The Klein View of Geometry

We will describe several geometries in terms of groups and show how they are related.

table of contents

• introduction
• the klein view
• symmetries and symmetry groups
• the euclidean group
• the similarity group
• the inversive group
• the hyperbolic group
• the affine group
• the projective group
• fundamental theorems
• subgroups and their geometries
• geometrical invariants
• a weird geometry
• models of hyperbolic geometry
• hyperbolic and projective geometry
• a hyperbolic model of euclidean geometry
• concluding remarks