Analytic Projective Geometry John Bamberg

Analytic Projective Geometry John Bamberg – Ebook Instant Download/Delivery ISBN(s): 9781009260596,100926059,9781009260633,1009260634

Product details:

• ISBN 10: 1009260634
• ISBN 13: 9781009260633
• Author: John Bamberg; Tim Penttila
  

Projective geometry is the geometry of vision, and this book introduces students to this beautiful subject from an analytic perspective, emphasising its close relationship with linear algebra and the central role of symmetry. Starting with elementary and familiar geometry over real numbers, readers will soon build upon that knowledge via geometric pathways and journey on to deep and interesting corners of the subject. Through a projective approach to geometry, readers will discover connections between seemingly distant (and ancient) results in Euclidean geometry. By mixing recent results from the past 100 years with the history of the field, this text is one of the most comprehensive surveys of the subject and an invaluable reference for undergraduate and beginning graduate students learning classic geometry, as well as young researchers in computer graphics. Students will also appreciate the worked examples and diagrams throughout.

Table contents:

Part I. The Real Projective Plane
1. Fundamental Aspects of the Real Projective Plane

2. Collineations

3. Polarities and Conics

4. Cross-Ratio

5. The Group of the Conic

6. Involution

7. Real Affine Plane Geometry from a Projective Perspective

8. Euclidean Plane Geometry from a Projective Perspective

9. Transformation Geometry: Klein’s Point of View

11. From Perspective to Projective

12. Remarks on the History of Projective Geometry

Part II. Real Projective 3-Space

13. Fundamental Aspects of Real Projective Space

14. Triangles and Tetrahedra

15. Reguli and Quadrics

16. Line Geometry

17. Projections

18. A Glance at Inversive Geometry

Part III. Higher Dimensions

19. Generalising to Higher Dimensions

20. The Klein Quadric and the Veronese Surface

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