Generalizations of Casey's theorem for higher dimensions

DOI10.1134/S199508021801002XzbMath1392.51003OpenAlexW2792251774MaRDI QIDQ2412935

Nikolaĭ Vladimirovich Abrosimov, Vladislav Vasil'evich Aseev

Publication date: 6 April 2018

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s199508021801002x

zbMATH Keywords

Ptolemy's theoremCasey's theoremgeneralized \(k\)-sphereproblem of Apollonius

Mathematics Subject Classification ID

Elementary problems in Euclidean geometries (51M04) Euclidean analytic geometry (51N20)

Related Items (2)

The Four Point Condition: An Elementary Tropicalization of Ptolemy’s Inequality ⋮ Bipartite sets of spheres and Casey-type theorems

Cites Work

• Unnamed Item
• An analogue of Ptolemy's theorem and its converse in hyperbolic geometry
• An interpretation of Casey's theorem and of its hyperbolic analogue
• Casey's theorem in hyperbolic geometry

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