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212814

1830–1930: a century of geometry

epistemology, history and mathematics

Édité parLuciano BoiDominique FlamentJean-Michel Salanskis

Résumé

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.

Détails | Table des matières

The birth of non-euclidean geometry Christian Houzel

pp.1-21

https://doi.org/10.1007/3-540-55408-4_49
Riemann's vision of a new approach to geometry Erhard Scholz

pp.22-34

https://doi.org/10.1007/3-540-55408-4_50
Poincaré and Klein

groups and geometries

J. J. Gray

pp.35-44

https://doi.org/10.1007/3-540-55408-4_51
Klein, Lie, and the "Erlanger programm" David E. Rowe

pp.45-54

https://doi.org/10.1007/3-540-55408-4_52
Apparent contours from Monge to Todd Bernard Teissier

pp.55-62

https://doi.org/10.1007/3-540-55408-4_53
L'Espace

concept abstrait et/ou physique ; la géométrie entre formalisation mathématique et étude de la nature

Luciano Boi

pp.63-90

https://doi.org/10.1007/3-540-55408-4_54
Geometrie und Erfahrung Françoise Balibar

pp.91-97

https://doi.org/10.1007/3-540-55408-4_55
The geometric challenge of Riemann and Clifford Ruth FarwellChristopher Knee

pp.98-106

https://doi.org/10.1007/3-540-55408-4_56
Poincaré et Enriques

deux points de vue différents sur les relations entre géométrie, mécanique et physique

Giorgio Israel

pp.107-126

https://doi.org/10.1007/3-540-55408-4_57
Physical geometry and special relativity

Einstein et Poincaré

Michel Paty

pp.127-149

https://doi.org/10.1007/3-540-55408-4_58
Transport parallèle et connexions en géométrie et en physique Jean-Pierre Bourguignon

pp.150-164

https://doi.org/10.1007/3-540-55408-4_59
De la géométrie formelle à l'algèbre abstraite Hourya Sinaceur

pp.165-174

https://doi.org/10.1007/3-540-55408-4_60
Le principe de dualité

sa signification historique et epistémologique

Ludovico Geymonat

pp.175-177

https://doi.org/10.1007/3-540-55408-4_61
The formal and the transcendental in mathematics Gilles-Gaston Granger

pp.178-183

https://doi.org/10.1007/3-540-55408-4_62
Un panorama des mathématiques René Thom

pp.184-191

https://doi.org/10.1007/3-540-55408-4_63
Mathematical progress as synthesis of intuition and calculus Klaus Volkert

pp.192-198

https://doi.org/10.1007/3-540-55408-4_64
What is space? Hans Freudenthal

pp.199-204

https://doi.org/10.1007/3-540-55408-4_65
La "lineale Ausdehnungslehre" (1844) de Hermann Günther Grassmann Dominique Flament

pp.205-221

https://doi.org/10.1007/3-540-55408-4_66
La capture de l'extension comme dialectique géométrique

Dimension et puissance selon l'Ausdehnung de Grassmann (1844)

Gilles Châtelet

pp.222-244

https://doi.org/10.1007/3-540-55408-4_67
Helmholtz and Poincaré's considerations on the genesis of geometry Gerhard Heinzmann

pp.245-249

https://doi.org/10.1007/3-540-55408-4_68
Le continu contre l'espace Jean-Michel Salanskis

pp.250-264

https://doi.org/10.1007/3-540-55408-4_69
Geometrical concepts in quantum physics Gilles Cohen-Tannoudji

pp.265-269

https://doi.org/10.1007/3-540-55408-4_70
Physics and differential geometry Tullio Regge

pp.270-272

https://doi.org/10.1007/3-540-55408-4_71
Actuality of transcendental æsthetics for modern physics Jean Petitot

pp.273-304

https://doi.org/10.1007/3-540-55408-4_72

Détails de la publication

Maison d'édition: Springer

Lieu de publication: Dordrecht

Année: 1992

Pages: 304

Collection: Lecture Notes in Physics


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: 402

DOI: 10.1007/3-540-55408-4

ISBN (hardback): 978-3-540-55408-0

ISBN (digital): 978-3-540-47058-8

Citation complète:

Boi Luciano, Flament Dominique, Salanskis Jean-Michel (éd.), 1992, 1830–1930: a century of geometry: epistemology, history and mathematics. Dordrecht, Springer.