The principle of duality in Euclidean and in absolute geometry

DOI10.1007/S00022-016-0314-6zbMath1372.51005OpenAlexW2297322919MaRDI QIDQ523404

Rolf Struve

Publication date: 20 April 2017

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

Full work available at URL: https://doi.org/10.1007/s00022-016-0314-6

zbMATH Keywords

Euclidean geometryabsolute geometryBachmann's metric planesco-Euclidean geometryGödel's completeness theoremprinciple of duality

Mathematics Subject Classification ID

Other geometric groups, including crystallographic groups (20H15) Absolute planes in metric geometry (51F05) Reflection groups, reflection geometries (51F15)

Related Items (2)

A theory of duality in Euclidean geometry ⋮ Absolute isotropic geometry

Cites Work

• An axiomatic foundation of Cayley-Klein geometries
• Non-euclidean geometries: the Cayley-Klein approach
• Die Dualität von Inzidenz und Senkrechtstehen in der absoluten Geometrie
• Worlds Out of Nothing
• DAVID HILBERT. David Hilbert's lectures on the foundations of geometry, 1891-1902. Michael Hallett and Ulrich Majer, eds. David Hilbert's Foundational Lectures; 1. Berlin: Springer-Verlag, 2004. ISBN 3-540-64373-7. Pp. xxviii + 661
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