# Area and perimeter foliations on spaces of polygons

Aziz El Kacimi Alaoui and Abdellatif Zeggar – GJM, Volume 4, Issue 1 (2019), 18-29.

We describe all families of star-shaped n-polygons in the Euclidean plane with prescribed perimeter and area; they are leaves of a foliation $\mathcal F$ on the space ${\mathcal P}_n^\ast$ of star-shaped polygons. In so doing, we study and record some geometric properties of convex polygons, for instance their inscriptibility in a circle and their regularity in relation with perimeter and area.

#### Milestones:

Received: November 04, 2018
Published online: May 16, 2019

#### Authors:

Aziz El Kacimi Alaoui and Abdellatif Zeggar
Université Polytechnique Hauts-de-France,
EA 4015 - LAMAV, FR CNRS 2956,
F-59313 Valenciennes Cedex 9, France.