Asymmetric polygons with maximum area

TL;DR

This paper investigates the problem of constructing maximum area asymmetric polygons inscribed in a circle, with vertices chosen from given diameters, motivated by ethnomusical applications.

Contribution

It introduces a novel geometric problem of maximizing area for asymmetric polygons with vertices on circle diameters, providing solutions for specific configurations.

Findings

Derived algorithms for maximum area asymmetric polygons

Characterized properties of optimal polygons under given constraints

Applied results to ethnomusical data analysis

Abstract

We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given $n$ diameters of a circle and a positive integer $k<n$, this paper addresses the problem of computing a maximum area asymmetric $k$-gon having as vertices $k<n$ endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciological applications.