Topics in Geometry
John O'Connor
CONTENTS
Introduction
Foundations
The linear groups
Examples of linear groups
Isometries of
R
^{n}
Isometries of the line
Isometries of the plane
Isometries in 3 dimensions
Symmetry groups in the plane
Frieze groups
Platonic solids
Finite symmetry groups of
R
^{3}
Full finite symmetry groups in
R
^{3}
Affine geometry
Affine theorems
Similarity geometry
Projective spaces
Homogeneous coordinates
Topology of projective spaces
Projective spaces of vector spaces
The projective groups
More projective groups
Some theorems in plane projective geometry
Duality
Conics
Elliptic geometry
Summary of results
Advanced Topics in Geometry
Lattices
The crystallographic restriction
The point groups
Shift vectors
Classification of crystallographic groups
I: Point group is cyclic
II: Point group is
D
_{1}
III: Other point groups
Geometry quotations
More geometry quotations
Exercises
Exercises 1
Exercises 2
Exercises 3
Exercises 4
Exercises 5
Exercises 6
Exercises 7
Exercises 8
Exercises 9
Advanced Geometry Exercises
Further Advanced Exercises
JOC MT3818 Geometry March 2003
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