Ebenen mit Kongruenz

DOI10.1007/BF01230121zbMath0537.51019OpenAlexW2316804047MaRDI QIDQ792631

Kay Soerensen

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1007/bf01230121

zbMATH Keywords

reflection geometryaffine planes with a congruence relationcongruence axioms

Mathematics Subject Classification ID

Ordered geometries (ordered incidence structures, etc.) (51G05) Congruence and orthogonality in metric geometry (51F20)

Related Items (12)

The Steiner-Lehmus theorem and ``triangles with congruent medians are isosceles hold in weak geometries ⋮ Negation-free and contradiction-free proof of the Steiner-Lehmus theorem ⋮ A geometric characterization of the real absolute planes. ⋮ The Axiomatic Destiny of the Theorems of Pappus and Desargues ⋮ The Thomsen-Bachmann correspondence in metric geometry. II ⋮ Spaces with congruence ⋮ Introduction of measures for segments and angles in a general absolute plane ⋮ The simplest axiom system for plane hyperbolic geometry revisited ⋮ Symmetric sets with midpoints and algebraically equivalent theories ⋮ Some geometric characterizations of Pythagorean and Euclidean fields ⋮ Two remarks on ordering in absolute planes ⋮ A remark about absolute planes

Cites Work

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• Zur Begründung metrischer affiner Ebenen
• Metrische affine Ebenen
• Kennzeichnung verallgemeinerter euklidischer Ebenen durch Ähnlichkeitsrelationen
• Fanosche metrische affine Ebenen
• Pseudo-Euklidische Ebenen und Euklidische Räume
• Eine Winkelmetrik zur Begründung euklidisch-metrischer Ebenen
• Finite Incidence Structures with Orthogonality
• Metrische Relationen in affinen Ebenen
• The Fundamental Theorems of Elementary Geometry. An Axiomatic Analysis

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