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Travel Diary of Mathematician Yamaguchi Kanzan
Problem 11 This problem, proposed by Sawa Masayoshi in 1821, is from the sangaku of the Syosya temple. As shown in the figure, five circles of radii a, b, and c are inscribed in a segment of a large circle. If a = 72 and b = 32, then find c. The result for the general case is on page 280.
c
a
a b
b
Problem 12 Also proposed by Sawa Masayoshi, this problem remains unsolved. As shown below, an ellipse is inscribed in a right triangle with its major axis parallel to the hypotenuse. Within the ellipse are inscribed two circles of radius r. A third circle of radius r touches the ellipse and the two shorter sides of the triangle, a and b. Find r in terms of a and b.
b
r r r a
Y14 7th of March: The mathematician Horiike Hisamichi hung several sangaku, one of which was in the Kibitsu shrine in Okayama and another in the Suzuka in Ise, far from Okayama. (Neither of these tablets survives.) Yamaguchi wrote, “I have visited the Kibitsu shrine in Okayama and found a sangaku problem proposed by mathematician Horiike in 1804, which I have recorded in my diary.�