Since you mentioned knitting (and I agree with your analogy), check out the great intuition you can get about hyperbolic geometry via crochet and knitting. See

Since you mentioned knitting (and I agree with your analogy), check out the great intuition you can get about hyperbolic geometry via crochet and knitting. See how "parallel" lines act and the angle sums of triangles end up smaller than 180 degrees: http://theiff.org/oexhibits/oe1e.html http://theiff.org/oexhibits/oe1e.html A TED lecture is linked: http://geknitics.com/2010/11/sunday-knitting-science-hyperbolic-geometry/ http://geknitics.com/2010/11/sunday-knitting-science-hyperbo... Hyperbolic baby pants also convertible into a 2-holed torus (not while on baby I guess), with added note that on 2-holed tori you can make maps that require 8 colors instead of just 4 like maps on the plane or sphere: http://www.ravelry.com/projects/smbelcas/hyperbolic-pants-2 http://www.ravelry.com/projects/smbelcas/hyperbolic-pants-2 Geometry, topology, map-coloring theorems, crafts: all things many kids never get to do anymore.