523 - 527.
Transformation Geometry and The Artwork Of M.C. Escher
Sheila Haak
Analyzing the symmetries and transformations in Escher's drawings.
Techniques for producing such drawings.
69, (1976) 647 - 652.
Master Of Tessellations: M.C. Escher, 1898 - 1972
E.R. Ranucci
An account of Escher's contributions to geometry.
67, (1974) 299 - 306.
How To Draw Tessellations Of The Escher Type
Joseph L. Teeters
Title tells all.
67, (1974) 307 - 310.
A Simple Sorting Sequence
David R. Duncan and Bonnie Litwiller
Fitting regular polygons about a point in the plane.
67, (1974) 311 - 315.
Designs With Tessellations
Evan M. Maletsky
Activities involving polygons.
67, (1974) 335 - 338.
Activities: Tessellations
L. Carer Bolster
Covering the region about a point in the plane with regular polygons.
66, (1973) 339 - 342.
A Tiny Treasury Of Tessellations
Ernest R. Ranucci
Coverings of the plane.
61, (1968) 114 - 117.
Mosaics By Reflections
J. Maurice Kingston
Coverings of the plane.
50, (1957) 280 - 286.
TOPOLOGY
How to Make a Mobius Hat
Joan Ross
By crocheting.
78, (1985) 268 - 269.
Some Novel Mobius Strips
Charles Joseph Metthews
Suggestions for developing models.
65, (1972) 123 - 126.
Another "Zip The Strip"
Jean J. Pederson
A model of a Mobius strip.
65, (1972) 669.
Topology - Through The Alphabet
Ernest R. Ranucci
Using letters of the alphabet to look at topological concepts.
65, (1972) 687- 689.
Zip The Strip
C. A. Long
A discarded zipper becomes a model for a Mobius strip.
64, (1971) 41.
Dressing Up Mathematics
Jean J. Pederson
Sewing up a one-sided dress, etc.
61, (1968) 118 - 122.
A Topological Problem For The Ninth Grade Mathematics Laboratory
Jerome A. Auclair and Thomas P. Hillman
Map coloring and a related exercise on the geoboard.
61, (1968) 503 - 507.
The Construction Of Skeletal Polyhedra
John McClellan
Topological properties and models.
55, (1962) 106 - 111.
Topology: Its Nature and Significance
R. L. Wilder
History, discussion of concepts, applications.
55, (1962) 462 - 475.
The Theory Of Braids
Emil Artin
Topology and group theory.
52, (1959) 328 - 333.
Topology For Secondary Schools
Bruce E. Meserve
Suggestions for topics to be presented.
46, (1953) 465 - 474.
What Is Topology?
Francis C. Hall
An introduction to the topic.
34, (1941) 158 - 160.
TRANSFORMATIONAL GEOMETRY
Geometry, Iteration, and Finance
A. Landy Godbold, Jr.
Relation of calculation of balances to transformations on the number line.
(889, 1996) 646 - 651
Guidelines for Teaching Plane Isometries In Secondary School
Adela Jaime and Angel Gutiérrez
Connecting Research to Teaching. Isometries as a link for different branches of
mathematics or for mathematics and other sciences.
(88, 1995) 591 - 597
Geometric Transformations - Part 1
Susan K. Eddins, Evelyn O. Maxwell, and Floramma Stanislaus
Activities. Opportunities to become familiar with translations, rotations, and
reflections.
(87, 1994) 177 - 181, 187 - 189
Geometric Transformations - Part 2
Susan K. Eddins, Evelyn O. Maxwell, and Floramma Stanislaus
Activities. Coordinate approaches to transformations utilizing matrices.
(87, 1994) 258 - 261, 268 - 270
Reflections on Miniature Golf
Nancy N. Powell, Mark Anderson, and Stanley Winterroth
A transformational geometry project involving the designing of holes for miniature
golf courses.
(87, 1994) 490 - 495
Integrating Transformation Geometry into Traditional High School Geometry
Steve Okolica and Georgette Macrina
Moving transformation geometry ahead of deductive geometry.
(85, 1992) 716 - 719
Line and Rotational Symmetry
Nancy Whitman
Activities for introducing the concepts of line and rotational symmetry.
Includes some investigations of quilt patterns.
(84, 1991) 296 - 302
An Application of Affine Geometry
Thomas W. Shilgalis
A discussion of affine properties and the use of affine concepts in
obtaining geometric results.
(82, 1989) 28 - 32
Which Method Is Best?
Edward J. Barbeau
Synthetic, transformational, analytic, vector, and complex number
proofs that an angle inscribed in a semicircle is a right angle.
(81, 1988) 87 - 90
Elementary Affine Transformation Models
James B. Barksdale, Jr.
An analytic approach to some algebraic problems.
(81, 1988) 127 - 130
Reflection Patterns for Patchwork Quilts
Duane DeTemple
Forming patchwork quilt patterns by reflecting a single square back
and forth between inner and outer rectangles. Investigating the
periodic patterns formed. BASIC program included.
79, (1986) 138 - 143.
Reflective Paths to Minimum-Distance Solutions
Joan H. Shyers
The uses of reflections in order to find paths of minimum length.
79, (1986) 174 - 177, 203
The Bank Shot
Dan Byrne
Geometry of similar triangles and reflections applied to pool.
79, (1986) 429 - 430, 487.
Where Is the Ball Going?
Jack A. Ott and Anthony Contento
Examination of ball paths on a pool table. BASIC routine included.
79, (1986) 456 - 460.
Reflections on Miniature Golf
Beverly A. May
Using reflections to determine bank shots.
78, (1985) 351 - 353.
A Piagetian Approach to Transformation Geometry via Microworlds
Patrick W. Thompson
The use of a computerized microworld called Motions to allow students
to work with transformation geometry.
78, (1985) 465 - 471.
Transformation Geometry: An Application of Physics
Ken A. Dunn
An analytic approach to transformations in the Euclidean plane and
in the Minkowski plane.
77, (1984) 129 - 134.
General Equations for a Reflection in a Line
J. Taylor Hollist
An analytic development.
77, (1984) 352 - 353.
Visual Thinking with Translations, Half-Turns, and Dilations
Tom Brieske
Visual imagery applied to composition of functions.
77, (1984) 466 - 469.
Geometric Transformations On A Microcomputer
Thomas W. Shilgalis
Microcomputer programs to demonstrate motions and similarities.
75, (1982) 16 - 19.
Pythagorean Theorem and Transformational Geometry
Medhat H. Rahim
A proof utilizing translations and rotations.
72, (1979) 512 - 515.
Geometric Transformations and Music Composition
Thomas O'Shea
Relations between musical procedures (transposition, inversion, etc.)
and transformations of the plane.
72, (1979) 523 - 528.
Line Reflections In The Plane, - A Billiard Player's Delight
Gary L. Musser
Applications, complex numbers, reflections and aiming a cue ball.
71, (1978) 60 - 64.
A Strip Of Wallpaper
Joseph A. Troccolo
Symmetries and transformations involving wallpaper patterns.
70, (1977) 55 - 58.
Mathematical Reflections and Reflections On Other Isometries
Thomas D. Bishop and Judy K. Fetters
Transformation geometry activities using mirrors.
69, (1976) 404 - 407.
Exploring Skewsquares
Alton T. Olson
A transformational consideration of properties of quadrilaterals
having congruent, mutually perpendicular diagonals.
69, (1976) 570 - 573.
Transformation Geometry and The Artwork Of M.C. Escher
Sheila Haak
Analyzing the symmetries and transformations in Escher's drawings.
Techniques for producing such drawings.
69, (1976) 647 - 652.
Real Transformations From Complex Numbers
Robert D. Alexander
Complex numbers and transformation geometry.
69, (1976) 700 - 709.
Application Of Groups and Isomorphic Groups To Topics In The
Standard Curriculum, Grades 9 - 11
Zalman Usiskin
Relations of some groups and geometry.
Part I. 68, (1975) 99 - 106.
Part II. 68, (1975) 235 - 246.
A Finite Field As A Facilitator In Algebra and Geometry Classes
Marc Swadener
Some uses of a finite field to exemplify geometric concepts.
68, (1975) 271 - 275.
Elementary Linear Algebra and Geometry via Linear Equations
Thomas J. Brieski
Relations of the set of solutions of a homogeneous linear equation,
the coordinate plane and the set of translations of the plane.
68, (1975) 378 - 383.
Applications Of Transformations To Topics In Elementary Geometry,
Stanley B. Jackson
Introduces some simple transformations which are intuitively appealing
and explores ways in which they can be used to work with geometric
concepts.
Part I. Half-turns and reflections. 69, (1975) 554 - 562.
Part II. Homothety and rotation. 69, (1975) 630 - 635.
Do Similar Figures Always Have The Same Shape
Paul G. Kumpel, Jr.
Transformational geometry applied to conics with a hint about cubics.
68, (1975) 626 - 628.
The Logarithmic Spiral
Eli Maor
Analytic geometry of the spiral, some work with transformations.
67, (1974) 321 - 327.
Transformations In High School Geometry Before 1970
Z. Usiskin
A discussion of early appearances of transformational approaches in
secondary texts.
67, (1974) 353 - 360.
A Key Theorem In Transformational Geometry
Daniel Pedoe
Product of rotations.
67, (1974) 716 - 718.
Fixed Point Theorems In Euclidean Geometry
Stanley R. Clemens
Theorems about dilations and their applications to the theorems of
Menelaus, Ceva and Desargues.
66, (1973) 324 - 330.
Recreation: Hexiamonds
Raymond E. Spaulding
Developing the concepts of symmetry and rigid motion.
66, (1973) 709 - 711.
A Transformation Approach To Tenth-Grade Geometry
Z.P. Usiskin and A.F. Coxford
Uses of reflections, symmetry, congruence and similarity.
65, (1972) 21 - 29.
A Theorem On Lines Of Symmetry
Thomas W. Shilgalis
If a figure has exactly two lines of symmetry, must they be
perpendicular?
65, (1972) 69 - 72.
Transformations In High School Geometry
Frank M. Eccles
Some suggestions for introducing geometry through the use of
transformations.
65, (1972) 103, 165 - 169.
A Transformation Proof Of The Collinearity Of The Circumcenter,
Orthocenter and Centroid Of A Triangle
Thomas W. Shilgalis
Using a dilation and a half-turn.
65, (1972) 635 - 636.
The High-School Geometry Controversy: Is Transformation Geometry The Answer?
Richard H. Gart
Discusses several proposals which favor the inclusion of
transformational geometry and answers them.
64, (1971) 37 - 40.
The Use Of Elastic For Illustrating Homothetic Figures
Alexander Arcache
A model for demonstrating homotheties.
61, (1968) 54.
Rotations, Angles and Trigonometry
Robert Troyer
Transformation geometry, vectors, and trigonometry.
61, (1968) 123 - 129.
Congruence Geometry For Junior High School
J. Sanders and J. Richard Dennis
Development of transformations and some applications to theory.
61, (1968) 354 - 369.
On Similarity Transformations
James Hardesty
Images and curvature.
61, (1968) 278 - 283.
Reflections and Rotations
Burton W, Jones
Any plane motion is the product of at most three reflections.
54, (1961) 406 - 410.
The Geometry Of Space and Time
Edward Teller
Some discussion of invariants.
54, (1961) 505 - 514.
Illustrating Simple Transformations
William Koenen
A device for demonstrating rotations.
49, (1956) 467 - 468.
TRIANGLES
Morgan's Theorem
Tad Watanabe, Robert Hanson, and Frank D. Nowosielski
Investigating the area of a hexagon formed in the interior of a triangle by certain n- sectors of the angle.
(889, 1996) 420 - 423
Using a Surface Triangle to Explore Curvature
James Casey
Investigating triangle angle sums on various surfaces, e.g., bananas, soap bottles,
watermelons, etc.
(87, 1994) 69 - 77
The Sidesplitting Story of the Midpoint Polygon
Y. David Gau and Lindsay A. Tartre
The midline of a triangle theorem. Varignon's theorem. Extensions to pentagons
and other polygons.
(87, 1994) 249 - 256
Golden Triangles, Pentagons, and Pentagrams
William A. Miller and Robert G. Clason
Informal investigations of recursion. The golden ratio, Fibonnaci sequence, regular
polygons, and pentagrams.
(87, 1994) 338 - 344, 350 - 353
Counting Embedded Figures
Timothy V. Craine
Activities. How many triangles, squares, rectangles, etc., are there in a given
figure?
(87, 1994) 524 - 528, 538 - 541
Heron's Remarkable Triangle Area Formula
Bernard M. Oliver
Heron's proof and a modern short proof.
(86, 1993) 161 - 163
The Use of Dot Paper in Geometry Lessons
Ernest Woodward and Thomas Ray Hamel
Area, perimeter, congruence, similarity, Cevians.
(86, 1993) 558 - 561
SSA and the Steiner-Lehmus Theorem
David Beran
Conclusions which can be drawn from an SSA correspondence and a
proof of the Steiner-Lehmus theorem.
(85, 1992) 381 - 383
Area of a Triangle
Donald W. Stover
Sharing Teaching Ideas. An alternate method for finding the area of
a triangle given the lengths of the sides.
(83, 1990) 120
Why is the SSA Triangle Congruence Theorem Not Included in Textbooks?
Daniel B. Hirschhorn
A plea for the inclusion of a special instance of SSA.
(83, 1990) 358 - 361
SSA: The Ambiguous Case
Carolyn J. Case
Sharing Teaching Ideas. Presents a chart for investigating SSA.
(82, 1989) 109 - 111
Triangles of Equal Area and Perimeter and Inscribed Circles
Jean E. Kilmer
A triangle has equal area and perimeter if and only if it can be
circumscribed about a circle of radius 2.
(81, 1988) 65 - 70
Primitive Quadruples for the Law of Cosines
Mark A. Mettler
Investigating a*a = b*b + c*c - 2bc cos A for A = 60, 90, 120 degrees.
(81, 1988) 306 - 308
Reopening the Equilateral Triangle Problem: What Happens If . . .
Douglas L. Jones and Kenneth L. Shaw
Investigations arising from a question about the sum of the distances
from an interior point to the sides of an equilateral triangle.
(81, 1988) 634 - 638
Let ABC Be Any Triangle
Baruch Schwartz and Maxim Bruckheimer
Drawing a triangle that does not look special.
(81, 1988) 640 - 642
The Peelle Triangle
Alan Lipp
Information which can be deduced from the triangle about points, lines,
segments, squares, and cubes. A relation to Pascal's triangle.
80, (1987) 56 - 60.
Two Views of Oz
John Pancari and John P. Pace
Using the Scarecrow's Pythagorean-like utterance to define the
fundamental isosceles triangle of Oz.
80, (1987) 100 - 101.
Another Approach to the Ambiguous Case
Bernard S. Levine
Using the law of cosines to set up a quadratic equation.
80, (1987) 208 - 209.
A Geometric Proof of the Sum-Product Identities for Trigonometric Functions
Joscelyn Jarrett
Utilizing points on a unit circle.
80, (1987) 240 - 244.
Rethinking the Ambiguous Case
Allen L. Peek
Again relating the solution of the problem to the solution of a
quadratic equation.
80, (1987) 372.
Illustrating the Euler Line
James M. Rubillo
Finding the coordinates of the points on the line.
80, (1987) 389 - 393.
Some Theorems Involving the Lengths of Segments in a Triangle
Donald R. Byrkit and Timothy L. Dixon
Proof of a theorem concerning the length of an internal angle
bisector in a triangle. Other related results are included.
80, (1987) 576 - 579.
Integer-sided Triangles and the SSA Ambiguity
Abraham M. Glicksman
Some results concerning integer-sided triangles that contain a
60-degree angle.
80, (1987) 580 - 584.
Problem Solving in Geometry - a Sequence of Reuleaux Triangles
James R. Smart
Investigation of area relations for a sequence of Reuleaux
triangles associated with an equilateral triangle and a sequence
of medial triangles.
79, (1986) 11 - 14.
Did the Scarecrow Really Get A Brain?
Lowell Leake
An analysis of the Scarecrow's Pythagoras-like statement in
The Wizard of Oz.
79, (1986) 438 - 439.
A Property of Right Triangles and Some Classical Relations
Angelo S. DiDomenico
A Pythagorean triple relation which leads to other results including
Heron's formula and the law of cosines.
79, (1986) 640 - 643.
Drawing Altitudes of Triangles
Susan A. Brown
Graph paper exercises to reinforce the definition.
78, (1985) 182 - 183.
An "Ancient/Modern" Proof of Heron's Formula
William Dunham
Utilizing Heron's inscribed circle and some trigonometric results.
78, (1985) 258 - 259.
Investigating Shapes, Formulas, and Properties With LOGO
Daniel S. Yates
Logo activities leading to results on areas and triangle geometry.
78, (1985) 355 - 360. (See correction p. 472.)
Triangles, Rectangles, and Parallelograms
Melfried Olsen and Judith Olsen
Activities involving the manipulation of models of geometric figures.
76, (1983) 112 - 116.
An Improvement on SSA Congruence for Geometry and Trigonometry
Shraga Yushurum and David C. Kay
Conditions under which SSA yields congruence. A result for
non-Euclidean geometry is also presented.
76, (1983) 364 - 367.
SSA: When Does It Yield Triangle Congruence?
Bonnie H. Litwiller and David R. Duncan
One of three further conditions will guarantee the result.
74, (1981) 106 - 108.
Area = Perimeter
Lee Markowitz
When is the area of a triangle equal to its perimeter?
74, (1981) 222 - 223.
Those Amazing Triangles
Christian R. Hirsch
Activities. Morley's triangle. Outer Napoleon triangle.
74, (1981) 444 - 448.
80 Proofs From Around The World
Tony Trono
Proofs of "If the angle bisectors of a triangle are equal then
the triangle is isosceles."
74, (1981) 695 - 696.
The Golden Mean and An Intriguing Congruence Problem
David L. Pagini and Gerald E. Gannon
Another approach to triangles which have five non-corresponding
congruent parts but which are not congruent.
74, (1981) 725 - 728.
Isosceles Triangles With The Same Perimeter and Area
Mark E. Bradley
There can never be more than two isosceles triangles having a given
number as both perimeter and area.
73, (1980) 264 - 266.
Area and Cost Per Unit: An Application
Jan J. Vandever
Activities for practice with area formulas.
73, (1980) 281 - 284, 287.
Beyond The Usual Constructions
Melfried Olson
Activities leading to the Fermat point, Simpson line, etc.
73, (1980) 361 - 364.
Exploring Congruent Triangles
A. S. Green
A suggested method for the introduction of congruence of triangles.
73, (1980) 434 - 436.
Graphing - Perimeter - Area
Merrill A. Meneley
Activities dealing with areas and perimeters of polygons. Uses a
coordinate system.
73, (1980) 441 - 444.
Serendipity On The Area Of A Triangle
Madelaine Bates
When are the area and the perimeter of a triangle equal?
72, (1979) 273 - 275.
Right Or Not: A Triangle Investigation
Daniel T. Dolan
Activities leading to the development of relations between the
lengths of the sides of a triangle and its classification according
to angle size.
72, (1979) 279 - 282.
Pie Packing
William Jacob Bechem
Activities for investigating properties of 30 - 60 and isosceles
right triangles.
72, (1979) 519 - 522.
Tiling
Richard A. Freitag
Activities involving the replication of figures. Congruence and
similarity.
71, (1978) 199 - 202.
Computer Classification Of Triangles and Quadrilaterals - A Challenging
Application
J. Richard Dennis
Computer application, uses coordinates of vertices.
71, (1978) 452 - 458.
Tetrahexes
Raymond E. Spaulding
Activities involving congruence and symmetry.
71, (1978) 598 - 602.
Problem Posing and Problem Solving: An Illustration Of Their Interdependence
Marion A. Walter and Stephen I. Brown
Given two equilateral triangles, find a third whose area is the sum
of the areas of the first two. The Pythagorean Theorem and a
generalization.
70, (1977) 4 - 13.
The Key Duplicator: A Congruence Machine
Caroline Hollingsworth
The relation of a key duplicator to congruence of geometric figures.
70, (1977) 127 - 128.
Some Novel Consequences Of The Midline Theorem
Larry Hoehn
Application of the theorem concerning the segment joining the midpoints
of the sides of a triangle.
70, (1977) 250 - 251.
Almost Congruent Triangles With Integral Sides
John T.F. Briggs
Triangles having five parts of one congruent to five (non-corresponding)
parts of the other.
70, (1977) 253 - 257.
An Investigation Of Integral 60 and 120 Triangles
Richard C. Muller
Law of cosines investigation. Computer related.
70, (1977) 315 - 318.
Notes On The Partial Converses Of A Familiar Theorem
William M. Waters, Jr.
Partial converses of the result that for an isosceles triangle the
bisector of the apex angle, the altitude to the base and the median
to the base are identical.
70, (1977) 458 - 460.
Congruence Extended: A Setting For Activity In Geometry
Gail Spittler and Marian Weinstein
Special (two part) triangle congruence theorems. Quadrilateral
congruence theorems.
69, (976) 18 - 21.
Some Additional Results Involving Congruence Of Triangles
Norbert J. Kuenzi, John A. Oman, and Robert W. Prielipp.
Some congruence results involving area and perimeter.
68, (1975) 282 - 283.
A New Look At The "Center" Of A Triangle
James E. Lightner
An approach to problems associated with medians, altitudes, and angle
bisectors of a triangle.
68, (1975) 612 - 615.
The Converses Of A Familiar Isosceles Triangle Theorem,
F. Nicholson Moore and Donald R. Byrkit
Converses, the difference between necessary and sufficient conditions,
use of counterexamples.
67, (1974) 167 - 170.
Are Triangles That Have The Same Area and The Same Perimeter Congruent?
Robert W. Prielipp
Some theorems about right triangles and a counterexample.
67, (1974) 157 - 159.
More About Triangles With The Same Area and The Same Perimeter
Donavan R. Lichtenberg
Device for decomposing a triangle with a given area and perimeter into
another having the same area and the same perimeter.
67, (1974) 659 - 660.
In Search Of The Perfect Scalene Triangle
Bro. L. Raphael, F.S.C.
Drawing a triangle which is noticeably not isosceles nor right.
66, (1973) 57 - 60.
A Generalization Of Vux Triangles
Charles Brumfiel
A vux triangle has one angle double another. Here we consider one
angle k times another.
65, (1972) 171 - 174.
Using The Laboratory Approach To Relate Physical and Abstract Geometry
Nancy C. Whitman
Activities involving the segment determined by the midpoints of
two sides of a triangle.
65, (1972) 187 - 189.
The Three-Point Problem
A. Day Bradley
Given a triangle ABC and the angles subtended by the sides of the
triangle at a point D in the same plane, find the distances DA, DB, and
DC. (The problem of Pothenot.)
65, (1972) 703 - 705.
An Old Stumbling Stone Revisited
Robert R. Poole
Trigonometry applied to the angle bisectors of an isosceles triangle.
63, (1970) 259.
Vux Triangles
Fitch Cheney
Triangles in which one angle is double another.
63, (1970) 407 - 410.
A Project In Mathematics
J. Garfunkel
Ten problems involving products of lengths of Cevians.
61, (1968) 243 - 248.
5 - Con Triangles
Richard G. Pawley
Triangles having five parts of one congruent to five (non-corresponding)
parts of the other.
60, (1967) 438 - 443.
Congruency Of Triangles By AAS
Don Ryoti
Two proofs of the theorem.
59, (1966) 246 - 247.
A Scale For "Scaleneness"
Evelyn B. Rosenthal
Uses (perimeter - squared)/area to establish a ranking.
58, (1965) 318 - 320.
A Dialogue On Two Triangles
Leander W. Smith
When will the perimeter and the area of a triangle be numerically equal?
57, (1964) 233 - 234.
Dr. Hopkins' Proof Of The Angle Bisector Problems
Sister Mary Constantia, S.C.L.
A direct proof of the result that if two angle bisectors are congruent
the triangle is isosceles.
57, (1964) 539 - 541.
Altitudes, Medians, Angle Bisectors and Perpendicular Bisectors Of The
Sides Of A Triangle
Harry Schor
Paper folding.
56, (1963) 105 - 106.
The Problem Of The Angle Bisector
Joseph Holzinger
If two angle bisectors of a triangle are congruent the triangle is
isosceles. The result is trigonometrically based.
56, (1963) 321 - 322.
Notes On The Centroid
Nathan Altshiller Court
Primarily historic.
53, (1960) 33 - 35.
The Use Of Congruence In Geometric Proofs
Carl Bergman
Using directed triangles in congruence proofs.
51, (1958) 23 - 26.
Micky's Proof Of The Medians Theorem
M. L. Keedy
Using informal deduction to prove that the medians of an isosceles
triangle are congruent.
51, (1958) 453 - 455.
Congruent Triangles (Fifth Case) and The Theorem Of Lehmus
Victor Thebault
A proof of a congruence theorem concerning angle bisectors.
48, (1955) 97 - 98.
On Certain Cases Of Congruence Of Triangles
Victor Thebault
Congruence theorems related to division ratios.
48, (1955) 341 - 343.
Quasi-Right Triangles
Adrian Struyk
Triangles such that the difference of two angles is 90 degrees.
47, (1954) 116 - 118.
More Than Similar Triangles
Charles Salkind
Triangles such that five parts of one are congruent to five
(non-corresponding) parts of the other.
47, (1954) 561 - 562.
A New Proof Of An Old Theorem
Francis A. C. Sevier
Deals with the angle bisectors of an isosceles triangle.
45, (1952) 121 - 122.
Relations For Radii Of Circles Associated With The Triangle
T. Freitag
Circumradius, inradius, etc.
45, (1952) 357 - 360.
Signed Areas Applied To "Recreations Of Geometry"
H.C. Trimble
Analytic approach to some triangle geometry. Danger in arguing from
a figure.
40, (1947) 3 - 7.
Escribed Circles
Joseph A. Nyberg
Geometry of the circles.
40, (1947) 68 - 70.
Dynamic Geometry
John F. Schact and John J. Kinsella
The use of triangle and quadrilateral linkages as teaching devices.
Some circle geometry.
40, (1947) 151 - 157.
A New Technique In Handling The Congruence Theorems In Plane Geometry
Ralph C. Miller
Using constructions.
36, (1943) 237 - 239.
The Congruence Theorems By A New Proof
H.C. Christofferson
The use of an assumption which enables one to avoid the use
of superposition.
28, (1935) 223 - 227.
Assuming The Congruence Theorems
Joseph A. Nyberg
What should be assumed and what should be proved?
24, (1931) 395 - 399.
Proving The Equality Of The Base Angles Of An Isosceles Triangle
Joseph A. Nyberg
Need we assume the existence of an angle bisector?
22, (1929) 318 - 319.
Isotomic Points Of The Triangle
Richard Morris
Isotomic points, Gergonne points, Nagel points.
21, (1928) 163 - 170.
Circles Through Notable Points Of The Triangle
Richard Morris
Circles through three, four, five, and six points.
21, (1928) 63 - 71.
Proof Of An Original Exercise
Walter Beyer
On the sides of a triangle ABC construct equilateral triangles AEC, CDB,
and BFA. Show that AD, BE, and CF are concurrent.
20, (1927) 91 - 92.
Interesting Work Of Young Geometers
J. T. Rorer
Three triangle theorems and an approximate trisection.
1, (1908-1909) 147 - 149.
VECTOR GEOMETRY
Which Method Is Best?
Edward J. Barbeau
Synthetic, transformational, analytic, vector, and complex number
proofs that an angle inscribed in a semicircle is a right angle.
(81, 1988) 87 - 90
The Corner Reflector
Whitney S. Harris, Jr.
Vector geometry applied to laser beam transmission.
76, (1983) 92 - 95.
Shipboard Weather Observation
Richard J. Palmaccio
Vector geometry used to determine wind velocity from a moving ship.
BASIC program provided.
76, (1983) 165 - 169.
The Use Of Vectors In Proving Classical Geometric Theorems
Paul A. White
An example of the use of vectors in geometry.
68, (1975) 294 - 296.
Vectors In The Eighth Grade
Nicholas Grant
Suggestions for the introduction of work with vectors in the
eighth grade.
64, (1971) 607 - 613.
Rotations, Angles and Trigonometry
Robert Troyer
Transformations, vectors, and trigonometry.
61, (1968) 123 - 129.
Some Results On Quadrilaterals With Perpendicular Diagonals
Steven Szabo
Uses vector techniques to classify these quadrilaterals.
69, (1967) 336 - 338.
An Approach To Euclidean Geometry Through Vectors
Steven Szabo
Begins with translations to motivate postulates then proceeds to
develop the system.
59, (1966) 218 - 235.
The Teaching Of Vectors In The German Gymnasium
Herman Athen
Techniques and applications.
I. Ages 10 - 16. 59, (1966) 382 - 393.
II. Ages 16 - 19. 59, (1966) 485 - 495.
Vectors In Algebra and Geometry
A.M. Glicksman
Geometric results obtained by the use of vectors and linear equations.
58, (1965) 327 - 332.
An Illustration Of The Use Of Vector Methods In Geometry
Herbert E. Vaughan
Some theorems about Cevians.
58, (1965) 696 - 701.
An Approach To Vector Geometry
Robert J. Troyer
A possible development of vector geometry for high school classes.
56, (1963) 290 - 297.
Complex Numbers and Vectors In High School Geometry
A.H. Pedley
Possible applications.
53, (1960) 198 - 201.
Vectors - An Aid To Mathematical Understanding
Dan Smith
Presents vectors as ordered pairs.
52, (1959) 608 - 612.
Applications Of Complex Numbers To Geometry
Allen B. Shaw
Many of the results are much like vector proofs.
25, (1932) 215 - 226.
Vectors For Beginners
Joseph B. Reynolds
Some geometric applications.
14, (1921) 355 - 361.
WHAT SHOULD BE TAUGHT?
Mathematical Structures: Answering the "Why" Questions
Doug Jones and William S. Bush
Axiomatic structures. Suggestions for teaching mathematical structure appropriate
for the secondary school.
(889, 1996) 716 - 722
A Core Curriculum in Geometry
Martha Tietze
The use of hands-on activities in the third year of an integrated
sequence for the non-college bound.
(85, 1992) 300 - 303
Integrating Transformation Geometry into Traditional High School Geometry
Steve Okolica and Georgette Macrina
Moving transformation geometry ahead of deductive geometry.
(85, 1992) 716 - 719
Problem Posing in Geometry
Larry Hoehn
Methods for creating geometry problems. Thirteen problems arising
from a familiar theorem.
(84, 1991) 10 - 14
Van Hiele Levels of Geometric Thought Revisited
Anne Teppo
Relating the van Hiele theory to the Standards.
(84, 1991) 210 - 221
STAR Experimental Geometry: Working with Mathematically Gifted Middle
School Students
Gary Talsma and Jim Hersberger
A description of a course for mathematically gifted middle
school students.
(83, 1990) 351 - 357
Geometry: A Remedy for the Malaise of Middle School Mathematics
Alfred S. Posamentier
Encourages the teaching of geometric concepts in the middle school.
(82, 1989) 678 - 680
Problem Solving: The Third Dimension in Mathematics Teaching
George Gadanidis
The examples used are primarily geometric in nature.
(81, 1988) 16 - 21
The 1985 Nationwide University Mathematics Examination
in the People's Republic of China
Jerry P. Becker and Zhou Yi-Yun
A short discussion of the examination, an observation that a great deal
of emphasis is placed on geometry. The examination questions are
presented.
80, (1987) 196 - 203.
Geometry in the Junior High School
Fernand J. Prevost
Suggested geometric topics for the Junior High School.
78, (1985) 411 - 418.
Logic for Algebra: New Logic for Old Geometry
Kenneth A. Retzer
Inferential logic should be taught in Geometry and sentential logic
in Algebra.
78, (1985) 457 - 464.
The Shape of Instruction in Geometry: Some Highlights from Research
Marilyn N. Suydam
"Why, what, when, and how is geometry taught most effectively."
Research findings on these questions.
78, (1985) 481 - 486.
Lets Put Computers Into The Mathematics Curriculum
Donald O. Norris
...and throw out plane geometry.
74, (1981) 24 - 26.
What Should Not Be In The Algebra and Geometry Curricula Of Average College
Bound Students
Zalman Usiskin
The curriculum is overcrowded. Criteria for the inclusion or exclusion
of topics are given. Suggestions are made for the deletion of topics.
73, (1980) 413 - 424.
What Do Mathematics Teachers Think About The High School Geometry Controversy?
A survey of the attitudes of secondary mathematics teachers concerning
geometry content.
68, (1975) 486 - 493.
Geometry and Other Science Fiction
Jerry Lenz
Bibliography (including some Science Fiction) chosen for its geometrical
content.
66, (1973) 529.
The Present Year-Long Course In Euclidean Geometry Must Go
Howard F. Fehr
Gives a sequence of geometrical topics which, it is argued, should be
in a six year unified study.
65, (1972) 151 -154.
An Improved Year Of Geometry
Bruce Meserve
Some suggestions for improving geometry teaching and developing a
comprehensive geometry program throughout the students' experience.
65, (1972) 103, 176 - 181.
The High School Geometry Controversy: Is Transformation Geometry The Answer?
Richard H. Gast
Discusses several proposals which favor the inclusion of
transformational geometry.
64, (1971) 37 - 40.
Analytic Geometry Is Not Dead
Lawrence C. Eggan
Argues for the existence of an analytic geometry course at the 12th
grade level.
64, (1971) 355 - 357.
The Geometric Continuum
Harold P. Fawcett
Some history of geometry in the schools (primarily secondary).
63, (1970) 411 - 420.
The Dilemma In Geometry
Carl B. Allendoerfer
Discussion, concluding with a suggested curriculum.
62, (1969) 165 - 169.
What Shall We Teach In High School Geometry?
Irving Adler
Goals, techniques, proposals.
61, (1968) 226 - 238.
What Should High School Geometry Be?
Charles Buck
Suggests that the course should be synthetic and begin with intuition.
61, (1968) 466 - 471.
The Modern Approach To Elementary Geometry
Oswald Veblen
Reprint of a 1934 article. Discusses bases for the formation of
attitudes toward elementary geometry.
60, (1967) 98 - 104.
Concerning Plane Geometry In The Textbooks Of Classes 7 and 8
Fritz Homagh
Translation of a 1966 German article dealing with textbook content.
60, (1967) 165 - 172.
A Proposal For The High School Mathematics Curriculum
Morris Kline
Contains some comments on tenth grade geometry.
59, (1966) 322 - 330.
The Role Of Geometry In The Eleventh and Twelfth Grades
Harry Levy
Geometric concepts in secondary geometry.
57, (1964) 130 - 138.
New Trends In Algebra and Geometry
Bruce E. Meserve
Course suggestions.
55, (1962) 452 - 461.
No Space Geometry In The Space Age?
Charles H. Smiley and David K. Peterson
Suggests a mathematically based astronomy course with an emphasis on
space geometry.
53, (1960) 18 - 21.
The Ball State Experimental Program
Charles Brumfiel, Robert Eicholz and Merrill Shanks
Contains a section (79 - 83) on the development of geometry.
53, (1960) 75 - 84.
A New Role For High School Geometry
Robert B. Christian
Students should be introduced to some elementary examples of abstract
ideas.
53, (1960) 433 - 436.
The SMSG Geometry Program
Edwin E. Moise
A description of its development.
53, (1960) 437 - 442.
Some Geometric Ideas For Junior High School
Irvin H. Brune
Course content suggestions.
53, (1960) 620 - 626.
For A Better Mathematics Program In High School
F. Lynwood Wren
Suggestions.
49, (1956) 100 - 111.
What Kind Of Geometry Shall We Teach?
M. Van Waynen
Applications of geometric methods to other fields.
43, (1950) 3 - 11.
Teaching For Generalization In Geometry
Frank B. Allen
Some examples. Suggested topics and techniques.
43, (1950) 245 - 251.
Tenth Year Geometry For All American Youth
Samuel Welkowitz
What should be involved in the plane geometry course.
39, (1946) 99 - 112.
The Objectives Of Tenth Year Mathematics
Harry Eisner
How should the geometry course be revised?
36, (1943) 62 - 67.
A Reply To Mr. Nygard
Norman N. Royall, Jr.
Detailed comments on {34, (1941) 269 - 273, see below}.
35, (1942) 179 - 181.
The War On Euclid
Charles Salkind
Comments on attempts to modify method and content in plane geometry.
35, (1942) 205 - 207.
The Habitat Of Geometric Forms
Charles R. Salit
Origin and occurrence of primary geometric forms.
35, (1942) 325 - 326.
What Mathematical Knowledge and Abilities For The Teacher Of Geometry Should
The Teacher Training Program Provide In Fields Other Than Geometry
Gertrude Hendrix
Answers the question posed.
34, (1941) 66 - 71.
What Specialized Knowledge Should The Teacher Training Program Provide
In The Field Of Geometry?
P. D. Edwards
Answers the question posed.
34, (1941) 113 - 118.
A Reorganization Of Geometry For Carryover
Harold D. Alten
Changing the geometry course so as to have students apply geometric
types of reasoning in other situations.
34, (1941) 51 - 54.
A Functional Revision Of Plane Geometry
P. H. Nygard
Revising the geometry course.
34, (1941) 269 - 273.
A Protest Against Informal Reasoning As An Approach To Demonstrative Geometry
Gertrude Hendrix
Calls for the use of formal deductive proofs.
29, (1936) 178 - 180.
The Abstract and The Concrete In The Development Of School Geometry
George Wolff
History, development, trends.
29, (1936) 365 - 373.
Third Report Of The Committee On Geometry
Ralph Beatley
Suggested programs in geometry. Bibliographical notes.
28, (1935) 329 - 379.
Bibliographical notes continued. Results of questionnaires.
28, (1935) 401 - 450.
Demonstrative Geometry In The Ninth Year
Joseph B. Orleans
Course outline.
26, (1933) 100 - 103.
Demonstrative Geometry For The Ninth Grade
W. D. Reeve
Reasons for teaching, postulates, three units of material.
26, (1933) 150 - 162.
An Attempt To Apply The Principles Of Progressive Education To The
Teaching Of Geometry
Leroy H. Schnell
Objectives, preliminary steps, one unit of material.
26, (1933) 163 - 175.
Second Report Of The Committee On Geometry
Ralph Beatley
List of materials examined. General observations.
26, (1933) 366 - 371.
Preliminary Report Of The Committee On Geometry
Ralph Beatley
Plans for study.
25, (1932) 427 - 428.
Notes On The First Year Of Demonstrative Geometry In Secondary Schools
Ralph Beatley
Materials used and comments.
24, (1931) 213 - 222.
Report Of The Committee On Geometry
Preliminary results.
24, (1931) 298 - 302.
Report Of The Second Committee On Geometry
Charles M. Austin
Comments, results, suggestions, and syllabi.
24, (1931) 370 - 394.
Proposed Syllabus In Plane And Solid Geometry
George W. Evans
A list of assumptions and theorems.
23, (1931) 87 - 94.
The Introduction To Demonstrative Geometry
E. H. Taylor
Present practices and objectives.
23, (1930) 227 - 235.
Geometry In The Junior High School
Marie Gugle
What should be taught? How should it be taught?
Course outline included.
23, (1930) 209 - 226.
A One Year Course In Plane and Solid Geometry
John C. Stone
Curriculum revision, history, aims of a course in geometry.
23, (1930) 236 - 242.
Geometry Measures Land
W. R. Ransom
Geometry has become too much an exercise in pure logic.
23, (1930) 243 - 251.
Rebuilding Geometry
George W. Evans
Arguments beyond the "Proposed Syllabus ..." . {See above.}
23, (1930) 252 - 256.
A Professional Course For The Training Of Geometry Teachers
H. C. Christofferson
Objectives, subject matter involved, pattern of teaching used.
23, (1930) 289 - 299.
Geometry As Preparation For College
W. R. Longley
Course modifications for the college bound.
23, (1930) 257 - 267.
Tenth Year Mathematics Outline
W. D. Reeve
Postulates and theorems.
23, (1930) 343 - 357.
Locophobia: Its Causes and Cure
George H. Sellech
Teaching locus problems. Some examples given.
22, (1929) 382 - 389.
Beginning Geometry and College Entrance
Ralph Beatley
Suggested topics for college preparatory courses.
21, (1928) 42 - 45.
The Teaching Of Proportion In Plane Geometry
Warren R. Good and Hope H. Chipman
Literature review, textbook analysis, proposed changes.
21, (1928) 454 - 465.
Solid Geometry Versus Advanced Algebra
W. F. Babcock
Which should be taught if both are not possible?
20, (1927) 478 - 480.
"Elementary Geometry" and The "Foundations"
H. E. Webb
What should be in a beginning course in geometry?
19, (1926) 1 - 12.
A Course In Solid Geometry
William A. Austin
Course description, teaching methods and content.
19, (1926) 349 - 361.
The Sequence Of Theorems In School Geometry
T. P. Nunn
Course organization and the reasons for it.
18, (1925) 322 - 332.
Craig's Edition Of Euclid: Its "Use and Application" of The Principal
Propositions Given
Agnes G. Rowlands
Comments on an 1818 text. Applications oriented.
16, (1923) 391 - 397.
Our Geometry In Egypt and China
William A. Austin
Contacts with foreign teachers.
16, (1923) 78 - 86.
Geometry As A Course In Reasoning
Henry P. McLaughlin
Shall rigid methods of proof be abandoned?
16, (1923) 491 - 499.
The Teaching Of Beginning Geometry
A. J. Schwartz
Historical beginnings, some suggested topics and approaches.
15, (1922) 265 - 282.
The Geometry Of The Junior High School
J. C. Brown
Constructive and intuitional geometry for the last half of the seventh
school year.
14, (1921) 64 - 70.
Terms and Symbols In Elementary Mathematics
National Committee On Mathematical Requirements
Recommendations for usage. Geometry on 108 - 112.
14, (1921) 107 - 118.
College Entrance Requirements In Mathematics
National Committee On Mathematical Requirements
A list of fundamental propositions and requirements is presented
in the geometry section.
14, (1921) 224 - 245.
The Future Of Secondary Instruction In Mathematics
Harrison E. Webb
Suggestions for changes in course content.
14, (1921) 337 -341.
An Outline Of Plane Geometry As Used In The Durfie High School
Robert F. Goff
Course outline.
10, (1917-1918) 158 - 160.
Final Report Of The Committee Of Fifteen On Geometry Syllabus
A good overview of the condition of high school geometry in 1912.
Historical Introduction (48-75); Logical Considerations (75-89);
Special Courses (92-109); Exercises and Problems (109-130);
Syllabus of Geometry (109-130).
5, (1912-1913) 46 - 131.
The Provisional Report Of The National Committee On A Geometry Syllabus
Howard F. Hart
Comments on {5, (1912-1913) 46 - 131, see above.}.
The syllabus will be famous for what it omits.
4, (1911-1912) 97 - 103.
Intuition and Logic In Geometry
W. Betz
Intuition in the teaching of geometry. The school cannot take the
attitude of the rigorous mathematician.
3, (1910,1911)
Some Suggestions In The Teaching Of Geometry
Isaac J. Schwatt
Content, methods, reasons for teaching.
2, (1909-1910) 94 - 115.
WHY SHOULD GEOMETRY BE TAUGHT?
Geometry: A Remedy for the Malaise of Middle School Mathematics
Alfred S. Posamentier
Encourages the teaching of geometric concepts in the middle school.
(82, 1989) 678 - 680
Explorative Writing and Learning Mathematics
Sandra Z. Keith
The suggestions can be applied to a geometry classroom.
(81, 1988) 714 - 719
The 1985 Nationwide University Mathematics Examination
in the People's Republic of China
Jerry P. Becker and Zhou Yi-Yun
A short discussion of the examination, an observation
that a great deal of emphasis is placed on geometry.
The examination questions are presented.
80, (1987) 196 - 203.
The Shape of Instruction in Geometry: Some Highlights from Research
Marilyn N. Suydam
"Why, what, when, and how is geometry taught
most effectively." Research findings on these questions.
78, (1985) 481 - 486.
Geometry Is More Than Proof
Alan Hoffer
Developing skills. Levels of mental development.
Informal development during the first semester, deductive
reasoning during the second semester.
74, (1981) 11 - 18.
Why Is Geometry A Basic Skill?
Wade H. Sherard III
Seven reasons given.
74, (1981) 19 - 21, 60.
Trends In Geometry
Jack D. Wilson
Reasons for teaching geometry.
46, (1953) 67 - 70.
Why Teach Geometry?
Kenneth E. Brown
Objectives of authors, teachers, and pupils.
43, (1950) 103 - 106.
On The Teaching Of Geometry
Rolland R. Smith
Comments on aims and methods.
42, (1949) 56 - 60.
Applying Geometric Methods Of Thinking To Life Situations
Elizabeth Loetzer Hall
The application of classroom methods of thinking
to real life situations.
31, (1938) 379 - 384.
Geometry and Life
Kenneth B. Leisenring
Geometry and deductive thinking. The value of studying geometry.
30, (1937) 331 - 335.
Teaching Geometry For The Purpose Of Developing Ability
To Do Logical Thinking
Gilbert Ulmer
The content of one such course.
30, (1937) 355 - 357.
A New Deal In Geometry
Henry H. Shanholt
Geometry as a study of reasoning.
29, (1936) 67 - 74.
Why Teach Geometry?
Vera Sanford
Development of reasoning ability.
28, (1935) 290 - 296.
Changes In The Teaching Of Geometry and Why We Teach It
Alice Ann Grant
Begins with a discussion of Euclid, eventually comes
to the development of reasoning ability.
27, (1934) 5 - 24.
Teaching An Appreciation Of Mathematics: The Need Of
Reorganization In Geometry
E. Russell Stabler
Teaching geometry for the purpose of developing an
appreciation of the nature of mathematical systems.
27, (1934) 30 - 40.
Demonstrative Geometry For The Ninth Grade
W. D. Reeve
Reasons for teaching, postulates, three units of material.
26, (1933) 150 - 162.
The Future Geometry
Barnet Rudman
Discussion of transfer of learning, especially with respect to
the study of geometry.
25, (1932) 27 - 32.
Functional Geometry
Charles Salkind
A reaction to "The Future Geometry".
25, (1932) 484 - 486.
Solid Geometry In The High School
A. B. Coble
Why should solid geometry be taught?
24, (1931) 424 - 428.
The Functions Of Intuitive and Demonstrative Geometry
Laura Blank
What are intuitive and deductive geometry? What is the purpose
and usefulness of each?
22, (1929) 31 - 37.
Teaching Geometry Into Its Rightful Place
J. O. Hassler
Toward what purposes shall the efforts of
the geometry teacher be directed?
22, (1929) 333 - 341.
Some Objectives To Be Realized In A Course In Plane Geometry
Sister Alice Irene
Description and results of a teaching experiment.
22, (1929) 435 - 446.
What Are The Real Values Of Geometry?
Winona Perry
Geometric facts and the ability to draw conclusions.
21, (1928) 51 - 54.
Is Geometry Possible?
Jeanette F. Statham
Reasons for encouraging students to study geometry.
21, (1928) 353 - 356.
Popularizing Plane and Solid Geometry
Gertrude V. Pratt
Suggestions for securing and maintaining interest in geometry.
21, (1928) 412 - 421.
Fads and Plane Geometry
H. D. Merrell
Educational fads and their effect on the teaching of geometry.
20, (1927) 5 - 18.
Objectives In Teaching Demonstrative Geometry
W. D. Reeve
A list of objectives for plane and solid geometry courses.
20, (1927) 435 - 450.
Purpose, Method and Mode Of Demonstrative Geometry
W. W. Hart
Why should demonstrative geometry be taught?
How should it be taught?
17, (1924) 170 - 177.
Geometry As A Course In Reasoning
Henry P. McLaughlin
Shall rigid methods of proof be abandoned?
16, (1923) 491 - 499.
Some Classroom Experiences In Teaching Geometry
G. I. Hopkins
Comments by a teacher with 30 years of experience.
8, (1915-1916) 21 - 30.
Educational Value Of Geometry
F. F. Decker
Geometry should be taught because it is a deductive system.
5, (1912-1913) 31 - 35, 41 - 45.
Final Report Of The National Committee Of Fifteen On Geometry Syllabus
A good overview of the condition of high school geometry in 1912.
Historical Introduction (48-75); Logical Considerations (75-89);
Special Courses (89-92); Exercises and Problems (92-109);
Syllabus of Geometry (109-130).
5, (1912-1913) 46 - 131.
Should Formal Geometry Be Taught In The Elementary Schools?
If So, To What Extent?
D. J. Kelly
It should be blended into the arithmetic of the eighth grade.
4, (1911-1912) 144 - 149.
Some Suggestions In The Teaching Of Geometry
Isaac J. Schwatt
A discussion of many things.
2, (1909-1910) 94 - 115.
The Aims In Teaching Geometry and How To Attain Them
W. E. Bond
Three aims, difficulties with them, and some suggested remedies.
1, (1908-1909) 30 - 36.
The Aims Of Studying Plane Geometry and How To Attain Them
E. P. Sisson
How can a teacher be most effective?
1, (1908-1909) 44 - 47.