Area and perimeter foliations on spaces of polygons

2019/02/12 by Alaoui, Aziz El Kacimi, Zeggar, Abdellatif
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.04455

Abstract

We describe all families of star-shaped n-polygons in the Euclidean plane with prescribed perimeter and area ; they are leaves of a foliation F on the space of star-shaped n-polygons. By the way, we study some geometric properties of convex polygons, for instance their inscriptibility in a circle and their regularity in relation with the perimeter and the area.

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