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Ptolemy's equation and kin

Published 14 Jul 2025 in math.MG and math.CO | (2507.10444v1)

Abstract: Three-term relations of the form AB+CD=EF arise in multiple mathematical contexts, including the Ptolemy equation for a cyclic quadrilateral, Casey's theorem on bitangents, Penner's relation for lambda lengths, and Pl\"ucker's identity for the maximal minors of a 2x4-matrix. In this note, we explain how these different occurrences of the 3-term relation can be directly obtained from each other.

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