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Titlebook: Geometry of Surfaces; John Stillwell Textbook 1992 Springer Science+Business Media New York 1992 Area.Fractal.curvature.differential geome

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書目名稱Geometry of Surfaces
編輯John Stillwell
視頻videohttp://file.papertrans.cn/384/383832/383832.mp4
叢書名稱Universitext
圖書封面Titlebook: Geometry of Surfaces;  John Stillwell Textbook 1992 Springer Science+Business Media New York 1992 Area.Fractal.curvature.differential geome
描述Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un- til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba- sic group theory (subgroups and cosets), an
出版日期Textbook 1992
關(guān)鍵詞Area; Fractal; curvature; differential geometry; manifold; polygon
版次1
doihttps://doi.org/10.1007/978-1-4612-0929-4
isbn_softcover978-0-387-97743-0
isbn_ebook978-1-4612-0929-4Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Science+Business Media New York 1992
The information of publication is updating

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Von der Zerlegung der Zahlen in Teile,s intended to model “flat” surfaces in the real world; yet all physical flat surfaces are of finite extent and have boundaries. It is not clear that such a surface would resemble ?. when extended indefinitely, even if small parts of it matched small parts of ?. with absolute precision. Indeed, we ma
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Di- und triklinometrisches System,t . ? ., more than one line through . which does not meet . Such a surface departs from the euclidean plane in the opposite way to the sphere, and the hyperbolic plane, in fact, emerged from the study of surfaces which “curve” in the opposite way to the sphere. The train of thought, in brief, was th
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,Die Gr??enordnung der Kardinalzahlen, function . such that each . ∈ . has an ε-neighborhood isometric to a disc of ?.. The proof of the Killing-Hopf theorem (Section 2.9) carries over word-for-word (provided “l(fā)ine”, “distance” etc., are understood in the hyperbolic sense), showing that any complete, connected hyperbolic surface is of t
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Besondere Behandlung des Falles , = 3, problem of classifying groups Γ. In the spherical and euclidean cases this problem is easy to solve, as we have seen in Chapters 2 and 3, because there are only a small number of possibilities. However, in the hyperbolic case the number of possibilities is infinite, and the problem is best clarifie
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Einleitung in die griechische Philologie sides of II according to the side pairing, is also an orbit space .Γ. Here . = . is S., ?., or ?.—the surface from which II originates—and Γ is the group generated by the side-pairing transformations of II. Because of its interpretation as an orbit space, . is also called an
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