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MODELS OF NON-EUCLIDEAN GEOMETRY
Tevian Dray
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Contents
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Front Matter
Colophon
Preface
Acknowledgments
GeoGebra
1
Introduction
Geometries and Models
Incidence Geometries
Four-Point Geometry
Five-Point Geometry
Fano Geometry
Spherical Geometry I
Overview
2
Euclidean Geometry
Euclidean Geometry
Constructions
Constructing a Compass
Duplicating an Angle
Congruence
3
Taxicab Geometry
Taxicab Geometry
Taxicab Circles
Using Taxicab Circles
Taxicab Ellipses
Taxicab Hyperbolas
More Taxicab Ellipses
4
Neutral Geometry
Neutral Geometry
Postulates
Neutral Constructions
Rectangles
Hyperbolic Geometry
5
The Poincaré Disk
The Poincaré Disk
Hyperbolic Constructions
Angle of Parallelism
Hyperbolic SAS
A Hyperbolic Model
6
The Klein Disk
The Klein Disk
Elliptic Constructions
Elliptic SAS
7
Elliptic Geometry
Elliptic Geometry
Stereographic Projection
Double Elliptic Geometry
Single Elliptic Geometry
The Polar Property
Spherical Geometry II
8
Area
Angle Defect
Hyperbolic AAA
Saccheri quadrilaterals
Hyperbolic Area
Angle Excess
Lunes
Hyperbolic Lunes
9
Projective Geometry
The Projective Plane
Topology
Quadrilaterals
Perspectivity
Desargues' Theorem
10
Tiling
Tiling the Euclidean Plane
Tiling the Sphere
Tiling the Klein Disk
Tiling the Poincaré Disk
11
Minkowski Space
Minkowski Space
Light Boxes
Hyperboloids
Curvature
Back Matter
Authored in PreTeXt
MODELS OF NON-EUCLIDEAN GEOMETRY
Tevian Dray
Department of Mathematics
Oregon State University
tevian@math.oregonstate.edu
Colophon
1
Preface
2
Acknowledgments
3
GeoGebra
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