2019•arXiv (Cornell University)Open access

Area and perimeter foliations on spaces of polygons

Aziz El Kacimi Alaoui, Abdellatif Zeggar

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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Key concepts: Perimeter, Geometry, Polygon (computer graphics), Regular polygon, Mathematics, Computer graphics (images), Computer science, Frame (networking)