It is said that during the Edo period hanging sangaku in temples and shrines was so popular that even women and children partook of the activity. While I am skeptical that sangaku was so popular as to involve a significant slice of the population, some sangaku have indeed been created by children. Here's one example.

This sangaku has been hung by Tanabe Shigetoshi, aged fifteen, in the year 1865 at the Meiseirinji temple in Ogaki City, Gifu prefecture.

The sangaku has a very simple solution, although it was anything but simple to come up with such a configuration.

References

1. H. Fukagawa, A. Rothman, Sacred Mathematics: Japanese Temple Geometry, Princeton University Press, 2008, p. 97

Copyright © 1996-2010 Alexander Bogomolny

By direct inspection

r = 3b + 4c, R = 5b + 4c, R = b + 2a, a + b = 2b + 4c.

Solving these simultaneously we see that b = 2c, a = 6c, and r = 10c.

Sangaku

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Copyright © 1996-2010 Alexander Bogomolny