Solving Sangaku With Traditional Techniques

TL;DR

This paper demonstrates how traditional Japanese mathematical techniques, specifically tenzan jutsu, can be used to solve historical sangaku geometry problems, illustrating the enduring relevance of these methods.

Contribution

It provides a comparative analysis of a 19th-century sangaku problem and a traditional Japanese algebraic method, showcasing their practical application.

Findings

Traditional techniques effectively solve historical sangaku problems.

Comparison reveals the mathematical depth of Japanese methods.

Highlights the cultural significance of sangaku and Japanese mathematics.

Abstract

Between 17th and 19th centuries, mathematically orientated votive tablets appeared in Shinto shrines and Buddhist temples all over Japan. Known as sangaku, they contained problems of a largely geometrical nature. In the 17th century, the Japanese mathematician Seki Takakazu developed a form of algebra known as tenzan jutsu. I compare one mathematical problem from the 1810 Japanese text Sanp\=o Tenzan Shinan solved using tenzan jutsu to a similar problem found on the Kijimadaira Tenman-g\=u shrine sangaku to show how sangaku problems can be solved using the traditional Japanese methods.