2017/07/28 by Serge Tabachnikov, Tabachnikov, Serge · 1 citation
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #math.MG
paper · pdf · doi:10.48550/arxiv.1707.09267
arxiv created 2017/07/28 · arxiv updated 2017/07/31
Given a planar pentagon, construct two new pentagons: the vertices of the first one are the intersection points of the diagonals of the original pentagon, and the vertices of the second one are the tangency points of the conic inscribed in the original pentagon. E. Kasner theorem, published in 1928, asserts that these two operations on pentagons commute. We extend Kasner's result to Poncelet polygons, that is, the polygons inscribed into a conic and circumscribed about a conic.