Hilbert’s Axiomatization of the Plane

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 8 in An Axiomatic Approach to Geometry, 2014, pp 305-353 from Springer

Abstract: Abstract Euclid’s axiomatics of geometry did contain some “gaps” … which were filled by “the consideration of the figure” to decide—for example—which of three given points on a line lies between the other two. Two millenniums later, Hilbert provides a complete system of axioms for the Euclidean plane; and just replacing the “uniqueness of the parallel” by the existence of several parallels, he gets a complete axiomatic system of non-Euclidean geometry.

Keywords: Neutral Geometry; Perpendicular Media; Congruent Segments; Strict Total Order; Faithful Mathematical Models (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01730-3_8

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DOI: 10.1007/978-3-319-01730-3_8

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