Travel Diary of Mathematician Yamaguchi Kanzan
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Y21 15th of July: “I have arrived at Tottori and stayed with Kitaro¯ . I met two aged persons who enjoy studying mathematics and astronomy.”
Y22 24th of July: “After entering Obama, I visited a mathematician Matsumoto Einosuke who is a disciple of Kurihara in Obama.” 7th of September: Yamaguchi visited a shrine, Tenman, in Hirokawa village in Takashima of Shiga. There he heard that a sangaku from 1748 was hanging in the shrine and recorded it in his diary. Two problems from this sangaku, which were proposed by Kashiwano Tsunetada, can be found as problems 15 and 16.
Problem 15 This problem of Tenman shrine in Hirokawa village was proposed by Kashiwano Tsunetada in 1748. Kashiwano wrote a preface on the tablet: “Mathematics is very important in ordinary life and I like to study mathematics. I have written my three favorite problems on this tablet A and have not written the answers for two of them. I am very glad if someone tries to solve the problems.” H Draw a circle of radius r = 2.4 touching the P hypotenuse AB and the side BC of right triangle ABC. From vertex C also draw the line CP, which is tangent to the circle. If the length CP = 13, find CH. r B
C
The answer is on page 281.
15th of September: “I have arrived at Lake Biwako once more. While visiting the Miidera temple in Shiga, I recorded two sangaku as follows: . . .” The first sangaku at the Miidera temple was hung by Ogura Yoshisada in 1817. Ogura wrote on it: “Mathematics is the origin of everything in the universe. In particular, when we investigate something in astronomy, mathematics is important. I was admitted to the Seki school when young and