- Cabri Geometry: Classroom Resources - The Math Forum
The Math Forum's page of links at the Forum and on the Web to dynamic interactive geometry classroom resources for Cabri Geometry. Books and Web sites; Frequently Asked Questions; exploring the basics; workshops; excerpts from the journal abraCAdaBRI;
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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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- 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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- Dave's Geometric Pix Gallery - David Joyce; Dept. of Mathematics & Computer Science, Clark University
Mandelbrot and Julia sets, with a generation form and an Explorer on which you can point and click to get more refined images;
Newton Basins and a form to generate them; a page describing tiling the hyperbolic plane; some wallpaper groups; a gallery
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- Distance Recipe (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
A technical definition of how to compute distance. Examples of distances; The Unit Disc Model; Passing from one model to another...
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- Don Hatch's Home Page - Don Hatch
Hyperbolic tessellations shown in various stages of truncation, and represented by their Schlafli symbols. Java applets explore hyperbolic tessellations, a magic Rubik's-like cube in four dimensions, polygon reciprocation (dual), modern portfolio theory
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- Escher and the Droste effect - B. de Smit and H. W. Lenstra Jr., Mathematisch Instituut, Universiteit Leiden, the Netherlands
Applying mathematics to Escher's Print Gallery. A mathematical analysis of Escher's "The Print Shop," including an image of the original print. See the article (PDF format) Artful Mathematics: The Heritage of M.C. Escher in the Notices of the AMS, bringing
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- Fixed Point Theory on the Web - M. A. Khamsi
Fixed Point Theory and Applications sites; Mailing List; Conferences: previous and forthcoming; books on fixed point theory; other interesting sites on the Web; bibliography database; abstracts; papers on fixed point theory; general information.
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- Gallery of Pseudospheres - Robert McLachlan
A short version of an article by Robert McLachlan, "A gallery of constant-negative-curvature surfaces," (Mathematical Intelligencer, Fall 1994, 31-37) about "pseudospherical" surfaces, equally "saddle-shaped" at each point, extensively studied in the
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- Geometry - Elmer G. Wiens; Egwald Web Services Ltd.
A collection of interactive geometric objects represented graphically including 3D-graphics, space curves, trigonometric functions, hyperbolic functions, and
the trajectory of projectiles.
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- Hyperbolic Geometry (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
A closed polyhedron cannot be made by snapping together seven equilateral triangles so that there are seven at every vertex, but if you persist and continue to snap together seven triangles at each vertex, you will actually construct an approximate model
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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 computer-animated hyperbolic space.
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- Hyperbolic Geometry Using Cabri - Tim Lister
A site that provides documentation for drawing in the hyperbolic plane (non-euclidean geometry) using Cabri. As examples, it explains several concepts of hyperbolic geometry providing visualizations in the form of figures, animated gifs, and downloadable
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- The Hyperbolic Surface Activity Page - Dr. Tom Holroyd
This page contains a postscript file and directions for constructing
a hyperbolic plane tesselation using paper, scissors, and tape. It
demonstrates why hexagons tile flat space, but heptagons require
curved space (and helps to introduce non-Euclidean
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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; triangle-tessellations; quadrangle-tessellations; two-holed cloth torus; Subsets of PSL_2(Z[w]), D=-3,
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- The Institute for Figuring - Margaret and Christine Wertheim, Co-Directors
"If mathematics is a language of pattern, its structures may be seen as the verses of a formal, yet fantastical poetics. Across the globe people have delighted in the harmonies of this language and the patterns discovered therein. These are the songs
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- Is Space Finite? - Luminet, Starkman, Weeks, Scientific American
Conventional wisdom says the universe is infinite. But it could be finite, merely giving the illusion of infinity. Upcoming measurements may finally answer this ancient question. Subtopics include: Comfort in the Finite; Eightfold; Cosmic Crystals; and
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- JAVA Gallery of Interactive On-Line Geometry - The Geometry Center
Applets illustrating geometry concepts. WebEQ, Hyperbolic Triangles, Lorenz Simulation, One-Dimensional Iteration, Tetris, Leap Fractal, Fractals from Iterated Function Systems, Kali: Wallpaper Patterns. Created by The Geometry Center.
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- Mark McClure
Mark McClure is an assistant professor at the University of North Carolina at Asheville researching real analysis, specifically fractal measure and dimension. Papers on these topics may be downloaded in gzipped PostScript format; a paper involving Julia
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- Mathbun - Chaim Goodman-Strauss
Mathematical graphics, featuring many fractals and tessellations. The category of mathematical objects includes photographs of jigsaw puzzles and outdoor sculpture; "math fun," of Zome and tilings.
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- Math WWW VL: Software - Dept. of Mathematics, Florida State University
Links to software sites for college-level mathematics.
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- Models of the Hyperbolic Plane - The Geometry Center
Descriptions of three hyperbolic plane models: the Klein model, the upper half plane model, and the Poincare model.
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- Navworld - Joseph Portney
A center for the art and science of navigation, providing navigational "cerebrations," famous historical accounts, interviews and biographies. See Earthshapes, different ideas of what the earth would look like if it were one of 12 different shapes (physical
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- On the Bass Note of a Schottky Group [PDF] - Peter G. Doyle
Using a classical method from physics called Rayleigh's cutting method, Doyle proves the conjecture of Phillips and Sarnak that there is a universal lower bound L2 > 0 for the lowest eigenvalue of the quotient manifold of a classical Schottky group,
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- Poincaré Notes - Dave Wilson
"A massively disorganised collection of macros and figures for the Poincaré Disk model of hyperbolic geometry." A page describing some Cabri macros relating to hyperbolic Geometry in the Poincare disc model.
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- SIAM Activity Group on Orthogonal Polynomials and Special Functions - Martin Muldoon
A group for promoting basic research in orthogonal polynomials and special functions; furthering the application of this subject in other parts of mathematics and in science and industry; and encouraging and supporting the exchange of information, ideas,
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- Topics in Geometry - Don Shimamoto, Swarthmore College
Six sketches related to hyperbolic geometry. One illustrates that hyperbolic reflection in the Poincare disk corresponds to Euclidean inversion. Two sketches illustrate transformations that may or may not be hyperbolic rotation and translation. One sketch
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- Vi Hart - Vi Hart
Blog, videos of math "doodling," instructions for slicing food mathematically, and more from the self-described recreational mathemusician who considers math a hobby, with "special interests in symmetry, polyhedra, and surreal complexity. This usually
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- Wilson Stothers' Geometry Pages - Wilson Stothers, University of Glasgow
A guide to the various geometry topics on Stothers' pages, including Euclidean, affine, projective, inversive, and hyperbolic geometries, and the Klein View of geometry. These pages began as an experiment in teaching projective conics using Cabri to provide
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- Z's Roguelike Stuff - Zeno Rogue
Mathematical games and projects include HyperRogue, a treasure-collecting, goblin-killing adventure set in non-Euclidean space -- specifically, a hyperbolic plane of negative curvature filled with elixirs and slime beasts; and Hydra Slayer, which begins
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