Coxeter- Projective Geometry (Second Edition)

Sean Raleigh, May 2, 2014

This book was created by students at Westminster College in Salt Lake City, UT, for the May Term 2014 course [i]Projective Geometry[/i] (Math 300CC-01). Coxeter's book, [i]Projective Geometry[/i] (Second Edition) is one of the classic texts in the field. This GeoGebraBook contains dynamic illustrations for figures, theorems, some of the exercises, and other explanations from the text. If you have any new or improved materials that could be added to this book, send me a link so I can add them: sraleigh@westminstercollege.edu.

Table of Contents

  1. Introduction
    1. Coxeter- Figure 1.4A (left)
    2. Coxeter-Figure 1.4 A (right)
    3. Coxeter- Figure 1.5A
    4. Coxeter- Figure 1.5B
    5. Coxeter- Figure 1.5C
    6. Coxeter - Figure 1.6 A (left)
    7. Coxeter - Figure 1.6 A (right)
    8. Coxeter - Figure 1.6 B
    9. Coxeter- Figure 1.6 C
    10. Coxeter- Figure 1.6D (left)
    11. Coxeter - Figure 1.6 D (right)
    12. Coxeter - Exercise 1.6.1
    13. Coxeter - Exercise 1.6.2
    14. Coxeter - Exercise 1.6.3
    15. Coxeter - Exercise 1.6.4
  2. Triangles and Quadrangles
    1. Coxeter- Theorem 2.21
    2. Coxeter- Theorem 2.22
    3. Coxeter- Theorem 2.23
    4. Coxeter- Theorem 2.24
    5. Coxeter- Exercise 2.2.1(i)
    6. Coxeter- Exercise 2.2.1(ii)
    7. Coxeter- Figure 2.3A
    8. Coxeter- Theorem 2.32
    9. Coxeter- Exercise 2.3.1
    10. Coxeter- Exercise 2.3.2
    11. Coxeter- Exercise 2.3.3
    12. Coxeter- Figure 2.4A
    13. Coxeter- Figure 2.5A - Theorem 2.51
    14. Coxeter- Exercise 2.5.1
    15. Coxeter- Exercise 2.5.2
    16. Coxeter- Exercise 2.5.3
    17. Coxeter- Exercise 2.5.4
    18. Coxeter- Exercise 2.5.5
    19. Coxeter- Exercise 2.5.6
  3. The Principle of Duality
    1. Coxeter- Exercise 3.1.1
    2. Coxeter - Excercise 3.1.2
    3. Coxeter- Exercise 3.2.1
    4. Coxeter- Exercise 3.2.2
    5. Coxeter- Exercise 3.2.3
    6. Coxeter- Exersice 3.2.4
    7. Coxeter- Figure 3.3 A
    8. Coxeter - figure 3.3 B
    9. Coxeter - Theorem 3.33
    10. Coxeter- Exercise 3.3.1
    11. Coxeter- Exercise 3.3.2
    12. Coxeter- Exercise 3.4.1
    13. Coxeter- Exercise 3.4.2
    14. Coxeter- Exercise 3.4.3
    15. Coxeter- Exercise 3.4.4
    16. Coxeter- Figure 3.5 A
    17. Coxeter- Exercise 3.5.1
    18. Coxeter- Exercise 3.5.2
    19. Coxeter - Excercise 3.5.3
  4. The Fundamental Theorem and Pappus's Theorem
    1. Coxeter- Figure 4.1A
    2. Coxeter- Figure 4.3A
    3. Coxeter- Figure 4.3B
    4. Coxeter- Theorem 4.41
    5. Coxeter- Figure 4.4A (Left)
    6. Coxeter- Figure 4.4A (Right)
  5. One-dimensional Projectivities
    1. Coxeter- Figure 5.1A
    2. Coxeter- Figure 5.1B
    3. Coxeter- Theorem 5.21
    4. Coxeter- Exercise 5.2.1
    5. Coxeter- Theorem 5.31
    6. Coxeter- Theorem 5.32
    7. Coxeter- Exercise 5.3.1
  6. Two-dimensional Projectivities
    1. Coxeter- Figure 6.1A
    2. Coxeter- Theorem 6.11
    3. Coxeter- Figure 6.1B
    4. Coxeter- Theorem 6.13
    5. Coxeter- Figure 6.2A
    6. Coxeter- Theorem 6.21
    7. Coxeter- Theorem 6.22 R not on o, OP
    8. Coxeter- Theorem 6.22 R on OP
    9. Coxeter- Figure 6.2B
    10. Coxeter- Figure 6.2C
    11. Coxeter- Theorem 6.23
    12. Coxeter- Exercise 6.2.1
    13. Coxeter- Theorem 6.32
    14. Coxeter- Figure 6.3A
    15. Coxeter- Theorem 6.41
    16. Coxeter- Figure 6.4A
    17. Coxeter- Theorem 6.42
    18. Coxeter- Figure 6.4B
  7. Polarities
    1. Coxeter- Figure 7.1A
    2. Coxeter- Figure 7.1B
    3. Coxeter- Theorem 7.13
    4. Coxeter- FIgure 7.2A
    5. Coxeter- Figure 7.3A
    6. Coxeter- Figure 7.4A
    7. Coxeter- Figure 7.5A
    8. Coxeter- Theorem 7.61
    9. Coxeter- Figure 7.7A
    10. Coxeter- Figure 7.7B
  8. The Conic
    1. Coxeter-Figure 8.1 A (left)
    2. Coxeter-Figure 8.1 A (right)
    3. Coxeter-Figure 8.1 B
    4. Coxeter-Figure 8.2 A (left)
    5. Coxeter-Figure 8.2 A (right)
    6. Coxeter-Theorem 8.31
    7. Coxeter-Theorem 8.32
  9. The Conic, Continued
    1. Coxeter- Theorem 9.14 - Figure 9.1D
    2. Coxeter- Theorem 9.15 - Figure 9.1E (left)
    3. Coxeter- Theorem 9.15 - Figure 9.1E (right)
    4. Coxeter- Theorem 9.21 - Figure 9.2A
    5. Coxeter- Theorem 9.22 - Figure 9.2B
    6. Coxeter- Theorem 9.23 - Figure 9.2C (left)
    7. Coxeter- Theorem 9.23 - Figure 9.2C (right)
    8. Coxeter- Theorem 9.31 - Theorem 9.32 - Figure 9.3A
    9. Coxeter- Theorem 9.41 - Theorem 9.42 - Figure 9.4A
    10. Coxeter- Section 9.5 (1)
    11. Coxeter- Section 9.5 (2)
  10. A Finite Projective Plane
  11. Parallelism
  12. Coordinates

1.

Introduction

  • 1. Coxeter- Figure 1.4A (left)
  • 2. Coxeter-Figure 1.4 A (right)
  • 3. Coxeter- Figure 1.5A
  • 4. Coxeter- Figure 1.5B
  • 5. Coxeter- Figure 1.5C
  • 6. Coxeter - Figure 1.6 A (left)
  • 7. Coxeter - Figure 1.6 A (right)
  • 8. Coxeter - Figure 1.6 B
  • 9. Coxeter- Figure 1.6 C
  • 10. Coxeter- Figure 1.6D (left)
  • 11. Coxeter - Figure 1.6 D (right)
  • 12. Coxeter - Exercise 1.6.1
  • 13. Coxeter - Exercise 1.6.2
  • 14. Coxeter - Exercise 1.6.3
  • 15. Coxeter - Exercise 1.6.4

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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2.

Triangles and Quadrangles

  • 1. Coxeter- Theorem 2.21
  • 2. Coxeter- Theorem 2.22
  • 3. Coxeter- Theorem 2.23
  • 4. Coxeter- Theorem 2.24
  • 5. Coxeter- Exercise 2.2.1(i)
  • 6. Coxeter- Exercise 2.2.1(ii)
  • 7. Coxeter- Figure 2.3A
  • 8. Coxeter- Theorem 2.32
  • 9. Coxeter- Exercise 2.3.1
  • 10. Coxeter- Exercise 2.3.2
  • 11. Coxeter- Exercise 2.3.3
  • 12. Coxeter- Figure 2.4A
  • 13. Coxeter- Figure 2.5A - Theorem 2.51
  • 14. Coxeter- Exercise 2.5.1
  • 15. Coxeter- Exercise 2.5.2
  • 16. Coxeter- Exercise 2.5.3
  • 17. Coxeter- Exercise 2.5.4
  • 18. Coxeter- Exercise 2.5.5
  • 19. Coxeter- Exercise 2.5.6

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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2.15.

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2.16.

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2.17.

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2.18.

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2.19.

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3.

The Principle of Duality

  • 1. Coxeter- Exercise 3.1.1
  • 2. Coxeter - Excercise 3.1.2
  • 3. Coxeter- Exercise 3.2.1
  • 4. Coxeter- Exercise 3.2.2
  • 5. Coxeter- Exercise 3.2.3
  • 6. Coxeter- Exersice 3.2.4
  • 7. Coxeter- Figure 3.3 A
  • 8. Coxeter - figure 3.3 B
  • 9. Coxeter - Theorem 3.33
  • 10. Coxeter- Exercise 3.3.1
  • 11. Coxeter- Exercise 3.3.2
  • 12. Coxeter- Exercise 3.4.1
  • 13. Coxeter- Exercise 3.4.2
  • 14. Coxeter- Exercise 3.4.3
  • 15. Coxeter- Exercise 3.4.4
  • 16. Coxeter- Figure 3.5 A
  • 17. Coxeter- Exercise 3.5.1
  • 18. Coxeter- Exercise 3.5.2
  • 19. Coxeter - Excercise 3.5.3

3.1.

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3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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3.17.

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3.18.

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3.19.

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4.

The Fundamental Theorem and Pappus's Theorem

  • 1. Coxeter- Figure 4.1A
  • 2. Coxeter- Figure 4.3A
  • 3. Coxeter- Figure 4.3B
  • 4. Coxeter- Theorem 4.41
  • 5. Coxeter- Figure 4.4A (Left)
  • 6. Coxeter- Figure 4.4A (Right)

4.1.

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4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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5.

One-dimensional Projectivities

  • 1. Coxeter- Figure 5.1A
  • 2. Coxeter- Figure 5.1B
  • 3. Coxeter- Theorem 5.21
  • 4. Coxeter- Exercise 5.2.1
  • 5. Coxeter- Theorem 5.31
  • 6. Coxeter- Theorem 5.32
  • 7. Coxeter- Exercise 5.3.1

5.1.

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5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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6.

Two-dimensional Projectivities

  • 1. Coxeter- Figure 6.1A
  • 2. Coxeter- Theorem 6.11
  • 3. Coxeter- Figure 6.1B
  • 4. Coxeter- Theorem 6.13
  • 5. Coxeter- Figure 6.2A
  • 6. Coxeter- Theorem 6.21
  • 7. Coxeter- Theorem 6.22 R not on o, OP
  • 8. Coxeter- Theorem 6.22 R on OP
  • 9. Coxeter- Figure 6.2B
  • 10. Coxeter- Figure 6.2C
  • 11. Coxeter- Theorem 6.23
  • 12. Coxeter- Exercise 6.2.1
  • 13. Coxeter- Theorem 6.32
  • 14. Coxeter- Figure 6.3A
  • 15. Coxeter- Theorem 6.41
  • 16. Coxeter- Figure 6.4A
  • 17. Coxeter- Theorem 6.42
  • 18. Coxeter- Figure 6.4B

6.1.

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6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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6.12.

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6.13.

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6.14.

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6.15.

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6.16.

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6.17.

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6.18.

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7.

Polarities

  • 1. Coxeter- Figure 7.1A
  • 2. Coxeter- Figure 7.1B
  • 3. Coxeter- Theorem 7.13
  • 4. Coxeter- FIgure 7.2A
  • 5. Coxeter- Figure 7.3A
  • 6. Coxeter- Figure 7.4A
  • 7. Coxeter- Figure 7.5A
  • 8. Coxeter- Theorem 7.61
  • 9. Coxeter- Figure 7.7A
  • 10. Coxeter- Figure 7.7B

7.1.

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7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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8.

The Conic

  • 1. Coxeter-Figure 8.1 A (left)
  • 2. Coxeter-Figure 8.1 A (right)
  • 3. Coxeter-Figure 8.1 B
  • 4. Coxeter-Figure 8.2 A (left)
  • 5. Coxeter-Figure 8.2 A (right)
  • 6. Coxeter-Theorem 8.31
  • 7. Coxeter-Theorem 8.32

8.1.

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8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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9.

The Conic, Continued

  • 1. Coxeter- Theorem 9.14 - Figure 9.1D
  • 2. Coxeter- Theorem 9.15 - Figure 9.1E (left)
  • 3. Coxeter- Theorem 9.15 - Figure 9.1E (right)
  • 4. Coxeter- Theorem 9.21 - Figure 9.2A
  • 5. Coxeter- Theorem 9.22 - Figure 9.2B
  • 6. Coxeter- Theorem 9.23 - Figure 9.2C (left)
  • 7. Coxeter- Theorem 9.23 - Figure 9.2C (right)
  • 8. Coxeter- Theorem 9.31 - Theorem 9.32 - Figure 9.3A
  • 9. Coxeter- Theorem 9.41 - Theorem 9.42 - Figure 9.4A
  • 10. Coxeter- Section 9.5 (1)
  • 11. Coxeter- Section 9.5 (2)

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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9.9.

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9.10.

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9.11.

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10.

A Finite Projective Plane


    This chapter does not contain any resources yet.

11.

Parallelism


    This chapter does not contain any resources yet.

12.

Coordinates


    This chapter does not contain any resources yet.

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