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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Foertsch, T., Schroeder, V. Ptolemy circles and Ptolemy segments. Arch. Math. 98, 571–581 (2012). https://doi.org/10.1007/s00013-012-0398-7
- Triangle Inequality
- Cross Ratio
- Convex Curve
- Unbounded Component
- Busemann Function