Introduction
- Foundations
- The linear groups
- Examples of linear groups
- Isometries of Rn
- 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 R3
- Full finite symmetry groups in R3
- 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
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- 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 D1
- III: Other point groups
Geometry quotations
More geometry quotations
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