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Geometry from a differentiable viewp...

McCleary, John, (1952-)

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Geometry from a differentiable viewpoint /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Geometry from a differentiable viewpoint // John McCleary.
Author:	McCleary, John,
Published:	Cambridge [England] ;Cambridge University Press, : 2013.,
Description:	xv, 357 p. :ill., maps ;27 cm.
Subject:	Geometry, Differential. -
ISBN:	9780521116077 (hbk.) :

Geometry from a differentiable viewpoint /
McCleary, John,1952-

Geometry from a differentiable viewpoint /John McCleary. - 2nd ed. - Cambridge [England] ;Cambridge University Press,2013. - xv, 357 p. :ill., maps ;27 cm.

Includes bibliographical references (p. 341-349) and indexes.

Spherical geometry -- Prelude and Themes : Synthetic Methods and Results --

"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"--

ISBN: 9780521116077 (hbk.) :US110.00

LCCN: 2012017159Subjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641 / .M38 2013

Dewey Class. No.: 516.3/6

Geometry from a differentiable viewpoint /
LDR:02637cam a22002654a 450 001 1464322
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008 130522s2013 enkab b 001 0 eng
010 $a 2012017159
020 $a 9780521116077 (hbk.) : $c US110.00
020 $a 0521116074 (hbk.)
020 $a 9780521133111 (pbk.)
020 $a 0521133114 (pbk.)
020 $a 9781139781626 (ebk.)
020 $a 1139781621 (ebk.)
035 $a AS-BW-102-N-01
040 $a DLC $c DLC $d DLC
050 0 0 $a QA641 $b .M38 2013
082 0 0 $a 516.3/6 $2 23
100 1 $a McCleary, John, $d 1952- $3 702143
245 1 0 $a Geometry from a differentiable viewpoint / $c John McCleary.
250 $a 2nd ed.
260 # $a Cambridge [England] ; $a New York : $b Cambridge University Press, $c 2013.
300 $a xv, 357 p. : $b ill., maps ; $c 27 cm.
504 $a Includes bibliographical references (p. 341-349) and indexes.
505 $g Prelude and Themes : Synthetic Methods and Results -- $t Spherical geometry -- $t Euclid -- $t The theory of parallels -- $t Non-Euclidean geometry -- $g Development : Differential Geometry -- $t Curves in the plane -- $t Curves in space -- $t Surfaces -- $t Curvature for surfaces -- $t Metric equivalence of surfaces -- $t Geodesics -- $t The Gauss-Bonnet Theorem -- $t Constant-curvature surfaces -- $g Recapitulation and Coda -- $t Abstract surfaces -- $t Modeling the non-Euclidean plane -- $t Epilogue : where from here?.
520 # $a "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"-- $c Provided by publisher.
650 # 0 $a Geometry, Differential. $3 523835