Hyperbolic model

 Thurston's paper model

 Row 1 with 20 chains looks like a line.

 R.2: Crochet a single stitch on every chain but make 2 sts on every 4th stitch.  It's called the rate of 5/4.  So R.2 has 25 sts now.

 Continue with this rate and we have a part of a hyperbolic plane as shown.  Note that I don't crochet all the way to the end of each row.

 Parallel line Post. in hyperbolic plane:  For any line and any point not on that line, there are at least two lines on that point that are parallel to the given line.

 When folding top to bottom and left to right the hyperbolic plane (on the top-right), a double cylinder  is formed.

 Crochet around a chain stitch with the rate 4/3, we get a pseudosphere.

 This model starts with a line of 20 chains and crochets with the rate 11/10 all the way to the end of each row.