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Chapter 5
Plate 5.2. Original illustration for problem 6, from Shiraishi Nagatada’s 1827 Shamei Sanpu. (Aichi University of Education Library.)
Problem 7 Kawano Michimuku, a student of the Fujita school, proposed this problem, which was written on a tablet hung in 1804 at the Udo shrine in Miyazaki prefecture. We know of it from Fujita Kagen’s 1807 version of the Zoku Shinpeki Sanp¯o . As shown in figure 5.6, ten circles of radius r touch each other externally and touch the large circle internally. If S is the area of the big circle minus the area of the ten little circles, find r in terms of S. Answer: 2r =
4S π(2 8 − 1)
.