 Discovering Polygons and Polyhedra  Paul Scott; applets by Bob Allanson
To encourage exploration of polygons and polyhedra in an interactive way, and to appreciate their
beauty. The site contains many diagrams and applets, and invites readers to explore and find
answers for themselves.
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 Dissections: Plane & Fancy  Greg Frederickson, Cambridge University Press
A book that explores an area of mathematical recreations, called geometric dissections, or the cutting of one or more figures into pieces that can be rearranged to form other figures. With an emphasis on using as few pieces as possible, these geometrical
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 Dissection (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on problems of cutting a region (such as a polygon into the plane) into pieces (possibly putting them together to form a different polygon). Related topics include tiling (in which the whole plane is cut
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 DLK MathsWork Software
Selfdifferentiating, topicspecific math software for Windows 3.1 and above, on number, shape and space, and data handling. All of the practice modules have on screen monitoring at three levels. Six problem modules designed to improve users' application
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 Dominoes Activity  Suzanne Alejandre
A classroom activity (similar to Pentomino + 1 = Hexomino; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored through manipulatives (paper dominoes). Students explore whether it is possible to cover a 6x5 grid with
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 Don Hatch's Home Page  Don Hatch
Hyperbolic tessellations shown in various stages of truncation, and represented by their Schlafli symbols. Java applets explore hyperbolic tessellations, a magic Rubik'slike cube in four dimensions, polygon reciprocation (dual), modern portfolio theory
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 Doodling and Miracles  Cut the Knot!, Alexander Bogomolny
Almost 100 years ago, Frank Morley proved a curious theorem from elementary geometry that had remained unknown until 1899. With time, the theorem became known in mathematical folklore as Morley's Miracle (Morley's Trisector Theorem is a more mundane term.)
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 Drums That Sound Alike  Ivars Peterson (MathLand)
Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normalmode vibrations. He outlines the progress made on Mark Kac's
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 Educational Videos and Software for K12  Allied Video Corporation
Educational videos, software, and Web page services. The math series includes The Assistant Professor math videos (Fractions and All Their Parts; All About Angles; What is Area?; What are Variables?; The Pythagorean Theorem; Which Way is Minus?; The World
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 Edutest: Online Assessment Resource
Assessment testing based on nationally recognized standards in Math and Language Arts for grades 28. Scoring is instant and both parents and teachers can review the tests and the correct answers with their students. The site has some information for
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 Eighth Grade (AAA Math)  John Banfill
Interactive math exercises, lessons, and games covering basic arithmetic concepts and methods, for eighth grade.
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 Erich's Packing Center  Erich Friedman
A huge collection of packing problems, each explained with graphics. 2D examples include Triangles in Squares, Circles in Squares, Squares in Squares, Triangles in Triangles, Circles in Triangles, Squares in Triangles, Triangles in Circles, Circles in
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 Essay Ideas  Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia
For a course on Using Computers in Mathematics Instruction. Friday the 13th (show there are at most three and at least one Friday the 13th in each year, consider when two consecutive months can be have Friday the 13th); Gingerbread Man (a Microsoft Excel
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 The Euler Line and the 9point Circle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A geometric explanation of the Euler Line  how complex numbers give us a broader outlook on the geometric configuration  and the 9point circle of a triangle ABC, which passes through the feet of the three altitudes, the midside points of ABC, and the
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 The Euler Line of a Triangle  David Joyce; Dept. of Mathematics & Computer Science, Clark University
A draggable geometry applet illustrating the centroid, circumcircle and circumcenter, and altitudes and orthocenter of a triangle, and the straight line they all lie on, the Euler line.
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 The Event Inventor  Kye Ewing
Science, math, and technology explorations with no experience necessary. (Explorations can often be done by older children with no help.) Make your own quadrant and cross staff and explore the world around you  measuring heights of buildings or trees
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 Examples of Essays  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Extended Concurrencies of the Triangle, J. Wilson; Parabolas Inscribed in a Triangle, G. Giddings; Polygonal Spirals, L. Shook and M. Callinan; Roots 2 and 5, J. Wilson; Those Amazing Palindromes, Shareef Bacchus; Tangrams, Greg Huberty; Phi: That Golden
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 Exercises in Math Readiness for University (EMR)  Dept. of Mathematics and Statistics, University of Saskatchewan
A collection of exercises with solutions/tutorials for high school mathematics topics important for university study in mathematics, sciences, engineering and commerce. Exercises at three degrees of difficulty, covering graphing, solving inequalities,
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 Explorations of a Problem with Two Squares  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Given a square of side s and segments drawn from each vertex to the midpoint of the second side, counting counterclockwise, the segments intersect to form a new square. What is the ratio of the area of the shaded square to the area of the original square?
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 ExploreMath.com  Third Millennium Press
Shockwave activities illustrating realtime correlations between equations and graphs to help students visualize and experiment with concepts from elementary algebra through precalculus: experiment with the graphs of functions, systems, and complex numbers.
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 Extended Concurrencies of a Triangle  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
An exploration: take any triangle ABC. Construct equilateral triangles externally on each side and locate the center of each equilateral triangle. Label these centers A', B', and C' for the triangle centers opposite angles A, B, and C. Construct lines
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 Eye Opener Series  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of Java applets that illustrate and thus help to solve or prove various math problems: Euclid's Proof of the Pythagorean Theorem; Construction problem; Disappearing Lines puzzle; Sam Loyd's fifteen; Sliders puzzle; Lucky 7 puzzle; Happy 8
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 Faceted Objects: Tanks to Teapots  Paul Flavin
A "Tiny Library of Faceted Surfaces." Cube, Venus de Milo Statue, Utah Teapot, M1 Tank, Ludwig Beethoven, magna Girl. For each object the format, number of vertices, number of facets, geometry (shape), bytes, and filename are listed.
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 Fagnano's Problem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An interactive discussion of H. A. Schwarz's and L. Fejér's solutions to Fagnano's problem: inscribe in a given acuteangle triangle the triangle of a minimum perimeter.
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 The Fibonacci Numbers, Pineapples, Sunflowers, and the Golden Mean  Don Cohen (The Mathman)
Mathematics from a Pineapple: Infinite sequences, limit of a sequence, ratios, fractions, and decimals. Also Looking at a Regular Pentagon. Sample problems with some answers from Chapter 7 of Don Cohen's worksheet book.
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 Figures and polygons  Mark Motyka, Math League Multimedia
Definitions and illustrations: Polygon; Regular polygon; Vertex; Triangle; Equilateral triangle; Isosceles triangle; Scalene triangle; Acute triangle; Obtuse triangle; Right triangle; Quadrilateral; Rectangle; Square; Parallelogram; Rhombus; Trapezoid;
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 Finding the Smallest Triangle  Jim Parks
A script for finding the triangle of minimum perimeter inscribed in a given triangle.
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 Finding the Sum of the Exterior and Interior Angles of a Polygon (SMILE)  David Drymiller, Morgan Park High School
A geometry lesson designed to teach students to find the sum of the interior angles and the sum of the exterior angles of any polygon; review linear measurement to the nearest sixteenth of an inch and angle measurement to the nearest degree; and construct
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 First Curriculum  Patricia Simis Lundy
A first grade early literacy curriculum. In the Discovery Zone introduces the scientific method; Weather or Not uses grids, mapping, measurement, and number sense; see Our Big Backyard, showing the integration in the various lessons of literature and
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 Flash Demos for Understanding Statistics  G. Donald Allen, Texas A&M University
Dynamic demonstrations to help foster an understanding of the graphing and variance for data sets. Create a histogram and show the variance; show the mean, variance, and correlation of selfselected data points; understand variance by creating data sets;
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 Flash Games  ATK Solutions, Inc.
Flash applets and games include rotating 3d cube; mind boggle square, which challenges you to slide a square across a surface by sliding other quadrilaterals into the unoccupied spaces; Futoshiki, which involves positioning counting numbers on a grid
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 Flexagon  Magnus Enarsson
"A flexagon is a polygon folded from paper with a very remarkable quality: you can turn it inside out to make it reveal hidden surfaces." History, including the original discovery of the trihexaflexagon by Arthur H. Stone, as he folded strips of paper
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 Flexagon Re'flex'ions
Several possibly new trihexaflexagon phenomena are presented, with a wide spectrum of findings including explorations with magic squares, palindromes, and much more.
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 Flexagons  Conrad, Hartline
Introduction: The story of the Flexagon; Building and Operating the Flexagon; The Covering Space Representation of Flexagon Operation.
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 Folding Maps  Ivars Peterson (MathTrek)
Erik D. Demaine of the computer science department at the University of Waterloo
in Ontario and his coworkers have developed an efficient method for recognizing when a creased sheet is foldable into a flat package (results are reported in an unpublished
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 Formula Determination (SMILE)  Clark Odom, Collins High School
A lesson designed to teach students to determine the number of degrees in any convex polygon. From the Patterns and Logic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Forum Geometricorum  Paul Yiu, Editor; Department of Mathematical Sciences, Florida Atlantic University
A journal on classical Euclidean geometry and related areas. The goal is to bring to a wide, international readership the beauty, elegance, and
usefulness of elementary geometry, in research and in teaching. The journal focuses on concrete but challenging
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 Four Construction Problems  Cut the Knot!, Alexander Bogomolny
Construct a triangle, given the three points in the plane that are the outer vertices of equilateral triangles constructed outward on the sides of the desired triangle. Construct a triangle, given the three points in the plane that are the centers of
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 Four Numerical Triangles in Nexus  Len Smiley
Three wellknown combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that
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 Fractiles7  Max Pelletier, Beverly Johnson
Magnetic tiles that use angles based on the number 7 and allow you to make designs with repeating and nonrepeating patterns. Create starbursts, spirals, butterflies, mandalas, flowers, spaceships, and more. Offers a good way to introduce tiling theory
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 Fractions, Simplifying Parts of Shapes: 1/2, 1/3, 1/4 (SMILE)  Sarah Austin, Mary Bethune School
A lesson designed to teach students that parts are equal to their counterparts; that combined parts equal a whole; that any shape can be divided equally into parts; and to draw shapes, separate them into equal parts and write them in fractional form.
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 Frequently Asked Questions About Trigonometry  J. David Eisenberg
An interactive site that explains the ideas behind trigonometry. With Java applets for experimenting with triangles and audio files for hearing the pronunciation of trigonometric terms.
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 From Lewis Carroll to Archimedes  Cut the Knot!, Alexander Bogomolny
On March 29, 1879, Vanity Fair began offering its subscribers a new weekly puzzle invented by Lewis Carroll... on March 17, 1953 Frank Gray, a research scientist at Bell Labs, filed patent no. 2632058, for the Gray code encoding
the vacuum tube. An ndigit
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 FUNdamentally MATH  Chip Publications
A commercial DOS/Windows program covering kindergarten through grade 12 math topics (Basic skills: Addition, subtraction, multiplication, division, negative numbers; Fractions: ordinary and decimal; Middle school geometry; Exponents: powers, roots, number
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 The FUNKtion  Appreciating Math through Art  ThinkQuest 1996
How to do really hard graphic stuff. Tilings, Fractals, Sierpinski Gaskets, animations, pictures, links. Math "crash courses" on Complex Numbers; Magnitude and the Pythagorean Theorum; Functions; and 3D.
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 Gary Haynes  Gary Haynes
Course syllabi, lesson plans, homework, and objectives. Visit "Tangrams and Other Games" for an interactive tangram story and a Flash presentation on how to develop an understanding of functions through the use of the motion sensor.
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 Gecko Stone  John August
Tessellated, interlocking concrete pavers and molds. Like Escher's reptile, the tessellating shapes are modified hexagons.
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 GED Math Graphics  Howard Myers
Graphical GED test preparation designed for addiction treatment nonprofits, domestic violence shelters, community based organizations, and other, traditionally resourceconstrained programs attended by disadvantaged or indigent students.
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 Geometiles  Yana Mohanty
Interlocking tiles for exploring plane and threedimensional geometry, among other math topics. Purchase provides access to a variety of workbooks. Blog posts by creator Mohanty, an electrical engineer who earned a PhD in mathematics before teaching college
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 GeomeTree  John Miller
Explore fractals with this treedrawing app for iPod, iPhone, and iPad. Choose the number of branches, angle between branches, and the common ratio of the levels in the tree. See, in particular, the exercises and open questions on GeomeTree for the
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