 A+ Compass  Art Stoner, Ed.D.
A compass for use on whiteboards, with radius to 14+ inches. Uses a variety of markers and is safe for all surfaces. Easy to use and accurate.
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 Association of Teachers of Mathematics (ATM)
A U.K.based association that aims to support the teaching and learning of mathematics by encouraging increased understanding and enjoyment of mathematics. It addresses all those concerned with mathematics education in primary schools, secondary schools,
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 Before Pythagoras: The Culture of Old Babylonian Mathematics  New York University Institute for the Study of the Ancient World
This archaeological exhibit explored the world of Old Babylonian mathematics through cuneiform tablets, and illustrates how the ancient civilization performed arithmetic on numbers based entirely on two symbols. Online highlights include images of a multiplication
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 Bob's Pages  Bob Allanson
A collection of geometry applets. Generate and modify polyhedra, investigate the Mandelbrot and Julia sets, or experiment with Pappus's arbelos, the porisms of Poncelet and Steiner, and a logarithmic spiral.
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 Cabri en Physique  Yves Cortial
Cabri en Physique propose près de 140 figures créées avec le logiciel de géométrie dynamique Cabri Géomètre dont une centaine d'animations en version CabriJava: d'illustrations de phénomènes
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 Center for Technology and Teacher Education  Curry School of Education, University of Virginia
An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com
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 Collaborative Mathematics  Jason Ermer
Videos for connecting "a worldwide community of mathematical problem solvers" and "cultivating a productive attitude toward challenging problems: one of creativity, resourcefulness, selfconfidence, and perseverance." Two and threeminutelong challenges
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 The Collapsing Compass  Godfried Toussaint
There has been considerable interest during the past 2300 years in comparing different models of geometric computation in terms of their computing power. One of the most wellknown results is the proof in 1672 due to Mohr that all constructions that can
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 College Math Prep for High School Students  C. J. Kentler and V. S. Manoranjan, Washington State University
Selfscoring problems, new with every click, to gauge a student's preparedness for college level math: operations, solving for a variable, solving linear equations, word problems, solving absolute value equations, solving inequalities, distance between
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 The Complexity of Geometric Constructions  François Labelle
Efficient constructions with straightedge and collapsing compass (the geometric tools of Euclid). The question of what can and cannot be constructed with this model of computation is basically answered by Galois Theory. This document deals with the minimum
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 The computation of certain numbers using the ruler and compass  Simon Plouffe, Journal of Integer Sequences
A method for computing some numbers bit by bit using only the ruler and compass, in particular the construction for arctan(X)/Pi. This method is a spigot algorithm and can be applied to numbers that are constructible over the unit circle and the ellipse.
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 Curves  Igor Gerasimov
This scientific animated screensaver draws the Archimedean spiral, cardioid, cycloid, cissoid of Diocles, folium of Descartes, deltoid, lituus, logarithmic spiral, nephroid, limacon of Pascal, semicubic parabola, strophoid, sinusoid, epicycloid, hypocycloid,
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 Dekov Software
Educational software, a journal of computergenerated Euclidean geometry, and a computergenerated encyclopedia of Euclidean geometry. Current software titles include: Solving Triangles (stepbystep solutions to triangle problems in elementary geometry);
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 Designing Geometric Figures  Tim Fahey
Geometric constructions: instructions for constructing a variety of geometric shapes and patterns. Symbols, basic constructions, basic shapes, and how to design patterns.
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 Doubling the Cube  MacTutor Math History Archives
Linked essay covering the history of and some solutions to the classical
problem in Greek mathematics of doubling or duplicating the cube, also called the
Delian problem; and on proving the impossibility of constructing a solution using only ruler
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 Eskimo Pi  Keith Devlin (Devlin's Angle)
"As everyone knows, in the last century, the State of Indiana passed a law legislating the value of pi to be 3. Well, perhaps it's a bit of an exaggeration to say that everyone knows it, but most people do. But that alone is very odd, since it is not
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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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 Fascinating Flat Facts about Phi  Ron Knott
Phi and twodimensional geometry  constructing the golden section: phi, Phi; Phi and the root5 rectangle; the shape of a piece of paper; Phi and the pentagon triangles; Penrose tilings; a rectangle/triangle dissection problem; the Golden Spiral; trigonometry
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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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 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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 Geometric Arts  Ghee Beom "Quincy" Kim
A site dedicated to geometry and visual perception: patterns, fractals, structures, rotations, spirographs, optical arts, knots, and more. Some constructions include the artist's reflections, instructions, and links to related sites and interactive applets.
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 Geometric Constructions  Arlen Strader; College of Education, Texas A&M University
A 1997 Java applet that simulates compassandruler constructions, with a lesson in its use.
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 Geometric Constructions  G.E. Martin; SUNY at Albany, Albany, NY
A book that offers a comprehensive introduction to geometric constructions in the classical sense, combining purely mathematical, historical, and philosophical arguments and viewpoints. Contents include: Euclidean Constructions; The Ruler and Compass;
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 Geometry Assistant  ThinkQuest 1998
An applet/application for drawing dynamic geometry constructions: move any movable point and Geometry Assistant will automatically recalculate and redraw the whole construction. The site includes a place to add your unsolved geometry problem, and a Library
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 Geometry Constructions  Barry Sanders
Constructions made using the Geometer's Sketchpad: Malfatti Circles (construct 3 circles internal to any triangle, each circle being externally tangent to the other two, and each touching adjacent sides of the triangle); Hart Circle (construct the circle
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 Geometry in Motion  Daniel Scher
Direct interaction with geometric diagrams, courtesy of JavaSketchpad. The contents include a variety of curvedrawing devices (Intersecting Circles, Falling Ladder, Van Schooten's Parabola, and more); also other activities such as Constant Perimeter
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 Glossary  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A glossary of terms that also serves as an alphabetical index to Bogomolny's site. Each term is linked to an illustrated essay.
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 Hamilton's Math to Build On  Johnny & Margaret Hamilton
Simple, straightforward explanations, drawings, questions and answers from the book Math to Build On by Johnny & Margaret Hamilton (copyright 1993). Excerpts offer pages on: Angles, Degrees, Variables & Constants; Squaring Numbers; Square Roots;
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 Helena A. Verrill  Department of Mathematics, Louisiana State University
Notes, links, handouts, and other materials from the courses that Verrill teaches, such as Solving Discrete Problems, Calculus, Elliptic Curves, and Modular Forms. She also provides a Java applet for a wallpaper drawing program and stepbystep illustrations
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 Interactive Mathematics Miscellany and Puzzles  Alexander Bogomolny
"The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based  the more beautiful is the result." This awardwinning site offers
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 Inversion Geometry  Paul Kunkel
The elementary concepts are explained, with a quick reference for other lessons that employ inversion geometry.
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 James P. Dildine  James P. Dildine
Interactive math lessons for exploring parabolas, triangle areas, Pythagorean triples, triangle angle sums (powered by a Cabri Java applet), cancer and mathematics (image analysis, and determining the area and perimeter of nonregular figures), systems
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 Mathematical Problems  Torsten Sillke
Some in German, most in English. Topics include graph theory, number theory, combinatorics (enumerations), geometry, algorithms and complexity, recreational mathematics, tiling and packing, dissections, probability, algebra, analysis. Also links to "MathNews"
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 Mathematiksoftware S I und SII (vorwiegend Shareware)  Monika Schwarze
Eine Zusammenstellung nützlicher Mathematikprogramme aus dem SharewareMarkt zur Aufarbeitung von Lernrückständen, Wiederholung und Stärkung der Sicherheit mathematischer Rechenroutinen. Vor allen die Programme für die SII dienen der Überprüfung gemachter
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 mathlab.com  Mehrdad Simkani
A Java applet of unmarked straightedge and collapsible compass tools to virtually draw the lines and circles fundamental to Euclidean geometry. The help page explains how to use the Euclid applet, and contains descriptions for constructing found in propositions
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 MathResources247.com  Ampac Enterprises, LLC
Educational math toys, games, activities, and teaching supplies such as MathSafari, Hot Dots, Math Ad Libs, overheads, geoboards, algebra tiles, balances, and play money (realistic looking coins).
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 Maths Outdoors  Juliet Robertson
Blog posts from an education consultant "passionate about getting children outside." Posts on learning math outside with a kinesthetic emphasis, which date back to September, 2008, have included "Leaf Logic," "Investigating Right Angles with Sticks,"
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 A Mechanism for Drawing Archimides Spiral  Liang Chen
A mechanism that can be used to draw Archimides Spiral, one of a group of curves that can be used for trisecting angles. The author's paper is available for downloading in postscript format.
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 A Nameless Number  Len Smiley
Trianglefree polygon dissections are a variant of the dissection questions of Catalan, Schroeder, and others: In a convex (n+2)gon with n+2 labeled nodes, what is a(n), the number of ways of drawing nonintersecting diagonals so that no triangles are
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 On the Square  Paul Kunkel
Given four arbitrary, unique points, A, B, C, and D, construct one line through each point such that the four lines form a square.
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 Orthocenter  Paul Kunkel
What is significant about the orthocenter of a triangle? Why does it even have a name? This investigation was prepared for a geometry teachers' workshop. It includes a lesson handout in Word format and was written for use in a computer lab with the Geometer's
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 Panagiotis Stefanides
Geometry presented at national conferences in Greece. Contents include: Quantization of Circle Duality; Logos Pyr Chronos; 'Buena Fortuna' (artwork); Geometric Mean Ratio (T) by Ruler and Compass; Quadrature Master Theorem; Corollary (Circle Circumference
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 Peanut Software for Windows  Rick Parris
Abstracts and links for downloading free mathematics software: Wingeom (highprecision geometric constructions); Winplot (generalpurpose plotting utility); Winstats (scatter plots, curve fitting, histograms, statistical data, and standard theoretical
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 Plane Geometry Web Pages  David Jaffe
Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity;
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 Platonic Solids  Buckley; Metropolitan School District of Pike Township, Indianapolis, IN
A demonstration of the construction of the five Platonic Solids from Book 13 of Euclid's Elements. Contents include: Prop 13  pyramid; Prop 14  octahedron; Prop 15  cube; Prop 16  icosahedron; Prop 17 dodecahedron; and a Glossary Of Terms.
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 Polygons Made To Order (SMILE)  Loretta Malone, Washington High School
A lesson designed to teach students to construct a regular polygon inscribed in a circle by using isosceles triangles with vertex angles at the center of the circle and legs as radii; determine the values of the angles; and discover that as the number
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 PUERTRA  Javier Sánchez González
The software package PUERTRA implemented a theoretical study of formal properties of Islamic geometrical art. PUERTRA modeled the Islamic rectilinear interlaced lattices found extensively in wood work (artesonado ceilings, mosque minbars, doors and windows,
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 Regular Polygon Formulas (Ask Dr. Math FAQ)  Math Forum
Formulas for finding the area, perimeter, etc. of a regular polygon, and constructing regular polygons with compass and straightedge, in particular the pentagon.
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 Religious Beliefs Made Visual: Geometry and Islam  Jane Norman, Consultant, Metropolitan Museum of Art
Although the shapes and structures are based on the geometry of Euclid and other Greek mathematicians, Islamic artists used them to create visual statements about religious ideas. A discussion of the use of geometric motifs in Islamic art, with instructions
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 SafeT Compass  Maddy, Maverick; James Garner
A compass with no sharp points, flat enough to use as a bookmark in a high school geometry or algebra text and safe enough for a child. Draw circles from 1/4 in. to 10 in. in diameter with this new flat compass. $2 each, 2 for $3 postpaid. See also their
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