Non-Euclidean Geometry

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 7 in An Axiomatic Approach to Geometry, 2014, pp 243-303 from Springer

Abstract: Abstract The fruitless attempts to prove Euclid’s parallel postulate, in particular the theory of limit parallels, lead eventually the mathematicians of the nineteenth century to consider that the negation of this postulate could possibly be taken as an axiom. The discovery of the models of non-Euclidean geometry—like the Beltrami–Klein and the Poincaré disk—give evidence that the negation of the parallel postulate is “as consistent as the parallel postulate”.

Keywords: Geometric Theory; Euclidean Geometry; Euclidean Plane; Characteristic Angle; Complete Axiomatization (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-01730-3_7

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