I've included here pointers to downloadable software,
for interactive or animated geometry.
But I'm not generally including web applets or other code intended for
use while
browsing, because there's just so much of it and it's an integral
part of many of the pages I link to rather than drawing attention to
itself as software.
Cinderella
multiplatform Java system for compass-and-straightedge construction,
dynamic geometry demonstrations and
automatic theorem proving.
Ulli Kortenkamp and Jürgen Richter-Gebert, ETH Zurich.
GeoProof interactive
geometry software including automated theorem proving methods.
Great
math programs. Xah Lee reviews mathematical software, focusing on
educational Macintosh applications. Includes sections on geometric
visualization, fractals, cellular automata, and geometric puzzles.
Line
designs for the computer. Jill Britton brings to the web material
from John Millington's 1989 book on geometric patterns formed by
stitching yarn through cardboard. The Java simulation of a Spectrum
computer running Basic programs is a little (ok a lot) clunky, and froze
Mozilla when I tried it, but there's also plenty of interesting static content.
Non-Euclidean
geometry with LOGO. A project at Cardiff, Wales, for using the LOGO
programming language to help mathematics students visualise
non-Euclidean geometry.
Oops
image warper, based on three simple geometric transformations.
Packing
results, D. Boll. C code for finding dense packings of circles in
circles, circles in squares, and spheres in spheres.
Peek, software for visualizing high-dimensional polytopes.
Perron
Number Tiling Systems.
Mathematica software for computing fractals that tile the plane from
Perron numbers.
Points on
a sphere. Paul Bourke describes a simple random-start hill-climbing
heuristic for spreading points evenly on a sphere, with pretty pictures
and C source.
Poly, Windows/Mac shareware
for exploring various classes of polyhedra including Platonic solids,
Archimedean solids, Johnson solids, etc. Includes perspective views,
Shlegel diagrams, and unfolded nets.
Polygon Puzzle
open source polyomino and polyform placement solitaire game.
Polytopia
CD-ROMs on tessellations, polyhedra, honycombs, and polytopes.
Postscript
geometry.
Bill Casselman uses postscript to motivate a course
in Euclidean geometry.
See also his Coxeter group graph paper,
and Ed Rosten's
postscript doodles.
Beware, however, that postscript can not really represent
such basic geometric primitives as circles, instead approximating them
by splines.
Realizing a
Delaunay triangulation. Many authors have written Java code for computing
Delaunay triangulations of points. But Tim Lambert's applet does the
reverse: give it a triangulation, and it finds points for which that
triangulation is Delaunay.
Rectangular cartograms: the game.
Change the shape of rectangles (without changing their area) and group
them into larger rectangular and L-shaped units to fit them into a
given frame. Bettina Speckmann, TUE. Requires a browser with support for
Java SE 6.
Vittoria Rezzonico's
Java applets. Hypercube and polyhedron visualization, and circle
inversion patterns. Requires both Java and JavaScript.
SpaceBric building blocks
and Windows software based on a tiling of 3d space by congruent
tetrahedra.
Sphere packing and kissing numbers.
How should one arrange circles or spheres
so that they fill space as densely as possible?
What is the maximum number of spheres that can simultanously touch
another sphere?
Spiral
generator, web form for creating bitmap images of colored
logarithmic spirals.
sqfig and sqtile,
software by Eric Laroche for generating polyominoes and polyomino
tilings.
Stella and Stella4d,
Windows software for visualizing regular and semi-regular polyhedra and
their stellations in three and four dimensions, morphing them into each other, drawing unfolded nets for
making paper models, and exporting polyhedra to various 3d design packages.
Wilson
Stothers' Cabri pages.
Geometric animations teaching projective conics,
hyperbolic geometry, and the Klein view of geometry as symmetry.
SymmeToy,
windows shareware for creating paint patterns, symmetry roses,
tessellated art and symmetrically decorated 3D polyhedron models.
Taprats
Java software for generating symmetric Islamic-style star patterns.
3d-XplorMath
Macintosh software for visualizing curves, surfaces, polyhedra,
conformal maps, and other planar and three-dimensional mathematical objects.
TileDreams
Windows software for creating symmetric patterns with rhombi.
vZome
zometool design software for OS X and Windows.
(Warning, web site may be down on off-hours.)
Wallpaper
patterns, R. Morris.
Kaleidoscope-like Java applet for making and transforming symmetric
tilings out of uploaded photos.
Wingeom,
freeware Windows geometric construction software.
WWW spirograph.
Fill in a form to specify radii,
and generate pictures by rolling one circle around another.
For more pictures of cycloids, nephroids, trochoids,
and related spirograph shapes, see David Joyce's
Little Gallery of Roulettes.
Anu Garg
has implemented spirographs in Java.
yukiToy. Shockwave plugin software for pushing around a few reddish spheres in
your browser window. But what exactly is the point?
(They're spheres, they don't have one, I guess.)