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 - 22). rn = a / (2 + n)2, n > 1.

  • Mie prefecture, 1844.

     

    Answer: r1 = a/4. rn = a / (n + 1)2, n > 1.

References

  1. H. Fukagawa, D. Pedoe, Japanese Temple Geometry Problems, The Charles Babbage Research Center, Winnipeg, 1989

    Write to:

    Charles Babbage Research Center
    P.O. Box 272, St. Norbert Postal Station
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    Canada R3V 1L6

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