Solving Sangaku With Traditional Techniques

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.