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An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field

2018/06/21 by Nicholas Phat Nguyen, Nguyen, Nicholas Phat
Mathematics · #Advanced Mathematical Theories #Commutative Algebra (math.AC) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1806.08356

openalex publication_date 2018/06/21 · openalex created_date 2018/07/10 · openalex updated_date 2026/07/28

Abstract

Using concepts and techniques of bilinear algebra, we construct hyperbolic planes over a euclidean ordered field that satisfy all the Hilbert axioms of incidence, order and congruence for a basic plane geometry, but for which the hyperbolic version of the parallel axiom holds rather than the classical Euclidean parallel postulate.

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