Universal Hyperbolic Geometry II: A pictorial overview

Details Universal Hyperbolic Geometry II: A pictorial overview Universal Hyperbolic Geometry II: A pictorial overview

2010-12-04

arxiv.org/abs/1012.0880v1

KoG 14 (2010) 1-23

Mathematics

Metric Geometry

33 pages, 58 colour figures

Scientific paper

This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely algebraic framework for hyperbolic geometry, valid over the rational numbers (and indeed any field not of characteristic two), and gives us many new and beautiful theorems. These results are accurately illustrated with colour diagrams, and the reader is invited to check them with ruler constructions and measurements.

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