A modern solution to the Gion shrine problem

TL;DR

This paper presents a simplified algebraic solution to the historic Gion shrine geometry problem, making the process more accessible while also analyzing solution existence and uniqueness.

Contribution

It introduces a more straightforward polynomial formulation of the problem, improving upon classical solutions and providing additional theoretical insights.

Findings

Polynomial is easier to write down than classical solutions

Solution existence and uniqueness are discussed

Provides a modern algebraic approach to a historical problem

Abstract

We give a new solution to the famous Gion shrine geometry problem from eighteenth-century Japan. Like the classical Japanese solution, ours is given in the form of a degree ten equation. However, our polynomial has the advantage of being much easier to write down. We also provide some additional analysis, including a discussion of existence and uniqueness.