 Toads And Frogs Puzzle in 2D  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A 2dimensional Frogs and Toads puzzle that is not much more complicated than its 1dimensional analogue, provided, of course, the latter is fully understood. Java applet.
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 The Topological Zoo  The Geometry Center
For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each
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 Topology Atlas  Shakhmatov and Watson; York University, Toronto, Ontario, Canada
A multipurpose center for electronic distribution of information related to topology, the mathematical study of surfaces, sometimes called "rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely
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 Topology (Graphics Archive, Special Topics)  The Geometry Center
Properties of objects that don't change when they are stretched or twisted (Klein bottle, Moebius band).
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 Totally Tessellated  Bhushan, Kay, & Williams
A comprehensive introduction to tessellations and tilings  the basic underlying mathematics and examples of tessellations in real life. The highly illustrated, printerfriendly site includes history (tessellations in mathematics and science, decorative
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Tour: M.C. Escher  Life and Work  National Gallery of Art, Washington, DC
A tour of four virtual rooms devoted to the art of M. C. Escher. For each graphic a larger picture with accompanying commentary is available by clicking on a small picture. The gallery has more than 400 works by Escher with many images available online.
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 A Tour of Fractions  Math Forum
The Web often seems more like a maze than an organized set of resources. To help you find what you need, the Math Forum presents a 'tour' of fractions, offering links to lessons, activities, and materials, questions and answers from Ask Dr. Math, and
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 Tractrix Java Applet Class  PHD Computer Consultants Ltd
Download Tractrix.zip, a Java applet that makes the kind of pretty swirling patterns which Dutch mathematician Huygens originally named in 1692. Specify applet width and height, background and foreground color, coordinate pairs that will identify corners,
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 Traffic Signs  Richard C. Moeur
Graphics of the most commonly used traffic signs in the United States, useful for challenging students to find symmetrical signs (in addition to polygons).
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 Transformations  David A. Reid
A transformation is a onetoone mapping on a set of points. The most common transformations map the points of the plane onto themselves, in a way which keeps all lengths the same. These transformations are called isometries. Another common sort of transformation
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 Transformulas  Jedidiah Butler
Blog about transformational geometry, subtitled "picture = 100 formulas." Posts, which feature Butler's original GeoGebra applets and teaching notes, date back to March, 2014: "One Formula ... to Rule them All," "Circles Part 2: Angle Relationships,"
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk, Carnegie Mellon University
A triangle that generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Created
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 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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