
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 3dimensional 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 writeup accompanying your presentation. 12 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 unitdistance 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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