Jeff Weeks’

Topology and Geometry Software

Traditional apps visionOS apps

Curved-Space Pool Hall

Shoot some pool in curved space.

visionOS

Crystal Explorer

Immerse yourself in crystals to understand and enjoy their structure.

visionOS

Torus Chess

Play chess on a wraparound board.

visionOS

3-Torus Maze

Solve 3D mazes in a wraparound space.

visionOS

Torus Games

Eight familiar games introduce children age 10 and up to the concept of a finite yet unbounded universe.

iOS, macOS, Windows

KaleidoPaint

Create colorful symmetrical paintings based on the 17 tiling patterns.

iOS

KaleidoTile

Explore polyhedra and tessellations while creating colorful works of art.

iOS, macOS, Windows

Curved Spaces

Fly in a multiconnected universe (for math and physics students).

iOS, macOS, Windows

4D Maze

Have fun solving 4D mazes (for everyone).

iOS, macOS, Windows

4D Draw

Draw simple 4D figures (for geometry students).

iOS, macOS

Crystal Flight

Fly freely in crystals (for everyone).

iOS, macOS

Other Resources

The Shape of Space 3rd edition

A gentle introduction to topology and geometry, with full-color figures throughout.

Arabic translation: شكل الفضاء

How to Sew a Hyperbolic Blanket

Step-by-step instructions for sewing a hyperbolic surface from fleece.

Source code for visionOS apps

Hyperbolic Games

Kali

SnapPea

Non-Euclidean billiards in VR

Body coherence in curved-space virtual reality games

Recent Updates

2024-8-21	3-Torus Maze	New application
2024-8-7	Curved-Space Pool Hall	Immersive space appears only when you tap Play button
2024-7-28	Curved-Space Pool Hall	Shows where your hands are in the curved space Uses half-length cue stick to keep hands visible Allows higher table for greater comfort No longer shows empty table when control panel is up
2024-7-27	Crystal Explorer	Double tap (instead of single tap) to close a crystal, to avoid closing accidentally

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