Convex polygon and integer programming

Document Type : Original Paper

Authors

Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

In this work, polygons of the integer sides are introduced. Moreover, by considering some Pythagorean-like relationships on these polygons, we prove that for all n-polygons of the aforementioned relationship, Pythagorean quasi-relations are satisfied. Furthermore, it is proved that the central angle of these polygons is not more than a constant value, so these polygons are always convex. Moreover, a nonlinear integer programming model for obtaining the integer sides of these polygons is presented.

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