Bipartite sets of spheres and Casey-type theorems

DOI10.1007/s00025-019-0973-3zbMath1409.51016OpenAlexW2915044572WikidataQ128487959 ScholiaQ128487959MaRDI QIDQ667588

Hiroshi Maehara, Horst Martini

Publication date: 28 February 2019

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-019-0973-3

zbMATH Keywords

Cayley-Menger determinantsemi-metric spacePtolemy's theorembipartite sets of spheresCasey's theorem

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Elementary problems in Euclidean geometries (51M04) Möbius geometries (51B10) Elementary problems in hyperbolic and elliptic geometries (51M09)

Related Items (1)

On double-\(k\)-systems of spheres

Cites Work

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• From line-systems to sphere-systems -- Schläfli's double six, Lie's line-sphere transformation, and Grace's theorem
• Feuerbach's relation and Ptolemy's theorem in \(\mathbb{R}^ n\)
• Generalizations of Casey's theorem for higher dimensions
• An interpretation of Casey's theorem and of its hyperbolic analogue
• Casey's theorem in hyperbolic geometry
• Der Caseysche Satz
• Six mathematical gems from the history of distance geometry
• Two Applications of the Generalized Ptolemy Theorem
• New Foundation of Euclidean Geometry
• A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space
• Topics in Elementary Geometry
• Geometry. I, II. Transl. from the French by M. Cole and S. Levy

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