A 49th Degree Challenge

I always thought of Sangaku as Temple Geometry, although many of the tablets posed problem in algebra and calculus. Here is one example from [Fukagawa and Rothman]. The tablet may still be seen at the Asahikanzeon temple in Sabae. It was presented by Momota in 1807 and recorded in his travel diary by Yamaguchi Kanzan.

The tablet asks for a solution in integers to a system of three equations

a system of three equations

The tablet gives a solution to this particular system, viz.,

x = 57,
y = 47,
z = 37

and also derives an equation of degree 49 for a more general problem. While it is not difficult to find the above triple by a simple trial-and-error method, even deriving the 49th degree equation as has been done by Momota is a challenge.

Let me know if you find a way to perform the feat.

References

  1. H. Fukagawa, A. Rothman, Sacred Mathematics: Japanese Temple Geometry, Princeton University Press, 2008, pp. 252-253

Sangaku

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