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The Sequence of Touching Circles

Published online by Cambridge University Press:  03 November 2016

John Satterly
John Satterly*
Affiliation:
University of Toronto
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Extract

This problem has been treated in many Geometries (Casey, Forder, Steiner) and in the Mathematical Gazette, and by Frederick Soddy.

Perhaps I can add a little of interest.

Type
Research Article
Information
The Mathematical Gazette , Volume 44 , Issue 350 , December 1960 , pp. 263 - 268
Copyright
Copyright © Mathematical Association 1960

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References

1 Mathematical Gazette A. P. Rollett Vol. 21, 1937, 412; Vol 22, 1938, 257; Б. H. Neville Vol. 22, 1938, 288; A. N. Krishnaswami Ayyangar Vol. 22, 1938, 288; J. M. Child Vol. 32, 1948, 52; Richard Beetham, Vol. 37, 1953, 53.

2 Frederick Soddy, “The Kiss Precise,” Nature, Val. 137, 1936, 1021 and Vol. 139, 1937, 62.

3 Two integral solutions of Eq. (4) are (1) a, b, с equal to 23, 46, 69 respectively when the r's are 6 and —38, (2) а.b.с. equal to 15, 15, 10 when the r's are 2 and —30. A very near integral solution occurs when а, b, с are 8, 7 and 5 when the r's are 0.9976… and – 15.0003—