Geometry in History (Hardcover, 2019)

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 Schr odinger : 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.