Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T14:47:24.975Z Has data issue: false hasContentIssue false
  • English
  • Français

The Sequence of Touching Circles

Published online by Cambridge University Press:  03 November 2016

John Satterly
John Satterly*
Affiliation:
University of Toronto
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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—