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

This paper demonstrates how a nineteenth century Japanese votive temple problem known as 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 ${\bar{O}}hara$ Toshiaki (?-1828). Our investigation into the solution of ${\bar{O}}hara$ 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.