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.