Software and Animations
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
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.
mathematical art, Xah Lee.
multiplatform Java system for compass-and-straightedge construction,
dynamic geometry demonstrations and
automatic theorem proving.
Ulli Kortenkamp and Jürgen Richter-Gebert, ETH Zurich.
packing and discrete complex analysis. Research by
Ken Stephenson including pictures, a bibliography, and downloadable circle packing
- Cognitive Engineering
Lab, Java applets for exploring tilings, symmetry, polyhedra, and
screen-saver module makes patterns with various Kaleidoscopic symmetries.
software for visualization of Voronoi diagrams, Delaunay triangulations,
minimum spanning trees, and matchings, U. Köln.
- Gavrog, a Java package for
visualizing 2d and 3d ornamental patterns with high degrees of symmetry.
Java-based software for constructing and measuring polyhedra
by transforming and slicing predefined starting blocks.
Java applets by Fergus C. Murray
produce screensaver-like interactive images.
See also his
mathematical animations and
turned on -- making geometry dynamic. A book on the use of
interactive software in teaching.
- GeoProof interactive
geometry software including automated theorem proving methods.
math programs. Xah Lee reviews mathematical software, focusing on
educational Macintosh applications. Includes sections on geometric
visualization, fractals, cellular automata, and geometric puzzles.
software for modeling and visualizing convex polyhedra and plane
now seems to be incorporated as a module in a larger
Matlab library for multi-parametric analysis.
- Hyperbolic Geometry using Cabri
- Hyperdimensional Java.
Several web applets illustrating high-dimensional concepts, by
- HyperGami program for unfolding polyhedra, also described in
article from the American Scientist.
- Information on
Pentomino Puzzles and Information on Polyominoes, from
F. Ruskey's Combinatorial Object Server.
- Interactive Delaunay triangulation and Voronoi diagrams:
VoroGlide, Icking, Klein, Köllner, Ma, Hagen.
D. Watson, CSIRO, Australia.
Baker et al., Brown U.
Paul Chew, Cornell U.
applets on mathematics, Walter Fendt.
- Java gallery of geometric algorithms, Z. Zhao, Ohio State U.
- Java quadric surface raytracer, P. Flavin.
open-source software for visualizing Cayley graphs of Coxeter groups
as symmetric 4-dimensional polytopes.
software for visualizing tilings of the sphere, Euclidean plane, and
software for making symmetrical drawings based on any of the 17 plane
demo. Java applet by Jacob Marner.
sacred geometry software.
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.
- Logical art and the
art of logic, pentomino art, philosophy, and DOS software,
Math with Java. Interactive applets to help students grasp the
meaning of mathematical ideas.
volume and surface area calculator for the Palm.
on Archimedean polyhedra, Robert Webb.
hyperbolic tilings and software for creating them, J. Mount.
- Non-Euclidean games implemented in Shockwave by students in an
advanced high school geometry class:
double-torus minesweeper, and
geometry with LOGO. A project at Cardiff, Wales, for using the LOGO
programming language to help mathematics students visualise
image warper, based on three simple geometric transformations.
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.
Number Tiling Systems.
Mathematica software for computing fractals that tile the plane from
- 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.
applet, Wil Laan.
7.0 Macintosh shareware.
CD-ROMs on tessellations, polyhedra, honycombs, and polytopes.
Bill Casselman uses postscript to motivate a course
in Euclidean geometry.
See also his Coxeter group graph paper,
and Ed Rosten's
Beware, however, that postscript can not really represent
such basic geometric primitives as circles, instead approximating them
- Prolog soma-cube puzzle program
interactive shockwave museum exhibits for exploring geometric concepts
such as symmetry, tiling, and wallpaper groups.
- Quicktime VR and mathematical visualization.
- 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.
- Reconstruction of a closed curve from its elliptic Fourier descriptor.
The ancient epicycle theory of planetary motion, animated in Java.
- 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
- Sensitivity analysis for traveling salesmen,
C. Jones, U. Washington.
Still a good title, and now the geometry has been made more
entertaining with Java and VRML.
software for calculating singular algebraic curves and surfaces, R. Morris.
- SnapPea, powerful software for computing geometric properties of
knot complements and other 3-manifolds.
- Soma cube
- SpaceBric building blocks
and Windows software based on a tiling of 3d space by congruent
- 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
generator, web form for creating bitmap images of colored
- sqfig and sqtile,
software by Eric Laroche for generating polyominoes and polyomino
- 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.
of the dodecahedron stereoscopically animated in Java by Mark Newbold.
Stothers' Cabri pages.
Geometric animations teaching projective conics,
hyperbolic geometry, and the Klein view of geometry as symmetry.
windows shareware for creating paint patterns, symmetry roses,
tessellated art and symmetrically decorated 3D polyhedron models.
Java software for generating symmetric Islamic-style star patterns.
Macintosh software for visualizing curves, surfaces, polyhedra,
conformal maps, and other planar and three-dimensional mathematical objects.
Windows software for creating symmetric patterns with rhombi.
- The tiling puzzle games of
OOG. Windows and Java software for tangrams, polyominoes, and polyhexes.
- Touch-3d, commercial
software for unfolding 3d models into flat printouts, to be folded back
up again for quick prototyping and mock-ups.
- Ukrainian Easter Egg.
This zonohedron, computed by a Mathematica notebook I wrote, provides a lower bound for the complexity of the set of
centroids of points with approximate weights.
- UMass Gang
library of knots, surfaces, surface deformation movies, and
minimal surface meshing software.
polyhedra in POV-ray format, by Russell Towle.
- Virtual Image,
makers of CD-ROMS of ray-traced mathematical animation.
- Visualizations of 4d hypercube (Java applet).
zometool design software for OS X and Windows.
(Warning, web site may be down on off-hours.)
patterns, R. Morris.
Kaleidoscope-like Java applet for making and transforming symmetric
tilings out of uploaded photos.
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.
has implemented spirographs in Java.
- Yantram sacred art toolbox.
Software for creating various kinds of symmetric fractal mandala.
- 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.)
From the Geometry Junkyard,
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
from a common source file.