The Four Point Condition: An Elementary Tropicalization of Ptolemy’s Inequality

DOI10.1080/00029890.2023.2285695arXiv2111.10328OpenAlexW4390047734MaRDI QIDQ6124356

Facundo Mémoli, Mario San Martin Gomez

Publication date: 27 March 2024

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.10328

Mathematics Subject Classification ID

Trees (05C05) Elementary problems in Euclidean geometries (51M04) Inequalities and extremum problems in real or complex geometry (51M16) Elementary problems in hyperbolic and elliptic geometries (51M09) Tropical geometry (14Txx)

Cites Work

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• Strong hyperbolicity
• Dodgon's determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN
• A note on the metric properties of trees
• Generalizations of Casey's theorem for higher dimensions
• Probability and real trees. Ecole d'Eté de Probabilités de Saint-Flour XXXV -- 2005. Lecture given at the Saint-Flour probability summer school, July 6--23, 2005.
• Sätze über das Sehnenviereck in der sphärischen und hyperbolischen Geometrie
• An analogue of Ptolemy's theorem and its converse in hyperbolic geometry
• Seiten und Diagonalen eines Kreisvierecks in der hyperbolischen Geometrie
• Casey's theorem in hyperbolic geometry
• PTOLEMAIC SPACES AND CAT(0)
• A note on the tree realizability of a distance matrix
• An Analogue of Ptolemy's Theorem in Spherical Geometry
• A metric characterization of "spherical" surfaces in n-dimensional hyperbolic space
• Algebraic Statistics for Computational Biology

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