Table of Contents

Ch. 0 Introduction

Ch. 1 Axiom System
1.1.1 Introduction
1.1.2 Examples
1.1.3 History
1.2 A Finite Geometry
1.3 Finite Projective
1.4 Applications

Ch. 2 Neutral Geom.
2.1.1 Introduction
2.1.2 History
2.1.3 Analytic Models
2.2 Incidence Axioms
2.3 Distance/Ruler Axioms
2.4.1 Plane Separation Axiom
2.4.2 Angle & Measure
2.5.1 Supplement Postulate
2.5.2 SAS Postulate
2.6.1 Parallel Lines
2.6.2 Saccheri Quad.
2.7.1 Euclid. Parallel Post.
2.7.2 Hyperbolic Parallel Post.
2.7.3 Elliptic Parallel Post.
2.8 Euclid/Hyper/Elliptic
Birkhoff's Axioms
Hilbert's Axioms
SMSG Axioms

Ch. 3 Transformational Geom.
3.1.1 Introduction
3.1.2 History
3.2.1 Definitions
3.2.2 Analytic Model
3.2.3 Affine Transformation
3.3.1 Isometry
3.3.2 Model/Collinearity
3.3.3. Model/Isometry
3.4.1 Direct Isometry
3.4.2 Model/Direct
3.5.1 Indirect Isometry
3.5.2 Model/Indirect
3.6.1 Similarity Trans.
3.6.2 Model/Similarity
3.7 Other Affine Transformations

Ch. 4 Projective
4.1.1 Introduction
4.1.2 Historical
4.2.1 Axioms
4.2.2 Basic Theorems
4.2.3 Independence
4.3 Duality
4.4 Desargues' Thm.
4.5.1 Harmonic Sets
4.5.2 Music/Harmonic
4.6.1 Dfn. Projectivity
4.6.2 Fundamental Thm.
4.6.3 Proj./Harmonic
4.6.4 Alternate Constr.
4.7.1 Conics
4.7.2 Pascal's Thm.
4.7.3 Tangents to Conics

Internet Resources
Index
Sketchpad Sketches
JavaSketchpad Sketches
Tegrity Videos
Flash Videos
Logic Review
References
Acknowledgements

Timothy Peil
Mathematics Dept.
MSU Moorhead
Last Update
    February 6, 2007