Starting from just a sheet of paper, by folding, stacking, crumpling, tearing, we will explore a rich variety of phenomena, from magic tricks and geometry to elasticity and the traditional Japanese art of origami. Much of the lecture consists of actual table-top demos, which you can try later with friends and family.
Pentagramma Mirificum (the miraculous pentagram) is a beautiful geometric construction studied by Napier and Gauss. Its algebraic description yields the simplest instance of cluster transformations, a remarkable family of recurrences which arise in diverse mathematical contexts, from representation theory and enumerative combinatorics to theoretical physics and classical geometry (Euclidean, spherical, or hyperbolic).
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