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Journal of Geometry

, Volume 5, Issue 1, pp 15–26 | Cite as

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.

Keywords

High Dimension Alternative Interpretation Degenerate Case Singular Case Circle Tangent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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