 Geometry of SelfContacting Binary Fractal Trees  Michael Frame; Union College, Schenectady, NY
Animations illustrating the constructions of binary fractal trees, with branch scaling chosen so some points of the left and right branches intersect, but only at the branch tips. The animations show how the geometry of the tree, and of the branch tips,
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 The Geometry Pages  Cathi Sanders
Illustrated essays designed to intrigue and inspire you to learn more about geometry and its many applications in art, engineering, science, and more. Includes the following topics: Lines (History, Elements of Geometry, Polygons, Tessellations); Numbers
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 Geometry  Paul Bourke
Explorations and renderings of various surfaces and forms, including knots, surfaces, 3D shapes, curves, algorithms, tilings, plexagons, etc. Formulae for Quadrics (Surfaces of degree 2); Superellipse and superellipsoid; SuperToroid (3D); Plexagons; Hexagonal
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 Geometry through Art  Norman Shapiro
Lesson ideas, facilitation suggestions, lists of materials needed, and handouts to photocopy. Norman Shapiro focuses on the student as investigator, learning through doing, and using perception to stimulate the motivation for more developed concepts and
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 George Washington: Surveyor and Mapmaker  Library of Congress
An essay on George Washington's lifelong association with geography and cartography, "Tracing the Maps in George Washington's Life" contains the chapters Washington as Public Land Surveyor  Boyhood and Beginnings; Washington as Public Land Surveyor 
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 Giuseppe Zito Pictures
A gallery of fractal images generated by chance from a database of around 50,000 planar dynamical systems by Zito's program, Ufattr, with some commentary.
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 Global Climate Change: Research Explorer  the Exploratorium
Explore scientific data relating to the atmosphere, the oceans, the areas covered by ice and snow, and the living organisms in all these domains. Get a sense of how scientists study natural phenomena, how researchers gather evidence, test theories, and
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 The Golden Section In Art, Architecture and Music  Ron Knott
An introduction with illustrations and references to some applications and occurrences of the Fibonacci series and the Golden Ratio in architecture, art and music. The constant Phi has been used to design architecture, from the Parthenon in Athens to
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 GrafEq Gallery  Pedagoguery Software
A gallery that demonstrates the visual range of graphs that can be produced using GRAFEQ graphing software, with a rogue's gallery of troublesome graphs. The archived graphs are possible because of the expressive power of general implicit relations. Each
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 GrafEq  Pedagoguery Software
An intuitive, flexible program for producing graphs of implicit relations. Graph equations encountered in the secondary precalculus math curriculum: linear functions, polynomial functions, conics, trigonometric functions, exponential functions, relations
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 Grafica Obscura  Paul Haeberli
An evolving computer graphics notebook: a compilation of technical notes, pictures and essays. Contents include: Paper and Plotter: A 3D Surface; Laser Cutting for Rapid Manufacturing; Geometric Paper Folding: Dr. David Huffman; Paper and Light (An inexpensive
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 Grand Illusions  Hendrik Ball
A "site for the enquiring mind, with optical illusions, scientific toys, visual effects, and even a little magic." Includes a number of feature articles on vision, photography, mirrors, optical toys, movies, etc. See, in particular, the geometrical optical
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 Graph Galleries  Microcal Software, Inc.
Select one of 5 Subject Specific Graph Galleries to view an array of industryspecific graphs, or explore graph types (3D surface graphs; contour graphs; bar, box, & column gallery; line gallery; line & symbol gallery; or scatter gallery). See
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 Graphics for Complex Analysis  Douglas N. Arnold; Institute for Mathematics and its Applications
A collection of graphical demonstrations of concepts in complex analysis developed for a course at McAllister. Most are animated so that the original curves are continuously deformed into the image curves, and the eye can follow which points move where;
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 Graphics for Complex Analysis (Java version)  Douglas N. Arnold; Institute for Mathematics and its Applications
A collection of graphical demonstrations using Java of concepts in complex analysis developed for a course at McAllister. Most are animated so that the original curves are continuously deformed into the image curves, and the eye can follow which points
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 Graphics for the Calculus Classroom (Java version)  Douglas N. Arnold; Institute for Mathematics and its Applications
Excerpts with Java animations from a collection of graphical demonstrations developed for first year calculus. Includes: Differentials and differences, computing the volume of water in a tipped glass, Archimedes' calculation of pi, how the ball bounces,
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 Graphing Calculator for Mac and Windows  Pacific Tech
Graphing Calculator calculates and displays two and threedimensional mathematical objects easily, and saves animations as QuickTime movies. The site includes a list of features, a guided tour, a picture gallery, a free demo, and ordering capabilities,
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 Graphing Cubic Polynomials  Jim Carlson, University of Utah
A Java graph with changeable coefficients. Draw the graph, zoom in or out, click on any point to get approximate coordinates. Arc length and rise/run calculated.
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 Graphmatica  Keith Hertzer, kSoft, Inc.
An equation plotter with numerical and calculus features. Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. Up to 25 graphs on screen at once. Offers copy to clipboard (bitmap and WMF),
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 GraphPanel  David Binger; Centre College
A Java application that supports the interactive editing of simple graphs with labels. The program can produce PostScript images of the graphs, and these PostScript files can be included directly in TeX documents or converted (using other programs) to
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 Graphs about Charts and Charts about Graphs  Ben Greenman
Humorously selfreferential charts and "metacharts," such as "How Much I Had to Manipulate the Data to Make It Seem Like Things Were Looking Up," "Percent Chance These Bars Are Too Thin to See," "How Hard It Was to Draw a Perfectly Straight Line Before,
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 The Great Golden Pyramid  Tony Smith
The largest of the Giza pyramids is usually called the Great Pyramid. It can also be called the Great Golden Pyramid, because its geometry is that of the Golden Mean. Pictures and diagrams of the interior and exterior architecture, with explanations of
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 Greg Egan's Home Page
Information, illustrations, and Java applets that supplement some of the works of the science fiction author. The Applets Gallery includes groups of rotations in three dimensions and in four dimensions; Escher, inspired by the artist's conflicting orientation
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 Groupe Fractales (INRIA)  Benoît Leblanc and Frédéric Raynal
A group of researchers studying the application of fractal techniques to complex systems, especially signal processing. Introduction to the theoretical aspects of fractal analysis; genetic algorithms; introduction to timescale analysis, in French; applications,
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 Guide to the Mandelbrot Set  Paul Derbyshire
Explore the Mandelbrot set with a fractaldrawing program: images of wellknown portions of the set, their locations, comments on miniature images of the Mandelbrot set that arise from different formulas, and Julia sets.
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 GVU Center  Jarek Rossignac; Georgia Tech
The Graphics, Visualization & Usability Center, envisioning a world in which computers are used as easily and effectively as are automobiles, stereos, and telephones, and collaborating on research projects in Visualization, Animation, VR, Design,
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 Hamiltonian Circuit Algorithm  Ashay Dharwadker
A new algorithm for finding Hamiltonian circuits in graphs with a
constructive proof of Dirac's theorem, applications to finding Knight's
Tours and a demonstration program, by Ashay Dharwadker.
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 Hand Made Manipulative Instructions  Margo Lynn Mankus
Pattern block cutouts: triangles, squares, smaller and larger rhombuses, trapezoids, and hexagons. Baseten blocks in sets of ones, tens, and hundreds; and basefive blocks in sets of ones, fives, and twentyfives. XYblock sets of X, X2, XY, Y, and Y2
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 Highland Tessellations  Karen M. Stagge, Highland Middle School, Libertyville, IL
Tessellations A La Escher: an introductory unit based on MECC's Tesselmania! software and the graphics of M.C. Escher, to help students realize the importance of mathematics in the art world. Also links to work done by students at other schools.
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 Hip Hop Times Tables  Pop Lock and Learn Pty Ltd
Pop, Lock and Learn hip hop times tables is meant to help kids learn multiplication through stories, using repetition with varied tempos, and explaining math tricks and clues over cleverly produced beats. The CD is accompanied with graphic learning aids
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 How round is your circle?  Bryant, John; and Sangwin, Chris
These photos and QuickTime movies accompany the book How Round Is Your Circle? Where Engineering and Mathematics Meet. See, in particular, the illustrations of how to drill a square hole. Sections include Falling apart (the Pythagorean Theorem, Dudeney's
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 How to Knit a Moebius Band (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
Directions for using two colors to knit a band that can be cut apart into a Moebius strip, expanded by Maria IanoFletcher from an original recipe by Miles Reid.
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 Hyperbolic Geometry (Graphics Archive, Special Topics)  The Geometry Center
A definition of hyperbolic geometry and illustrations of hyperbolic structures, with a link to Not Knot, a guided tour through computeranimated hyperbolic space.
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 hyperbolic surfaces  Gabriele E. Meyer
Photos of Meyer's fiber arts: Seifert surfaces, Poincaré disks, and other hyperbolic surfaces knit from yarn. For more of her fabric sculptures, visit http://www.math.wisc.edu/~meyer/airsculpt/hyperbolic1.html. Meyer, a lecturer in the Department
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 Hyperbolic Tessellations  David Joyce; Dept. of Mathematics & Computer Science, Clark University
The hyperbolic plane has more space in it then the Euclidean plane. There are only three regular tessellations of the Euclidean plane, namely {3,6} in which equilateral triangles meet six at each vertex, {4,4} in which squares meet four at each vertex,
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 Hyperbolic Tilings  Sascha Rogmann
A link to Rogmann's thesis (in German) and to pages on shells around the dodecahedron; 1+110+3458 cubes; hyperbolic buckyballs; hyperbolic animations; triangletessellations; quadrangletessellations; twoholed cloth torus; Subsets of PSL_2(Z[w]), D=3,
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 Hyperspace Structures: Exploring the Fourth Dimension  Burbanks, Beardmore
Mpeg Movies and pictures illustrate: 1. The Hypercube: a 4 dimensional analogue of the cube. Details of its construction, along with movies of a spinning hypercube. 2. An "Inflated Hypercube": approximating the hypersphere. 3. Hypertorus: Adding together
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 IFS (Iterated Function Systems) for 2D and 3D Visualization  Craig M. Wittenbrink
Using fractal interpolation to graphically represent two and threedimensional scalar data: download article in PDF or PostScript format, and view related images.
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 Illustrated 4D Computer Graphics  Kirby Urner, 4D Solutions
Curriculum Concepts from the Fuller School. Primitive topologies: nonEuclidean definitions of points, lines, planes as nonzero, parameterized entities, with light affecting properties in ray traced views; Concentric hierarchy: a reference frame relating
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 Images Created by Man & Chaos  Alan Beck
Some personal observations on fractal art and artists. "...the fractal artist does not create but explores, does not manufacture but discovers. Instead of being repelled by computers, such adventurers revel in them, as European mariners of old rejoiced
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 The Image Warper (METIP)  Steve Tanimoto; Mathematics Experiences Through Image Processing
A PC program for MSWindows that supports exploratory learning and enjoyable activities involving geometric transformations and image distortion. Simple transformations such as rotation, translation or scaling can be specified with single line segmentss.
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 Imaging the Imagined  Paul Flavin
Modeling with Math and a Keyboard: the art and science of modeling; the math, theory and practice of rendering, imaging, and animation. An introduction to raytracing and the Quadric surfaces; Platonic Solids and Polyhedra; 'Tensegrity' (tension) structures;
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 Impossible World  Vlad Alexeev
About impossible figures in art. These figures can be painted on paper but cannot be represented in space. There are many artworks by M.C. Escher, Jos de Mey, Sandro del Prete and many other artists. Also, you can view animations and read articles about
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 Information is Beautiful  David McCandless
Compelling graphic presentations on health supplements, plane accidents by final destination, government spending, time travel in popular film and TV, and many other "facts, data, ideas, subjects, issues, statistics, and questions"  all with the minimum
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 Instructional Resources  Microsoft Corporation
Microsoft's instructional resources are divided into lesson plans (math), howto articles, and tutorials. You may search each section's resources by age group, Microsoft product, theme or learning area. See also the Design Gallery Live.
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 Integer Jim's Math Squad  Jim Bennett
Creative ways to use art, writing, research, and Internet projects to make math more exciting for students. The Math Squad art projects are yearlong projects; rather than "lesson oriented," they create an "adventure theme" that facilitates math instruction.
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 Interactive Java Applets  Fergus Murray
Dragoric (The animated fractal toy); Toroidia (Adventures in toroidal geometry); Trochor (Fun with trochoids). See also Fergus Murray's Mathematical Graphics Page, and his mathematical animations.
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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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 International Snow Sculpture Championships: Team Minnesota  Department of Mathematics and Computer Science, Macalester College
Team Minnesota's Enneper surface entry earned second place in the Breckenridge International Snow Sculpture Championships of 2000. The site also includes photos of their planning, design, and implementation stages, the acceptance speech, and the team's
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 The Internet Mathematics Challenge  Julie Houston and David Trask
Explore the geometry of architecture, and share your observations with the students who built this site. With a Javaenabled browser, mouse over pictures of buildings to find the angles, arches, and other geometric figures appearing in Durham Cathedral,
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