Geometry on the Web

There are many excellent (and many not so excellent) web sites on geometric topics such as polyhedra, tilings and symmetry; many of these sites contain outstanding graphics, and extensive lists of links. Here are a few nice sites that I have come across, though searching the web will most likely lead you to many other worthwhile sites.

Geometry in General

• Geometry Junkyard http://www.ics.uci.edu/~eppstein/junkyard/

A very nice site covering all sorts of geometric topics, with many excellent links. A very good place to start searching for specific topics.

• Geometry in Action http://www.ics.uci.edu/~eppstein/geom.html

By the same person who does "Geometry Junkyard," this set of links focuses on real world applications of geometry.

• Geometry Center http://www.scienceu.com/geometry/

The Geometry Center is a mathematical research institute that, in addition to promoting research, wants to reach out to a broader public.

Symmetry

• Symmetry and the Shape of Space http://comp.uark.edu/~strauss/symmetry.unit/old.html
• Dror Bar-Natan's Symmetry Page http://www.math.toronto.edu/~drorbn/Gallery/Symmetry/index.html
• Examples of Symmetry Groups http://fac-web.spsu.edu/math/tile/symm/types/index.htm
• Historical Examples of Symmetry Groups http://fac-web.spsu.edu/math/tile/grammar/index.htm

Alhambra

• Alhambra http://www.alhambradegranada.org/en/
• More Alhambra http://home.earthlink.net/~mayathelma/sitebuildercontent/sitebuilderfiles/alhambra.tlc.2004.pdf
• Yet More Alhambra http://www2.dm.unito.it/paginepersonali/ferrarese/ECoGeA/tassellazioni/Alhambra.pdf

Tessellations

• Tessellations.org http://www.tessellations.org

Polyhedra

• Virtual Reality Polyhedra http://www.georgehart.com/virtual-polyhedra/vp.html

This site has a very thorough discussion of various types of polyhedra, as well as outstanding graphics. To view the graphics you need special software, which can be downloaded for free, as explained at this site.

• Symmetry, Crystals and Polyhedra http://www.uwgb.edu/dutchs/symmetry/symmetry.htm

This site has some very good pictures of various categories of polyhedra.

• MathWorld by Eric W. Weisstein -- Polyhedra http://mathworld.wolfram.com/Polyhedron.html

Extensive discussion of polyhedra.

Higher Dimensions

• Flatland http://www.math.brown.edu/~banchoff/gc/Flatland/
• Flatland http://www.ibiblio.org/eldritch/eaa/FL.HTM

Both of these sites have the complete text (with original illustrations) of "Flatland," the classic tale of a creature from a two-dimensional world who encounters higher dimensions.

• Writings of Charles Hinton http://www.ibiblio.org/eldritch/chh/hinton.html

Hinton wrote various works related to higher dimensions, as well as stories about a two-dimensional world that is rather different from that found in "Flatland."

• Stereoscopic Animated Hypercube http://dogfeathers.com/java/hypercube2.html
• HyperSpace Polytope Slicer http://dogfeathers.com/java/hyperslice.html
• Peek http://www.graphics.cornell.edu/~gordon/peek/peek.html

These websites show projections and slices of four-dimensional cubes (and other objects).

M. C. Escher

• Official Escher Website http://www.mcescher.com/gallery/
• Escher http://www.mathacademy.com/pr/minitext/escher/
• Math and the Art of M. C. Escher http://euler.slu.edu/escher/index.php/Math_and_the_Art_of_M._C._Escher

Escher was neither a great artist nor a mathematician, but he was a rare person whose work so remarkably straddled art and mathematics.