Sequences of Touching Circles
Many a Sangaku come in groups of related problems of which the ones below serve an example. All are easily resolved on the basis of another one from Miyagai prefecture. (So I just give a location and a date. The notations are reasonably obvious.)
Tokyo prefecture, 1789.
Answer: rn = ((n - 2)/√r1 + 1/√r2)-2,
n > 2.
Osaka prefecture, 1801.
Answer: r1 = a·(3 - 2√2). rn = a / (√2 + n)2,
n > 1.
Mie prefecture, 1844.
Answer: r1 = a/4. rn = a / (n + 1)2,
n > 1.
H. Fukagawa, D. Pedoe, Japanese Temple Geometry Problems, The Charles Babbage Research Center, Winnipeg, 1989
Charles Babbage Research Center
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