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Full Description
In the first half of the 19th century geometry changed radically, and withina century it helped to revolutionize both mathematics and physics. It also put the epistemology and the philosophy of science on a new footing. In this volume a sound overview of this development is given by leading mathematicians, physicists, philosophers, and historians of science. This interdisciplinary approach gives this collection a unique character. It can be used by scientists and students, but it also addresses a general readership.
Contents
The birth of non-Euclidean geometry.- Riemann's vision of a new approach to geometry.- Poincare 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 geometrie entre formalisation mathematique et etude de la nature.- Geometrie und Erfahrung.- The geometric challenge of Riemann and Clifford.- Poincare et Enriques : deux points de vue differents sur les relations entre geometrie, mecanique et physique.- Physical geometry and special relativity. Einstein et Poincare.- Transport parallele et connexions en Geometrie et en Physique.- De la Geometrie Formelle a l'Algebre Abstraite.- Le Principe de Dualite : sa Signification Historique et Epistemologique.- The formal and the transcendental in mathematics.- Un Panorama des Mathematiques.- Mathematical progress as synthesis of intuition and calculus.- What is space?.- La "lineale ausdehnungslehre" (1844) de Hermann Gunther Grassmann.- La capture de l'extension comme dialectique geometrique : Dimension et puissance selon l'ausdehnung de Grassmann (1844).- Helmholtz and Poincare's considerations on the genesis of geometry.- Le continu contre l'espace.- Geometrical concepts in quantum physics.- Physics and differential geometry.- Actuality of transcendental aesthetics for modern physics.
