Chapter 1 
Flatland 
Edwin Abbott’s Flatland: A Romance of Many Dimensions weaves Victorian social satire with a gentle introduction to worlds of 2, 3, and 4 dimensions. This beautifully written book still costs less than $2. 
Chapter 2 
Gluing 
Play eight familiar games on a torus. The games let you scroll the board freely, to see that the torus is finite yet has no boundary.  
Threedimensional torus games should become available in a few years (once other projects are done).  
The video The Shape of Space takes you on a computeranimated tour of the 3torus and other spaces. 
Chapter 3 
Vocabulary 
Chapter 4 
Orientability 
The eight familiar games may be played on a Klein bottle as well as a torus. Just choose Klein bottle from the games’ topology menu.  
When 3D torus games become available, there’ll be an option for nonorientable spaces as well.  
The video The Shape of Space constructs the Klein space and takes you on a computeranimated flight. 
Chapter 5 
Connected Sums 
Chapter 6 
Products 
Product Spaces software lets you fly about a forest in S² × E. 
Chapter 7 
Flat Manifolds 
The Curved Spaces software includes flat spaces as well, in spite of its name. It has no games, but the graphics are good. Includes all ten flat 3manifolds, as well as several geometrically different versions of the 3torus, some of which are quite beautiful and surprising. You can see the manifolds in stereoscopic 3D if you have redblue glasses. 
Chapter 8 
Orientability vs. TwoSidedness 
Chapter 9 
The Sphere 
Chapter 10 
The Hyperbolic Plane 
Chapter 11 
Geometries on Surfaces 
The Surface Explorer lets you create your own worlds, including mountains, lakes, houses, castles, fields, fences, etc., and walk about in them. The terrain topology can be any closed surface. (Thus the 3dimensional space is a surface cross a line.) 
Chapter 12 
The GaussBonnet Formula and the Euler Number 
The Surface Explorer includes a set of activites introducing the Euler number and the GaussBonnet formula. 
Chapter 13 
FourDimensional Space 
Chapter 14 
The Hypersphere 
Download the Curved Spaces software and open the sample file PoincaréDodecahedralSpace.gen. Press the leftarrow key a few times to open the walls, and you’ll see a tiling of the hypersphere by 120 dodecahedra. 
Chapter 15 
Hyperbolic Space 
Download the Curved Spaces software and open the sample file HyperbolicSmall.gen. You’ll see a tiling of the hyperbolic space by infinitely many copies of a small polyhedron. If you have a pair of redblue glasses, turn off Fog, turn on Stereo, and start flying around. Even though hyperbolic space is much roomier than flat space, your stereoscopic vision creates the illusion that all of hyperbolic space sits inside a ball. 
Chapter 16 
Geometries on ThreeManifolds I 
The Curved Spaces
software includes this chapter’s manifolds:

Chapter 17 
Bundles 
Chapter 18 
Geometries on ThreeManifolds II 
The Surface Explorer (see Chapter 11) lets you walk in any close surface cross a line, but you’re stuck on the surface and can’t fly.  
Product Spaces software lets you fly freely about a forest in S² × E, E² × E, and H² × E. 
Chapter 19 
The Universe 
Chapter 20 
The History of Space 
Chapter 21 
Cosmic Crystallography 
Chapter 22 
Circles in the Sky 
The latest information on the MAP satellite and efforts to detect the topology of space is available on the Cosmology News page. 
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