# An algorithm to find maximum area polygons circumscribed about a convex polygon

## TL;DR

This paper introduces an algorithm to find the maximum area convex polygon circumscribed about a given convex polygon, providing solutions for general and regular polygons, and disproving a related conjecture.

## Contribution

It presents a novel O(n^3) algorithm for maximum area circumscribed polygons and offers explicit solutions for regular polygons, also disproving a conjecture.

## Key findings

- Algorithm computes maximum area circumscribed polygons in O(n^3) time
- Explicit solutions provided for regular polygons
- Disproves a conjecture of Farris

## Abstract

A convex polygon Q is circumscribed about a convex polygon P if every vertex of P lies on at least one side of Q. We present an algorithm for finding a maximum area convex polygon circumscribed about any given convex n-gon in O(n^3) time. As an application, we disprove a conjecture of Farris. Moreover, for the special case of regular n-gons we find an explicit solution.