Ptolemy's equation and kin
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916995700621312 |
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| author | Waddle, Katie |
| author_facet | Waddle, Katie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ptolemy's equation and kin Waddle, Katie Metric Geometry Combinatorics 51K99 (Primary) 51M25, 97G40 (Secondary) 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. |
| title | Ptolemy's equation and kin |
| topic | Metric Geometry Combinatorics 51K99 (Primary) 51M25, 97G40 (Secondary) |
| url | https://arxiv.org/abs/2507.10444 |