Abstract
We use generalised cross-ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of symmetric Riemannian spaces of rank 1 and of negative curvature.
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Acknowledgments
The author would like to thank Zoltán M. Balogh and John R. Parker for some useful discussions and suggestions.
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In memoriam patris mei: Demos I. Platis, 1926–2002.
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Platis, I.D. Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1. Geom Dedicata 169, 187–208 (2014). https://doi.org/10.1007/s10711-013-9850-5
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DOI: https://doi.org/10.1007/s10711-013-9850-5