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An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field
Published 21 Jun 2018 in math.HO and math.AC | (1806.08356v4)
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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