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

127 108 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

Commentary
Publisher PDF

0 0 0
Like this paper and download? You can publish your own PDF file online for free in a few minutes! Sign Up

File loading please wait...

Recommend Papers

Perspective and Projective Geometry 9780691197388

An inquiry based approach to learning the connections between geometry and art. Note: This is a simultaneous release.

112 3 60MB Read more

Projective Geometry [Paperback ed.] 0387967524, 9780387967523

The purpose of this book is to revive some of the beautiful results obtained by various geometers of the 19th century, a

295 22 2MB Read more

Modern Analytic Geometry

472 89 56MB Read more

Caesy Analytic Geometry

101 79 Read more

Projective differential geometry and linear differential equations

629 13 503KB Read more

Analytic methods in arithmetic geometry

2,282 109 2MB Read more

Lectures in Geometry, Semester I: Analytic Geometry [1] 0828524610, 9780828524612

201 74 9MB Read more

Calculus and Analytic Geometry [3d ed.]

The 'real' Thomas' Calculus. Contains Part 1 and Part 2 (18 chapters) 3rd edition, second printing (1961)

126 78 95MB Read more

Classical Geometry: Euclidean, Transformational, Inverse and Projective 9781118679197, 2013042035

183 43 31MB Read more

Analytic Geometry [3 ed.] 053401030X, 9780534010300

This respected text makes extensive use of applications and features items such as historical vignettes to make the mate

334 37 21MB Read more