Analytic Projective Geometry [1 ed.] 1009260596, 9781009260596, 9781009260626

Projective geometry is the geometry of vision, and this book introduces students to this beautiful subject from an analy

128 108 19MB

English Pages xii, 462 [475] Year 2023

Table of contents :
Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xii

Part I - The Real Projective Plane
pp 1-2

1 - Fundamental Aspects of the Real Projective Plane
pp 3-11

2 - Collineations
pp 12-30

3 - Polarities and Conics
pp 31-42

4 - Cross-Ratio
pp 43-82

5 - The Group of the Conic
pp 83-99

6 - Involution
pp 100-162

7 - Real Affine Plane Geometry from a Projective Perspective
pp 163-183

8 - Euclidean Plane Geometry from a Projective Perspective
pp 184-240

9 - Transformation Geometry: Klein’s Point of View
pp 241-245

10 - The Power of Projective Thinking
pp 246-287

11 - From Perspective to Projective
pp 288-316

12 - Remarks on the History of Projective Geometry
pp 317-320

Part II - Real Projective 3-Space
pp 321-322

13 - Fundamental Aspects of Real Projective Space
pp 323-337

14 - Triangles and Tetrahedra
pp 338-347

15 - Reguli and Quadrics
pp 348-367

16 - Line Geometry
pp 368-387

17 - Projections
pp 388-396

18 - A Glance at Inversive Geometry
pp 397-404

Part III - Higher Dimensions
pp 405-406

19 - Generalising to Higher Dimensions
pp 407-420

20 - The Klein Quadric and the Veronese Surface
pp 421-433

Appendix: Group Actions
pp 434-435

References
pp 436-456

Index
pp 457-462

Analytic Projective Geometry [1 ed.]
1009260596, 9781009260596, 9781009260626

Author / Uploaded
John Bamberg
Tim Penttila

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