Geometry in History

Plato on Geometry and the Geometers.- Topology and Biology: From Aristotle to Thom.- Time and eriodicity from Ptolemy to Schrödinger: Paradigm Shifts vs Continuity in History of Mathematics.- Convexity in Greek Antiquity.- On the Concept of Curve: Geometry and Algebra, fromMathematicalModernity to MathematicalModernism.- From Euclid to Riemann and Beyond: How to Describe the Shape of the Universe.- A Path in History, from Curvature to Convexity.- The Axiomatic Destiny of the Theorems of Pappus and Desargues.- Projective Configuration Theorems: Old Wine into New Wineskins.- Poincaré’s GeometricWorldview and Philosophy.- Perturbing a Planar Rotation: Normal Hyperbolicity and Angular Twist.- René Thom and an Anticipated h-Principle.- Rigid and Flexible Facets of Symplectic Topology.- Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective.- Basic Aspects of Differential Geometry.- The Global Study of Riemannian-Finsler Geometry.- The Poincaré Conjectureand Related Statements.- A Glimpse into the Problems of the Fourth Dimension.- Memories fromMy Former Life: The Making of a Mathematician.- Index.