- 3-D Drawing and Geometry - Cathi Sanders
A Math Forum Summer 1998 Institute project that uses examples of paintings, architecture, etc. to analyze different types of 3-D drawings, and teaches students how to create them. Careers in 3-D drawing that use these techniques, from architecture to
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- 3D-XplorMath - Richard Palais
3D-XplorMath creates visualizations of mathematical objects and processes. This tool has built-in algorithms for displaying mathematical objects such as plane curves, space curves, surfaces, conformal maps, polyhedra, ordinary and partial differential
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- Aard 3D Puzzles - AardAsNails Software
Rubik's cube-like puzzles to solve online. Virtually twist and spin a pyramid, cube, diacube, or diamond, selecting solid or transparent views. Purchase the full version for up to ten levels of difficulty and preset problems.
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- About Rubik's Cube - Dan Knights
See the author's collection of Rubik's cubes, his solution and timing methods, thoughts on solving Rubik's Cube with your eyes closed, and suggestions for lubricating your cube and where to get them.
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- Algebra, Abstract and Concrete - Frederick M. Goodman
An undergraduate textbook (Prentice Hall, 1998). The book is intended to be useful for a course in modern algebra for beginners or a slightly more advanced course, or an undergraduate course on geometric aspects of group theory or Galois theory. Interactive
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- An Amazing, Space Filling, Non-Regular Tetrahedron - Peg Cagle and Joyce Frost, Park City Mathematics Institute
The rhombic dodecahedron derives its name from its twelve ("dodeca-") faces, all of which are congruent rhombi, each formed by joining two tetrahedra. In this article, Cagle and Frost explore these related polyhedra, showing how to exploit their space
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- The Angle Defect of a Polyhedron (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
The angle defect at a vertex of a polygon is defined to be 2 pi minus the sum of the angles at the corners of the faces at that vertex. What is the angle sum for a polygon (in the plane) with n sides? Determine the total angle defect for each of the 5
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- Annie's Sketchpad Activities - Annie Fetter
Handouts for activities that incorporate JavaSketchpad, including: making a presentation sketch; investigating the properties of quadrilaterals; the Euler segment; morphing a simple figure to a circle; Napoleon's theorem; drawing a box and its net; and
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- Antiprism - Adrian Rossiter
A set of programs for generating, manipulating, transforming, and viewing models of polyhedra. Open source, via the MIT license.
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- Art of the Tetrahedron - Ivars Peterson (MathTrek)
"Any four points in space that are not all on the same plane mark the corners of four triangles. The triangles in turn are the faces of a tetrahedron. It's the simplest of all polyhedra--solids bounded by polygons... To sculptor Arthur Silverman of New
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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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- Building an Icosahedron as a Class Project - Frederick J. Wicklin
A Teacher's Guide. This document describes how to build an icosahedron as a class project. The size is up to you. Step-by-step instructions are provided, as well as figures, diagrams, and templates.
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- Calculatorium - Nenad Mitrovic
JavaScript calculators for determining area, perimeter, surface area, volume, trigonometry, algebra, statistics, finance, conversions, health, and more. See also Calculatorium's timed, auto-scoring tests and typeset formulas.
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- CalmPlex: 3D Geometric Wooden Puzzles - R&A Media Inc. and Andy Snowie
A manufacturer of wood puzzles based on simple geometric shapes. Learn about the CalmPlex wooden puzzle, a twelve piece, mechanical put-together manipulative that makes an 8x8 checkerboard, a 4x4x4 cube and over 50 other tessellated shapes: details, solution
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- The Celestial Image of a Polyhedron (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
Using the celestial image of a polyhedron to get yet another proof of Descartes' angle-defect formula. What pattern is traced out on the celestial sphere when you move a flashlight around on the surface of a cube, keeping its tail as flat as possible
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- Cleave Books
Teacher Resources on Line (TRoL) include downloadable grid paper; T-tiles; dictionary exercises; shapes Bingo; MisMaths, an annotated collection of innumeracy and other math mistakes in news headlines; fact sheets; tables; formulas; a mathematical vocabulary
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- Clusters and Decagons - Ivars Peterson - Science News Online
A novel pattern made up of overlapping, 10-sided tiles may serve as a model of how atoms arrange themselves into a quasicrystalline structure.
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- Constructing Semi-Regular Tilings - Kevin Mitchell
A document based on a talk given at the Spring 1995 Meeting of the Seaway Section of the Mathematical Association of America. Contents include: Introduction and Historical Background; Notation and Definitions; General Theorems; Hyperbolic Results; and
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- Conteúdos Digitais em Matemática para o Ensino Médio - Kaleff, Ana Maria; and Humberto José Bortolossi - Universidade Federal Fluminense
Educational Java applets and lesson plans in Portuguese. Topics include real functions, algebra, permutations, polygons, tangrams, conic sections, solids of revolution, and other two- and three-dimensional geometry, which includes the English-language
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- coolmath.com: Cool Math - Karen
A searchable "amusement park of mathematics" for exploring math: functions, tessellations, polyhedra, limits, logs, fractals (with galleries), puzzles and problems, fun with numbers, how to succeed in math, careers in math. Also Cool Links for Math for
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- Cool Math Sites - Nina Heal
A links list in the following categories: puzzles, algebra, geometry, calculus, discrete math, statistics and probability, trigonometry and pre-calculus, books and reference, calculators and other technology, data, history, other links sites and internet-based
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- Course Project Suggestions (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
An list of suggestions for projects in geometry, topology, symmetry, making geometric solids, calendars, spherical and hyperbolic trigonometry, puzzles, models, etc. Projects were to be exhibited at the Geometry Fair at the end of the course.
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- Creative Java Puzzles - J. L. Read, Enchanted Mind
Games "good for exercising both sides of the brain." Knight's Tour: pass all the squares of the board with the knight, making only legal moves. Peg Solitaire: Remove all the pegs in the least amount of time, finishing with only one peg in the target hole.
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- Crystals: Crystallography & Systems - Suzanne Alejandre
A Math Forum Web Unit. Students studying polyhedra enjoy seeing the structures as they occur in the real world. Crystalline structures can be categorized into seven crystal systems: see photographs of beautiful crystals or make paper models of crystals
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- Cube-It - Education Development Center, Inc. (EDC)
A math group activity: you will need fifty cubes per group. Gather sugar cubes, wooden cubes, units from Dienes blocks or Cusinaire rods, or any manipulative that has a cubical shape. Students will: estimate the dimensions of the largest cube that can
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- Cube Roll - Cary and Michael Huang
Use the arrow keys to steer a cube along a path of squares towards a final square. Each successive level poses new restrictions based on which faces of the block can or cannot roll onto the square path, making a game out spatial thinking of polyhedral
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- Cuisenaire Math - ETA/Cuisenaire
From the makers of Cuisenaire Rods: Connecting Cuisenaire Rods, Cuisenaire Roddles (board games and puzzles that emphasize spatial reasoning skills), Cuisenaire Rods for the Overhead, Magnetic Cuisenaire Rods, and other manipulatives. Publications include
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- Daniel Willingham
From the author of Why Don't Students Like School? and When Can You Trust the Experts? (subtitled: "How to tell good science from bad in education"). See, in particular, Willingham's articles, such as "Why transfer is hard," "Why students remember or
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- Dave's Math Tables: Areas, Volumes, Surface Areas - David Manura
Formulas for and diagrams of: areas of polygons (square, rectangle, parallelogram, trapezoid, circle, ellipse, triangles); volumes of polyhedra (cube, rectangular prism, irregular prism, cylinder, pyramid, cone, sphere, ellipsoid); surface area (cube,
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- Defining Geometric Formulas (Ask Dr. Math FAQ) - Math Forum
Definitions of two- and three-dimensional figures in general, and a note on dimensions.
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- Delta Blocks - Hop David
A way to model different 3-D tessellations and a tool for studying geometry, crystallography, and polyhedra. Delta blocks were inspired by M. C. Escher's print "Flatworms," which he said demonstrates that one can build a house not only with the usual
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- Descartes' Formula (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
The angle defect at a vertex of a polygon was defined to be the amount by which the sum of the angles at the corners of the faces at that vertex falls short of and the total angle defect of the polyhedron was defined to be what one got when one added
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- Des Trucs et des Maths - Philippe Picart
Sur le nombre pi; le nombre d'or; le Rubik's cube; des ressources à télécharger; et "des trucs de maths divers," comme un JavaScript qui répond à la question "Quel jour de la semaine es-tu né?" Avec un coins des
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- Die-Cast Polyhedra Models - Pedagoguery Software
Sets of small die-cast solid aluminum polyhedra, in various colors, available for online purchase.
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- 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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- Distances on the surface of a cubical box - Henry Bottomley
An applet that demonstrates distances across the surface of a rectangular box. The first three boxes are the dimensions of the cuboid. To change them, type new numbers in and then press the "You choose" button. The text box offers six almost self-explanatory
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- DLK MathsWork Software
Self-differentiating, topic-specific 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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- Dodecahedron Measures - Paul Kunkel
An investigation of the formulas of the surface area and volume for the dodecahedron. With icosahedron extensions.
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- Domebook - Tom Camilli
Cardboard and transparent plastic geodesic domes built by children. Students start by constructing paper models, then apply scale factors to construct domes of any size using cardboard or wooden dowels and plastic sheeting. See pictures of classroom projects;
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- The DOR: Home of the Direct Opposite Reverse - David P. Sterner
Sterner developed this shape, which he calls a geometric "missing link", and has applications as a lens.
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- Drawing on Math - Tina Cardone
Blog by a public high school math teacher in Massachusetts who has participated in Boston University's PROMYS and the Institute of Advanced Studies' PCMI. Posts, which date back to August, 2011, have included "End of Year Reflections: Geometry Favorite
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- EasyCalculation.com
Free online mathematics converter, calculators, and other tools for numbers, unit conversions, hexa conversions, decimal conversions, binary conversions, area, trigonometry, analytical geometry, algebra (e.g., group work, Bernoulli inequality, Venn diagrams
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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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- Euclid
A VRML based project that demonstrates the construction of the five Platonic Solids from Book 13 of Euclid's Elements. The aim of the original Euclid project was to provide a clearer sense of the classical geometry of Euclid's Elements. It is hoped that
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- Euler Bricks and Perfect Polyhedra - Ivars Peterson (MathTrek)
"In the October Mathematics Magazine, Blake E. Peterson of Brigham Young University in Provo, Utah, and James H. Jordan of Washington State University in Pullman draw attention to perfect boxes and polyhedra. Their starting point is the problem of finding
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- Evil Mad Science - Evil Mad Science LLC
Producers of do-it-yourself (DIY) and open-source hardware designs in support of art, education, and accessibility. See, in particular, the d20 and d12 Handbags of Holding Kits (zippered bags in the shape of dodecahedra and icosahedra) and the kit for
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- Exploring Geometric Solids and Their Properties (i-Math Investigations) - Illuminations; National Council of Teachers of Mathematics (NCTM)
An online, interactive, multimedia math investigation. Investigating and then reasoning about the relationships within and between three-dimensional shapes is important for students in grades 3-5 as they continue to develop understanding about geometry
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- Five Triangles mathematics blog
This blog, which dates back to April, 2012, posts problems for middle and junior high school students. Topics have ranged from ratios and fractions to area and paths to quadratic equations and linear equations.
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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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- FoldPlay
Upload your photographs, print them out in FoldPlay's templates, then fold them into hex kaleidocycles, oct kaleidocycles, invertible cubes, and foldbooks. Also, instructions for folding nerdcatchers, sphericon pies, polygon puzzles, and other origami.
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