The instructions for crocheting a hyperbolic plane are surprisingly easy given the complex surface which is the result. Just perform increases at regular intervals, and soon your crochet will start to resemble a coral or flower, showing the wiggly shape characteristic of hyperbolic geometry.
Knit a hyperbolic mushroom
The instructions for knitting a hyperbolic mushroom are the same as those for crocheting a coral: perform increases at regular intervals. These little mushrooms knit up quickly and show that the strange shape of fungi is just a result of a simple mathematical rule.
The instructions for this modular origami dodecahedron involve assembling 30 units of origami, and can be made using a set of sticky notes. For an extra challenge, try creating this model using only three colours, so that the three different colours meet at each corner. It's harder than it looks!
(These activities were designed by Perth embroidery expert Ann-Marie Anderson-Mayes at Beautiful Stitches.)
A related craft idea is to create curved patterns from straight lines, in a technique called string art.
Make a Möbius strip
Möbius strips are weird and wonderful mathematical shapes which can be created using paper, crochet or knitting. Marvel at their strange one-sided nature, try to cut them in half, and experiment with what happens with different numbers of twists. Whatever you do, the Möbius strip will surprise you at every turn.