Xah Lee
This page lists some of the most excellent geometry software i've used, that does non-Euclidean geometry or higher-dimensional geometry, with visual emphasis.
stereop by John M Sullivan. This applet does stereographic projection of regular polyhedrons. User can choose any of cube, tetrahedron, octahedron, dodecahedron, icosahedron, and they are centrally projected onto a sphere. This sphere, is then stereo-graphically projected onto a plane. User can rotate the polyhedron, and see its image on the plane change accordingly. http://torus.math.uiuc.edu/jms/java/stereop/ Java (2006-08,)
MoebApplet. This Java applet does dynamic Mobius transformation. If you are studying Mobius Transformation, this is the best applet for it. You can drag the fixed points, the poles, and a few other critical points in the plane and see the image change as you move. Author is Paul Murray. http://www.users.bigpond.com/pmurray/Java/MoebApplet.html Java (2006-08)
Curved Space Jeff Weeks wrote a wondrous program that lets you fly thru various “warped” geometric spaces (3-manifolds). Source code and tutorial are included for programers. http://www.geometrygames.org/CurvedSpaces/index.html OSX Win
See also: some notes on manifolds.
KriviznaPlus and KriDva are “interactive screensavers”. That means, it runs like a screensaver but one can control it with the mouse. (press esc exits the program) According to the author Viktor Massalogin, KriviznaPlus draws the stereographic projection. And KriDva draws the stereographic projection of 4D sphere (x^2+y^2+z^2+z^2==r^2) to the 3D space. These programs are extremely fun and beautiful. I hope the author adds more explanations on the math. As of 2004, he added another version CPace. http://www.hot.ee/bntren/Program.html Win. (2003-10,2006-08)
NonEuclid by Joel Castellanos. It is a free software for drawing hyperbolic geometry. Its function is similar to Geometer's Sketchpad except it is not dynamic. Elements cannot be dragged around once drawn. The program comes with a wonderful tutorial on hyperbolic geometry. Available versions are: Macs 68k, Windows, and Java. Home page: http://cs.unm.edu/~joel/NonEuclid/. Java (2003-09,2006-08)
Hyperbolic Tesselations Applet is a Java applet that draws hyperbolic tilings. Superb! By Don Hatch. http://www.plunk.org/~hatch/HyperbolicApplet/ Java (2002,2006-08)
Space Jewels is a Java game, where you drive a spaceship in hyperbolic space to collect jewels. Author is Matthew Cook. http://www.paradise.caltech.edu/~cook/Workshop/Java/SpaceJewels/main.html. He has a write up here. Java (2002-07,2006-08)
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