Of all the sangaku on record, two have proved particularly difficult to solve. The Japanese mathematician Yamaguchi Kanzan (c. 1781–1850) collected them in his travel journal between 1817 and 1828.
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Some of the most famous sangaku figures echo other mathematical constructions, forging beautiful connections between results established in different places and at different times. Here is a particularly striking example.
With the country cut off almost entirely from the world during the Edo period, Japanese mathematics developed in isolation for more than a century and a half. It was during this period that highly distinctive geometric puzzles flourished and prospered.
Though Western in origin, the golden ratio is said to be everywhere. So we went looking for it in sangaku… and struggled to find it, except in a few rare figures. But perhaps we simply overlooked it!
A sangaku was originally a Japanese wooden votive tablet. It sometimes bears an engraved geometric figure with the statement of a problem, together with the solution or sometimes a hint.
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