18301930 A Century of Geometry Epistemology, History and Mathematics [Paperback]

In the first half of the 19th century geometry changedradically, and withina century it helped to revolutionizeboth mathematics and physics. It also put the epistemologyand the philosophy of science on a new footing. In thisvolume a sound overview of this development is given byleading mathematicians, physicists, philosophers, andhistorians of science. This interdisciplinary approach givesthis collection a unique character. It can be used byscientists and students, but it also addresses a generalreadership.In the first half of the 19th century geometry changedradically, and withina century it helped to revolutionizeboth mathematics and physics. It also put the epistemologyand the philosophy of science on a new footing. In thisvolume a sound overview of this development is given byleading mathematicians, physicists, philosophers, andhistorians of science. This interdisciplinary approach givesthis collection a unique character. It can be used byscientists and students, but it also addresses a generalreadership.The birth of non-Euclidean geometry.- Riemann's vision of a new approach to geometry.- Poincar? and Klein  groups and geometries.- Klein, Lie, and the Erlanger programm.- Apparent contours from Monge to Todd.- L'Espace : Concept abstrait et/ou physique ; la g?om?trie entre formalisation math?matique et etude de la nature.- Geometrie und Erfahrung.- The geometric challenge of Riemann and Clifford.- Poincar? et Enriques : deux points de vue diff?rents sur les relations entre g?om?trie, m?canique et physique.- Physical geometry and special relativity. Einstein et Poincar?.- Transport parall?le et connexions en G?om?trie et en Physique.- De la G?om?trie Formelle ? l'Alg?bre Abstraite.- Le Principe de Dualit? : sa Signification Historique et Epist?mologique.- The formal and the transcendental in mathematics.- Un Panorama des Math?matiques.- Mathematical progress as synthesis of intuition and calculus.- What is splsD