Area and perimeter foliations on spaces of polygons
Differential Geometry
2019-02-13 v1
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.
Cite
@article{arxiv.1902.04455,
title = {Area and perimeter foliations on spaces of polygons},
author = {Aziz El Kacimi Alaoui and Abdellatif Zeggar},
journal= {arXiv preprint arXiv:1902.04455},
year = {2019}
}