Geometry in History, 1st ed. 2019

Coordinators: Dani S. G., Papadopoulos Athanase

Language: Anglais

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640 p. · 15.5x23.5 cm · Hardback

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Foreword. - Table of contents. - Intro. - Chapter 1. Plato on Geometry and the geometers.- Chapter 2. Topology and biology : From Aristotle to Thom. - Appendix to the article Topology and biology : From Aristotle to Thom. - Chapter 3. Time and periodicity from Ptolemy to Schrodinger : Paradigm shifts in history of mathematics. - Chapter 4. Convexity in Greek antiquity. - Chapter 5. On the concept of curve : Geometry and algebra, from mathematical modernity to mathematical modernism. - Chapter 6. From Euclid to Riemann and Beyond : How to describe the shape of the universe. - Chapter 7. A path in history, from curvature to convexity. - Chapter 8. The axiomatic destiny of the theorems of Pappus and Desargues. - Chapter 9. Projective conguration theorems : Old wine into new wineskins. -​ Chapter 10. Poincare's geometric worldview and philosophy. - Chapter 11. Perturbing a planar rotation : Normal hyperbolicity and angular twist. - Chapter 12. Rene Thom and an anticipated h-principle. - Chapter 13. Rigid and exible facets of symplectic topology. - Chapter 14. Flat ane, projective and conformal structures on manifolds: A historical perspective. - Chapter 15. Basic aspects of dierential geometry. - Chapter 16. The global study of Riemannian-Finsler geometry. - Chapter 17. The Poincare conjecture and related statements. - Chapter 18. A glimpse into the problems of the fourth dimension. - Chapter 19. Memories from my former life : The making of a mathematician.

The editors are mathematicians whose work is well known (Dani in dynamics and ergodic theory, and Papadopoulos in geometry and topology of low dimensions). They are the authors of many research articles and monographs, and they edited several books. They have a broad view on the current research on geometry, on the history of the subject and on its impact in modern research. Dani is the editor-in-chief of Ganita Bharati (Bulletin of the Indian Society for History of Mathematics).

Highlights the main ideas in geometry by leading experts in the field

Showcases the main research problems in geometry and topology

Demonstrates the impact of history on current research in geometry

Presents the history of geometry as written by mathematicians