Geometry in History

by S. G. Dani, Athanase Papadopoulos

Overview

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.

Product Details

ISBN-13:	9783030136086
Publisher:	Springer International Publishing
Publication date:	10/19/2019
Edition description:	1st ed. 2019
Pages:	750
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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).

Table of Contents

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 Schrödinger : 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.

Editorial Reviews

The intended audience is that of the general mathematical community with an interest in how certain geometrical ideas developed and evolved over time. … This book allows the reader to grasp just how large the area of geometry is. … This volume would be a useful reference text in a library, where readers could use it to research the historical origins of certain geometrical topics and see how they developed over time.” (Brendan O'Sullivan, Irish Mathematical Society Bulletin, Issue 87, 2021)

From the Publisher