Ptolemy circles and Ptolemy segments

Abstract

In this paper we characterize Ptolemy circles and Ptolemy segments up to isometry. Moreover, we present an example of a metric sphere, which is Möbius equivalent but not homothetic to the standard metric sphere with its chordal metric.

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Correspondence to Thomas Foertsch.

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Foertsch, T., Schroeder, V. Ptolemy circles and Ptolemy segments. Arch. Math. 98, 571–581 (2012). https://doi.org/10.1007/s00013-012-0398-7

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Keywords

  • Triangle Inequality
  • Cross Ratio
  • Convex Curve
  • Unbounded Component
  • Busemann Function