This book introduces students to projective geometry from an analytic perspective, mixing recent results from the past 100 years with the history of the field in one of the most comprehensive surveys of the subject. The subject is taught conceptually, with worked examples and diagrams to aid in understanding.
This book introduces students to projective geometry from an analytic perspective, mixing recent results from the past 100 years with the history of the field in one of the most comprehensive surveys of the subject. The subject is taught conceptually, with worked examples and diagrams to aid in understanding.
John Bamberg is Associate Professor of Mathematics at the University of Western Australia, where he previously obtained his Ph.D. under the auspices of Cheryl Praeger and Tim Penttila. His research interests include finite and projective geometry, group theory, and algebraic combinatorics. He was a Marie Sk¿odowska-Curie fellow at Ghent University from 2006 to 2009, and a future fellow at the Australian Research Council from 2012 to 2016.
Inhaltsangabe
Preface 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. Affine plane geometry viewed projectively 8. Euclidean plane geometry viewed projectively 9. Transformation geometry: Klein's point of view 10. The power of projective thinking 11. From perspective to projective 12. Remarks on the history of projective geometry Part II. Two 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 Veronese surface Appendix: Group actions References Index.
Preface 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. Affine plane geometry viewed projectively 8. Euclidean plane geometry viewed projectively 9. Transformation geometry: Klein's point of view 10. The power of projective thinking 11. From perspective to projective 12. Remarks on the history of projective geometry Part II. Two 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 Veronese surface Appendix: Group actions References Index.
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