The parallel postulate

DOI10.1007/S11565-024-00572-YMaRDI QIDQ6657509

Victor V. Pambuccian

Publication date: 6 January 2025

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

zbMATH Keywords

simplicityparallel postulateabsolute geometryAristotle's axiom\textit{Lotschnittaxiom}

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of mathematics in the 21st century (01A61) Foundations of classical theories (including reverse mathematics) (03B30) Absolute planes in metric geometry (51F05) History of geometry (51-03) Desarguesian and Pappian geometries (51A30)

Cites Work

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• On simplicity of formulas
• The rise of non-Archimedean mathematics and the roots of a misconception. I: The emergence of non-Archimedean systems of magnitudes
• On M. T. Calapso's characterization of the metric of an absolute plane
• Aristotle's axiom in the foundations of geometry
• Die Modelle des Hilbertschen Axiomensystems der absoluten Geometrie
• On the stepwise construction of the parallel postulate
• Die absolute Wahrheit der euklidischen Geometrie. Eine kritische Untersuchung der Grundlagen der Geometrie. Beweise für die Wahrheit der Axiome und Postulate, insbesondere für die des Parallelenaxioms (V. Postulat \textit{Euklids}).
• Neue Begründung der \textit{Bolyai-Lobatschefskij}schen Geometrie.
• Briefwechsel zwischen Carl Friedrich Gauss und Wolfgang Bolyai.
• Die Legendre'schen Sätze über die Winkelsumme im Dreieck.
• Sui numeri transfiniti.
• Analytic studies on the theory of parallel lines
• Euler's inequality in absolute geometry
• The ubiquitous axiom
• Two statements characterizing the Euclidean metric of a metric plane
• The elementary Archimedean axiom in absolute geometry
• Two remarks on ordering in absolute planes
• Lippmann's axiom and Lebesgue's axiom are equivalent to the Lotschnittaxiom
• On the equivalence of Lagrange's axiom to the Lotschnittaxiom
• Über die Kreisaxiome
• Parallelaxiomet för en yta av oändlig utsträckning.
• Zur Parallelenfrage
• On a splitting of the parallel postulate
• Constructive Axiomatizations of Plane Absolute, Euclidean and Hyperbolic Geometry
• Ein elementargeometrischer Beweis von H. A. Schwarz vereinfacht und unabhängig vom Parallelenaxiom geführt
• Why Did Lagrange "Prove" the Parallel Postulate?
• Metric Geometries in an Axiomatic Perspective
• Conversations avec Jules Hoüel
• A further simplification of Tarski's axioms of geometry
• Quantum Gravity
• On sentences which are true of direct unions of algebras
• Equilateral triangles have minimal area and perimeter among all triangles containing a given circle in Hilbert planes

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