Non-Euclidean Geometries pp 109-114

Part of the Mathematics and Its Applications book series (MAIA, volume 581)

An Absolute Property of Four Mutually Tangent Circles

  • H.S.M. Coxeter

Abstract

When Bolyai János was forty years old, Philip Beecroft discovered that any tetrad of mutually tangent circles determines a complementary tetrad such that each circle of either tetrad intersects three circles of the other tetrad orthogonally. By careful examination of a new proof of this theorem, one can see that it is absolute in Bolyai’s sense. Beecroft’s double-four of circles is seen to resemble Schläfli’s double-six of lines.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • H.S.M. Coxeter
    • 1
  1. 1.University of TorontoTorontoCanada

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