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Geometry from a Differentiable Viewpoint
Rok: 1995
ISBN: 9780521414302
OKCZID: 110110453
Citace (dle ČSN ISO 690):
MCCLEARY, John. Geometry from a differentiable viewpoint. Cambridge: Cambridge University Press, 1994. xii, 308 s.
Hodnocení:
4.0 / 5
(6 hlasů)
Anotace
This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane. The main theorems of non-Euclidean geometry are presented along with their historical development. The author then introduces the methods of differential geometry and develops them toward the goal of constructing models of the hyperbolic plane. While interesting diversions are offered, such as Huygen's pendulum clock and mathematical cartography, the book thoroughly treats the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds.