Solving Sangaku: A Traditional Solution to a Nineteenth Century Japanese Temple Problem

TL;DR

This paper explores traditional Japanese Edo period mathematical methods to solve a 19th-century sangaku problem, comparing it with a modern approach and providing insights into historical techniques.

Contribution

It demonstrates the application of tenzan jutsu, a traditional symbolic manipulation method, to solve a historical sangaku problem, highlighting its contextual mathematical rules.

Findings

Traditional method successfully solves the problem

Provides new insights into Edo period mathematical rules

Connects historical techniques with modern understanding

Abstract

This paper demonstrates how a nineteenth century Japanese votive temple problem known as a sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603-1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of \=Ohara Toshiaki (?-1828). Our investigation into the solution of \=Ohara provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.