On the equivalence of Playfair's axiom to the parallel postulate
History and Overview
2019-03-15 v1 Metric Geometry
Abstract
We show that the classical equivalence of Euclid's parallel postulate and Playfair's axiom collapses in the absence of triangle congruence. In particular, we construct a non-SAS geometry that models the Playfair axiom but not the parallel postulate.
Keywords
Cite
@article{arxiv.1903.05233,
title = {On the equivalence of Playfair's axiom to the parallel postulate},
author = {Elizabeth T. Brown and Emily Castner and Stephen Davis and Edwin O'Shea and Edouard Seryozhenkov and AJ Vargas},
journal= {arXiv preprint arXiv:1903.05233},
year = {2019}
}
Comments
5 pages, 3 figures