Mathematics 305, Principles of Geometry

Preliminary course outline

Prerequisite: Math 107-108

Resources: Text Supplements, class notes, Geometer’s Sketch Pad

I Finite Geometries

• 4 line/4 point geometry
• Geometry of Farro and Young
• Geometry of Pappus

II Geometric Transformations

• Groups of Symmetry Transformations
• Euclidean plane isometries

III Constructions

• Basic constructions
• Constructible numbers
• Impossible constructions

IV Geometry of Inversion

• Basic concepts
• Invariance
• Applications

V Projective Geometry

• Fundamental concepts
• Axioms of projection
• Theorem of Pappus

VI Non-Euclidean Geometry