Equilateral triangles have minimal area and perimeter among all triangles containing a given circle in Hilbert planes

DOI10.1007/s00022-023-00688-0zbMath1523.51014OpenAlexW4386332764MaRDI QIDQ6076424

A. A. Nazaryan

Publication date: 21 September 2023

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-023-00688-0

zbMATH Keywords

areaperimeterHilbert planesinscribed circlesabsolute plane geometry

Mathematics Subject Classification ID

Absolute planes in metric geometry (51F05) Inequalities and extremum problems in real or complex geometry (51M16)

Cites Work

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• Die Modelle des Hilbertschen Axiomensystems der absoluten Geometrie
• On the existence of a equilateral triangle in \(H\)-planes
• Euler's inequality in absolute geometry
• Lippmann's axiom and Lebesgue's axiom are equivalent to the Lotschnittaxiom

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