October 3, 2025Open Access

Ptolemy's equation and kin

Key Points

Ptolemy's equation showcases a crucial three-term relation present across various mathematical contexts.
Key relations include those in Casey's theorem, Penner's relation, and Plücker's identity for matrices.
The note reveals how different occurrences of the relation can be derived from one another effectively.
This exploration highlights the interconnectedness of mathematical relationships in geometry and algebra.

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 Plücker'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.

Read Full Paperexternally

KI fragen

Bookmark

View Full Paper

Cite This Study

Katie Waddle (Mon,) studied this question.

synapsesocial.com/papers/68e040eda99c246f578b334d https://doi.org/https://doi.org/10.48550/arxiv.2507.10444

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

KI fragen

Bookmark

View Full Paper