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arXiv · 1806.08356

An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field

Nicholas Phat Nguyen
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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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Nicholas Phat Nguyen. 2018-06-21. An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field. https://arxiv.org/abs/1806.08356

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