An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field
History and Overview
2018-08-14 v4 Commutative Algebra
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.
Cite
@article{arxiv.1806.08356,
title = {An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field},
author = {Nicholas Phat Nguyen},
journal= {arXiv preprint arXiv:1806.08356},
year = {2018}
}
Comments
22 pages (including references). Latest version includes some minor revisions and typographical changes