Curved Spaces

Curved Spaces is a flight simulator for multi-connected universes. Because light itself wraps around such a space, inhabitants see their universe’s contents repeating in a crystalline pattern, like a hall of mirrors but with no reflection.

Curved Spaces is intended for undergraduates and graduate students studying 3‑manifolds, and has also found use as a research tool in topology and cosmology. Recreational math enthusiasts may instead prefer Torus Games, which offers 3D Mazes and 3D Tic-Tac-Toe in a variety of multi-connected 3D spaces, along with games on multi-connected 2D surfaces.

Download

Curved Spaces for iOS 14 or later (12 MB)

Curved Spaces for macOS 11 or later (8.7 MB)

Curved Spaces for Windows XP or later (1.9 MB)

Older versions

Source code (4.1 MB)

Last update

25 May 2022 (Version 4.2.2)

Added Turkish translation, thanks to Süleyman Saltuk Güngör.

Minor aesthetic changes for iOS 15.

Languages

English, Spanish, French, Italian, Japanese, Portuguese, Turkish, Chinese (simplified), Chinese (traditional)

License

Freeware (GNU General Public License)

Questions?
Contact Jeff Weeks.

With deepest thanks to the translators for their thorough, careful and most professional translation of Curved Spaces:
Alberto Pino Blanco y Cristian Armendariz-Picon, Roland Lehoucq, Daniela, Isabella Eva e Davide Bigatti, 竹内建 (Tatsu Takeuchi) and 澤田智宏 (Tom Sawada), Nuno Fernandes, Süleyman Saltuk Güngör, 邹燕清 (Yanqing Zou).

View this page in:
English Español Français Italiano 日本語 Português Türkçe 简体中文繁體中文

This material is based upon work supported by the National Science Foundation under Grant No. 1503701. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

[Return to Geometry Games home.]