An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field

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.

22 pages (including references). Latest version includes some minor revisions and typographical changes