‘You have heard of Fortunatus's Purse, Miladi? Ah, so! Would you be surprised to hear that, with three of these leetle handkerchiefs, you shall make the Purse of Fortunatus, quite soon, quite easily?’
In the mathematical wonderland of topology, we can hold the entire world in a bottle or in a purse. We will assemble this purse, dissect it, rearrange it, and see what it has to tell us about how our world fits together.
Fortunatus’s Purse and the Wealth of the World
Fortunatus’s Purse: a many-colored story
Starting with the instructions from a Lewis Carroll novel for making a twisted purse that contains the entire world, this talk takes a scenic tour through the realm of topology. The highlights include non-orientable surfaces, projective geometry, and map-coloring theorems, illustrated with models made of fabric, paper, ceramics, and beads.
The original version of this talk was a 15-minute presentation in the Special Session on Mathematics and Mathematics Education in the Fiber Arts at the Joint Mathematics Meetings in 2005. That lead to my chapter of the same name in Making Mathematics with Needlework: Ten Papers and Ten Projects, and to the expanded talk, which is one of my absolute favorites to give.Level
The talk uses some topological gluing diagrams and a little geometry in three-space, all of which are carefully explained during the talk, but this might be a stretch for an early high school audience. An undergraduate audience should follow all of the material and will find lots of fascinating new ideas.Mechanics