Topics in Geometry

John O'Connor

CONTENTS

Introduction
  1. Foundations
  2. The linear groups
  3. Examples of linear groups
  4. Isometries of Rn
  5. Isometries of the line
  6. Isometries of the plane
  7. Isometries in 3 dimensions
  8. Symmetry groups in the plane
  9. Frieze groups
  10. Platonic solids
  11. Finite symmetry groups of R3
  12. Full finite symmetry groups in R3
  13. Affine geometry
  14. Affine theorems
  15. Similarity geometry
  16. Projective spaces
  17. Homogeneous coordinates
  18. Topology of projective spaces
  19. Projective spaces of vector spaces
  20. The projective groups
  21. More projective groups
  22. Some theorems in plane projective geometry

  1. Duality
  2. Conics
  3. Elliptic geometry
Summary of results

Advanced Topics in Geometry
  1. Lattices
  2. The crystallographic restriction
  3. The point groups
  4. Shift vectors
  5. Classification of crystallographic groups
  6. I: Point group is cyclic
  7. II: Point group is D1
  8. III: Other point groups
Geometry quotations

More geometry quotations
Exercises
  1. Exercises 1
  2. Exercises 2
  3. Exercises 3
  4. Exercises 4
  5. Exercises 5
  6. Exercises 6
  1. Exercises 7
  2. Exercises 8
  3. Exercises 9
  4. Advanced Geometry Exercises
  5. Further Advanced Exercises

JOC MT3818 Geometry March 2003

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