I’ve been reading Clifford Pickover’s excellent and entertaining The Math Book. Its topics are arranged chronologically, with each entry just one page long and paired with a beautiful illustration. It’s the perfect book to keep by your easy chair, where you can pick it up and have a quick read.
One of the entries is about Archimedes’ Stomachion, which is pictured below. If you print it and cut out the pieces, there are 17,152 different ways you can arrange them into a square!
I constructed the one below using GeoGebra, but for a geometry class that is learning the classic straightedge and compass constructions, it would be a nice exercise to draw one using those tools. The only constructions necessary are midpoint of a segment and parallel line through a point.
Get out your scissors and have fun!