Geometry Show and Tell assignment
Choose a topic that interests you, broadly related to geometry or topology. Prepare:
One nice illustration of your topic that can be shown in class: a drawing, a 3-dimensional construction, or even a live demonstration. The illustration should be your own (e.g., it should not be copied/pasted from the Internet.)
A short presentation, at most 5 minutes, teaching the topic to your classmates. It should contain at least one completely rigorous mathematical definition or statement, and it should be a clear and interesting introduction to the main idea of your chosen topic. You are required to practice your presentation for a classmate beforehand. I will give you guidelines for this.
A short write-up accompanying your presentation. 1-2 pages ideally, and at most 3 pages. It should cite at least one math book or article (not just Wikipedia, for example).
Some possible topics, or pick your own in consultation with me:
The Platonic solids, sphere packings, Penrose tilings, Boy's surface, the Alexander horned sphere, finite geometries, how to turn your pants inside out with your feet tied up, the unit-distance chromatic number of the plane, the hairy ball theorem or "you can't comb a coconut," Brouwer fixed point theorem, Helly's theorem, amoebas, tropical geometry, billiards, dessins d'enfant, unfolding 3D polytopes without overlap, Teichmuller space and pants decompositions, Coxeter groups, Bricard's flexible octahedron, Ehrhart polynomials
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