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Projective evolutes of pentagons


Speaker: Sergei Tabachnikov, Penn State
Location: 2112 MSB
Start time: Thu, Jan 5 2023, 1:10PM

The evolute of a curve is the envelope of its normals. We consider a projectively natural discrete analog of this construction by defining projective perpendicular bisectors of the sides of a polygon in the projective plane, and we study the map that sends a polygon to the new polygon formed by the projective perpendicular bisectors of its sides. This map acts on the moduli space of projective polygons, and we analyze the case of pentagons; the moduli space is 2-dimensional in this case. The second iteration of the map has one integral whose level curves are cubic curves, and the transformation on these level curves has a positive entropy.