Geometry from a differentiable viewpoint /:
"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 pictu...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
2013.
|
| Ausgabe: | 2nd ed. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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"-- |
| Beschreibung: | 1 online resource (xv, 311 pages) : illustrations, maps |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9781139775595 1139775596 1139781626 9781139781626 9781139022248 1139022245 |
Internformat
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| 245 | 1 | 0 | |a Geometry from a differentiable viewpoint / |c John McCleary. |
| 250 | |a 2nd ed. | ||
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| 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 | ||
| 504 | |a Includes bibliographical references and indexes. | ||
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| 505 | 0 | |a 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. | |
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| author | McCleary, John, 1952- |
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| author_facet | McCleary, John, 1952- |
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| contents | 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. |
| ctrlnum | (OCoLC)817224948 |
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| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
| edition | 2nd ed. |
| format | Electronic eBook |
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| spelling | McCleary, John, 1952- https://id.oclc.org/worldcat/entity/E39PCjG8bRhPQKtcxQ8qj3yR4y http://id.loc.gov/authorities/names/n88298102 Geometry from a differentiable viewpoint / John McCleary. 2nd ed. New York : Cambridge University Press, 2013. 1 online resource (xv, 311 pages) : illustrations, maps text txt rdacontent computer c rdamedia online resource cr rdacarrier "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"-- Provided by publisher Includes bibliographical references and indexes. Print version record. 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. Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Géométrie différentielle. MATHEMATICS Topology. bisacsh MATHEMATICS Geometry Differential. bisacsh Geometría diferencial embne Topología embne Geometry, Differential fast Electronic book. Print version: McCleary, John, 1952- Geometry from a differentiable viewpoint. 2nd ed. New York : Cambridge University Press, 2013 9780521116077 (DLC) 2012017159 (OCoLC)794640236 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=490499 Volltext |
| spellingShingle | McCleary, John, 1952- Geometry from a differentiable viewpoint / 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. Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Géométrie différentielle. MATHEMATICS Topology. bisacsh MATHEMATICS Geometry Differential. bisacsh Geometría diferencial embne Topología embne Geometry, Differential fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054146 |
| title | Geometry from a differentiable viewpoint / |
| title_auth | Geometry from a differentiable viewpoint / |
| title_exact_search | Geometry from a differentiable viewpoint / |
| title_full | Geometry from a differentiable viewpoint / John McCleary. |
| title_fullStr | Geometry from a differentiable viewpoint / John McCleary. |
| title_full_unstemmed | Geometry from a differentiable viewpoint / John McCleary. |
| title_short | Geometry from a differentiable viewpoint / |
| title_sort | geometry from a differentiable viewpoint |
| topic | Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Géométrie différentielle. MATHEMATICS Topology. bisacsh MATHEMATICS Geometry Differential. bisacsh Geometría diferencial embne Topología embne Geometry, Differential fast |
| topic_facet | Geometry, Differential. Géométrie différentielle. MATHEMATICS Topology. MATHEMATICS Geometry Differential. Geometría diferencial Topología Geometry, Differential Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=490499 |
| work_keys_str_mv | AT mcclearyjohn geometryfromadifferentiableviewpoint |