 Trig According to Euclid  Len Smiley, Deborah Smiley
Four figures proving trigonometric addition and subtraction formulas for cosine and sine. Free of Cartesian coordinates, the proofs are synthetic and use a common, minimal diagram from Euclidean geometry.
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 Ultra Fractal Gallery  Frederik Slijkerman
A gallery of fractal images created using Ultra Fractal, a Windows shareware program.
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 Undergraduate Research Project in Random Tilings  Propp, Wilson
This project investigates different regions of random tilings of nxn squares with 1x2 dominoes: square, hexagon, fortress, dungeon, and Aztec diamond (the set of lattice squares completely inside a square tilted 45 degrees, discovering that the dominoes
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 The Uniform Polyhedra  Roman Maeder
A shortened version of the notebook Polyhedra.ma from Illustrated Mathematics [Gloor/Amrhein/Maeder95]. Uniform polyhedra have regular faces and congruent vertices. Allowing for nonconvex faces and vertex figures, there are 75 such polyhedra, as well
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 VEE: The Visual Elements of Euclid  Ralph Abraham
The Euclid Project is an exfoliation of the Elements of Euclid, the most important math text of all time. It will encompass several books, a CDROM, and an educational environment on the World Wide Web. Its components are: The Visual Elements of Euclid
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 The Virtual Mathematics Center  Martindale's Graduate & Undergraduate Center
Preprints and online journals from a wide variety of math and science organizations; Online math dictionaries and encylopedias; mathematics courses, tutorials and databases; courses by subject; related mathematics information and databases.
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 Virtual Math Museum  Richard Palais
A virtual "mathematical museum" being developed and improved by an international group of mathematicians called the 3DXM Consortium (the same group responsible for the development of the 3DXplorMath mathematical visualization program). Topics include
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 Virtual Polyhedra  George W. Hart
A growing collection of over 1000 virtual reality polyhedra to explore, complementing Hart's Pavilion of Polyhedreality. Includes instructions for building paper models of polyhedra including modular origami, with ideas for classroom use. Each of the
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 Virtual Skies  NASA Ames Education Division
Tutorials, interactive illustrations, career explorations, decisionmaking scenarios, and selftests in each of the following areas: weather, aviation research, airport design, air traffic management, navigation, communication, and aeronautics. A "Teacher's
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 A Virtual SpaceTime Travel Machine  JeanFrançois Colonna, École Polytechnique
Still Pictures and MPEG Animations (Images Fixes et Animations MPEG): Art and Science, Artistic Creation, Astrophysics, Celestial Mechanics, Deterministic Chaos, Deterministic Fractal Geometry, Fluid Mechanics, From the Infinitely Small to the Infinitely
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 Visia Math  Joël Gauvain
Software in French for graphical representations. Un didacticiel de mathématiques pour lycée ou collège. Vous pouvez en télécharger une version shareware ainsi que des fiches de travail pour les élèves.
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 Visions Of Chaos  Jason
A Windows application that generates fractals, cellular automata, attractors and other chaos simulations. Supports 2D images, 3D images and AVI movie creation. With galleries of fractals and Mandelbulbs; cellular automata and Lsystems music; and chaos
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 A Visual Dictionary of Special Plane Curves  Xah Lee
Materials that demonstrate interesting properties of plane curves visually. Many concepts or properties of plane curves, such as cusp, tangent, evolute,
involute, or envelope, are more readily explained by an illustration or animation. The mathematics
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 Visual Insight  American Mathematical Society
A "place to share striking images that help explain advanced topics in mathematics," as edited by John Baez. Twice monthly posts, which date back to August, 2013, have included "Atomic Singular Inner Function," "Catacaustic of a Cardioid {6,3,3}," "Honeycomb
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 Visual Intelligence: How We Create What We See  Donald D. Hoffman
Visual intelligence, cognitive scientist Donald Hoffman writes, is the power that people use to "construct an experience of objects out of colors, lines, and motions." The site includes: places to buy the book; the text of the preface; and animations
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 Visualization Laboratory of Geometric Objects  Mathematics Dept., Universidad Autónoma de México
An electronic journal and works from professors, researchers and students from the Mathematics department of the School of Science of the Universidad Autonoma de Mexico, with a gallery of geometric objects (fractals), and links to other Web pages. Versions
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 Visualization of Complex Dynamical Systems  Visualization and Animation Group, Institute of Computer Graphics, Vienna University of Technology
Software or technical reports to download (in gzipped PostScript format) related to the graphical representation of complex dynamical systems.
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 Visualizing complex analytic functions using domain coloring  Hans Lundmark; Linköping University, Sweden
An article that illustrates graphically some properties of complex analytic functions (also known as holomorphic functions), explaining how complexvalued functions can be visualized using domain coloring.
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 Visualizing Math
Tumblr of mathematical images begun June, 2013, by two high school students from Minnesota. Images have included "A panorama on a Möbius strip," "Fractal Trees by Robert Fathauer," "elegantly constructed proofs through visual inspection," "animation
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 Visual Mathematics (VisMath): Art and Science Electronic Journal of ISISSymmetry  Nagy, Jablan
The electronic journal of ISISSymmetry (International Society for Interdisciplinary Studies of Symmetry), published by the Mathematical Institute, Belgrade, Yugoslavia. Papers, conferences, the Nexus Network Journal of Architecture and Mathematics Online,
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 Visual Math Institute  Ralph Abraham, Director
Created in 1975 to administer grants from the State of California and the NSF. The "Visual Math Project" was created at UCSC for the development of computergraphic based materials for teaching university math: precalculus, calculus, linear algebra, and
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 Visual Math Learning: An interactive multimedia tutorial  Wayne Allen Bateman
An online tutorial, intended to teach students basic math concepts using interactive multimedia for aid in visualization. Proceed through the text (more sections are planned), or work with the individual exercises separately.
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 Vizual Statistix  Seth Kadish
Blog of statistics graphed by a Geoscience PhD who describes data visualization as his passion. Posts, which date back to January, 2012, have included "A Summation of Square Usage over 432 Chess Games"; a tiled plot showing the number of unique configurations
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 Voronoi Diagrams of Points, Segments and Arcs in 2D  Martin Held
VRONI is a software package for computing Voronoi diagrams of points and line segments in the Euclidean plane. Based on the Voronoi diagram, VRONI can also compute offset patterns or perform buffering. Since VRONI computes a Voronoi diagram of points
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 VRML Gallery of Electromagnetism  Rob Salgado
A collection of VRML worlds that visualize the vector fields of electromagnetism. Subcategories: addition; wedge product; raising and lowering of indices; unit vectors; charged point (Coulomb); two charged points; charged dipole; charged sphere; charged
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 Wallpaper Groups (Plane Symmetry Groups)  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Mathematicians classify plane patterns such as wallpaper patterns by means of symmetry groups  groups of transformations of the plane that leave the pattern invariant. A transformation slides, rotates, and reflects the plane into another position. Such
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 Wallpaper Groups: The Discontinuous Groups of Rotation and Translation in the Plane  Xah Lee
An undergraduate tutorial on wallpaper groups, with illustrations of the 17 wallpapers groups and a wallpaper gallery. Technically, the derivation of all discontinuous groups of rotation and translation in the plane. Contents include: Some Theorems on
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 Waterloo Fractal Compression Project  Edward R. Vrscay
A research project dedicated to the study of fractal analysis and Iterated
Function Systems/Fractal Transforms from theoretical and practical perspectives, focussing on image and signal compression. Both mathematical and nonmathematical introductions
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 Waterman Polyhedra and Maps  Steve Waterman
World maps based on close packing of spheres that resemble B.J.S. Cahill's octahedral butterfly world map, but with only five degree graticule. With links to the mathematics behind the cartography, polyhedra applications, and other original findings.
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 WebPisces  Gallery of Interactive Geometry, Geometry Center
A Webbased interface to the Pisces program that allows you to compute implicitly defined curves in the plane. Choose from several predefined functions and modify their parameters and domains. Pisces is a Platform for Implicit Surfaces and Curves and
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 weed's fractal gallery
A small gallery of fractal images and a few fractal links.
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 Weights and Measures  National Institute of Standards and Technology (NIST)
A virtual museum exhibit examining the role of the United States government in the development and standardization of weights and measures, in eight sections: America before standard weights and measures; Ferdinand Rudolph Hassler; The Office of Weights
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 What are Fractals?
A short description of fractals, with illustrations.
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 What is a Fractal?  Alan Beck; Glyphs
The word "fractal" was coined less than twenty years ago by Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision. Mandelbrot derived the term "fractal" from the Latin verb frangere,
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 What kind of math? Photo Challenge  Kathryn Mann
Pictures of math graduate students with wordbubbles showing "the kind of math that's right" for them. Submit your own group snapshots and subfields. Inspired by an observation that a flyer from the American Mathematical Society (AMS) reinforced sexist
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 What's the Problem? Geometry & Art through the Ages  Indianapolis Museum of Art
An exhibit exploring how some artists have used geometry as a creative tool. The site is divided into three topics: lines, polygons, and volume. Also provided as links from the left sidebar are a glossary and a list of references for further reading.
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 Why is the Area of a Circle Pi*r^2?  Eva Thury
An explanation of the formula for the area of a circle, based on "slicing" and rearranging the circle.
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 Wilson A. 'Snowflake' Bentley (18651931)  Tobias C. Brown
An American farmer who spent most of his life producing photomicrographs of snowflakes at his Jericho, Vermont farm. The site includes a Snow Crystal Display with a sequence of 26 images.
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 window into a math classroom  Sadie Estrella
A snapshotdriven blog subtitled "a glimpse into a math classroom once a day." Estrella's posts, enlivened with pictures of her students and of their work on classroom dryerase whiteboards, have included "Trying Math MetaCognition," "More Arguing about
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 Wolfram Research, Inc.
Wolfram is the maker of Mathematica, a software system for numeric and symbolic computation, data visualization, and programming; an interactive calculation tool and programming language to solve technical problems. Mathematica's electronic documents,
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 Wolfram Research in Precollege Education  Wolfram Research
"In the Classroom" highlights how some schools and organizations use Mathematica extensively in their curricula. The section on "Collaborative Initiatives" illustrates how businesses have teamed up with Wolfram Research to sponsor handson workshops,
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 The Wonders of Mathematics  Galileo Educational Network Association
Scores of different puzzles tailored for use in school math fairs. See also photo displays of recent math fairs.
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 World Mathematical Year 2000
On May, 6th, 1992, in Rio de Janeiro, the International Mathematical Union declared that the Year 2000 will be the World mathematical Year. The Declaration of Rio sets three aims: the great challenges of 21st Century; mathematics, a key for development;
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 A World of Color  Graphx Edge
Royaltyfree color fractal images and fractal collections available on CDROM. Also clip art, fonts, textures, and a Fractal Showcase.
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 World of Escher  World of Escher, Inc.
The world of M. C. Escher (18981972), the famous Dutch graphic artist most recognized for spatial illusions, impossible buildings, repeating geometric patterns (tessellations), and his incredible techniques in woodcutting and lithography. This site offers
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 World of Fractals  Adam Lerer
A general site about fractals, including image galleries, animations, descriptions of different types of animations, explanations, programs to download, and related links. See Types of fractals; read Understanding Fractals (The Basics, The Mathematics,
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 Xmorphia  Roy Williams
Pattern formation from differential equations  an exhibition of images and movies. Morphogenesis from a ReactionDiffusion System: Xmorphia is intended to show the variety of patterns that may be exhibited by a relatively simple parabolic partial differential
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 XNumber World  James Redin
With the Extended Numerical Keyboards with Structured DataEntry Capability method, enter a number in the same way as you think on the number; for example, input one million and fiftyseven with the four keystrokes 1, million, 5, and 7, in that order.
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 Xtoys  Michael Creutz
Download cellular automata simulators for the Xwindows operating system, or a PostScript document describing them. See also the gallery of examples.
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 Zome: Truncated 120cell  PCMI @ Math Forum: SSTP 2007
One of the activities at the 2007 Secondary School Teachers Program in the Park City Mathematics Institute was the construction of a truncated 120cell using Zometool. View both an explanation of the mathematics and photos of the construction.
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