ABSTRACT
What does this story about Bill’s sculpture tell us? You can create new shapes without really knowing the mathematics behind them. If you do not have a strong mathematical background but you have been doing crochet, you have perhaps already recognized that making the hyperbolic plane is in some ways reproducing a common beginner’s mistake in crocheting a hat: if you add too many stitches, instead of being nice and round (by now you know that this would demonstrate positive curvature ), the hat develops ruffl es (which have negative curvature ). You probably have already crocheted surfaces with negative curvature ; you just did not know that mathematicians have this name for them! Once you have made your own hyperbolic plane model, I am sure you will want to fi nd out what else you can learn from it.
