Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté. Image fixe : sans médiation
Auteur(s) : McCleary, John (1952-....)
Titre(s) : Geometry from a differentiable viewpoint [Texte imprimé] / John McCleary,...
Édition : 2nd ed.
Publication : Cambridge : Cambridge university press, 2013
Description matérielle : 1 vol. (XV- 357 p.) : ill. ; 27 cm
Comprend : Spherical geometry ; Euclid ; The theory of parallels ; Non-Euclidean geometry ;
Curves in the plane ; Curves in space ; Surfaces ; Map projections ; Curvature
for surfaces ; Metric equivalence of surfaces ; Geodesics ; The Gauss-Bonnet Theorem
; Constant-curvature surfaces ; Abstract surfaces ; Modeling the non-Euclidean
plane ; Epilogue: where from here?
Note(s) : Bibliogr. p. 341-349
"The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss, and
Riemann is a story that is often broken into parts - axiomatic geometry, non-Euclidean
geometry, and differential geometry. This poses a problem for undergraduates: Which
part is geometry? What is the big picture to which these parts belong? In this introduction
to differential geometry, the parts are united with all of their interrelations, motivated
by the history of the parallel postulate. Beginning with the ancient sources, the
author first explores synthetic methods in Euclidean and non-Euclidean geometry and
then introduces differential geometry in its classical formulation, leading to the
modern formulation on manifolds such as space-time. The presentation is enlivened
by historical diversions such as Hugyens's clock and the mathematics of cartography.
The intertwined approaches will help undergraduates understand the role of elementary
ideas in the more general, differential setting. This thoroughly revised second edition
includes numerous new exercises and a new solution key. New topics include Clairaut's
relation for geodesics, Euclid's geometry of space, further properties of cycloids
and map projections, and the use of transformations such as the reflections of the
Beltrami disk"--
Sujet(s) : Géométrie différentielle
Indice(s) Dewey :
516.36 (23e éd.) = Géométrie différentielle et géométrie intégrale
Identifiants, prix et caractéristiques : ISBN 9780521116077. - ISBN 0521116074 (rel.)
Identifiant de la notice : ark:/12148/cb435357564
Notice n° :
FRBNF43535756
(notice reprise d'un réservoir extérieur)
