Why were geometry problems hung in temples in Japan?

Because the tablet was an offering, a display and a challenge at once. Some presented an achievement, others invited the visitor to solve a problem, and the dedication itself carried religious and social meaning. A study of a nineteenth-century tablet showed how its solution rests on geometric methods developed in the Japanese mathematical tradition of the Edo period.

A painted wooden tablet hanging in a temple with circles and triangles on it looks like decoration, and beside the drawing appears the statement of a mathematical problem.

These tablets were dedicated to Shinto shrines and Buddhist temples in a period when Japan was almost entirely closed, and mathematics developed there separately from European mathematics, with methods of its own.

Their role is mixed. Some presented the author’s achievement, others invited the visitor to solve, and the dedication itself carried religious and social meaning. A temple is a place many people pass through, so the solution became a public event.

A study of a nineteenth-century tablet analyzed the inscription and the drawing and reconstructed the solution by the methods of the period, showing it rests on geometry developed in that same tradition. The paper analyzes one particular tablet, and the purposes and audiences of sangaku varied between temples, authors and periods.