Journal of Geometry

, Volume 5, Issue 1, pp 15–26

A note on a problem of Apollonius

  • J. M. Fitz-Gerald
Article

Abstract

Degenerate cases of the problem of Apollonius, to construct a circle tangent to each of three given circles, are discussed and exhaustively classified for proper circles (finite and non-zero radius). Singular cases are considered, and an outline of the extension of the problem to higher dimensions given. Amusing alternative interpretations of the results are obtained.

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References

  1. 1.
    Pedoe, D.: A Course of Geometry for Colleges and Universities, 101–205, Cambridge Univ. Press. (1970).Google Scholar
  2. 2.
    Pedoe, D.; “The Missing Seventh Circle”, Elemente der Mathematik, 25, 14–15. (1970).Google Scholar
  3. 3.
    Stoll, V.: “Zum Problem des Apollonius”, Math. Ann. 6, 613–632. (1873).CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag 1974

Authors and Affiliations

  • J. M. Fitz-Gerald
    • 1
  1. 1.Department of MathematicsUniversity of QueenslandSt. LuciaAustralia

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