Morikawa's Unsolved Problem

TL;DR

This paper proves that a classical Japanese geometry problem from the 19th century has no closed-form algebraic solution, using advanced mathematical techniques from multiple fields.

Contribution

It provides a rigorous proof of the nonexistence of a closed-form algebraic solution to a historically significant geometry problem, resolving a long-standing mathematical puzzle.

Findings

No closed-form algebraic solution exists for the problem.

The proof combines geometry, calculus, group theory, and Galois theory.

Resolves a historical problem from Japanese sangaku tablets.

Abstract

By combining theoretical and computational techniques from geometry, calculus, group theory, and Galois theory, we prove the nonexistence of a closed-form algebraic solution to a Japanese geometry problem first stated in the early nineteenth century. This resolves an outstanding problem from the sangaku tablets which were at one time displayed in temples and shrines throughout Japan.