PROJECTIVE GEOMETRY OF POLYGONS AND DISCRETE 4-VERTEX AND 6-VERTEX THEOREMS
Valentin Ovsienko, Serge Tabachnikov · Max Planck Institute for Plasma Physics · 2001
The paper concerns discrete versions of the three well-known results of projective differential geometry: the four vertex theorem, the six affine vertex theorem and the Ghys theorem on four zeroes of the Schwarzian derivative. We study geometry of closed polygonal lines in RP and prove that polygons satisfying a certain convexity condition have at least d + 1 flattenings. This result provides a new approach to the above mentioned classical theorems. ‡CNRS, Centre de Physique Theorique, Luminy Case 907, F–13288 Marseille, Cedex 9, FRANCE; mailto:[email protected] §Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA; mailto:[email protected]