关税 发表于 2025-3-21 19:45:23

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Pageant 发表于 2025-3-21 23:45:10

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隐士 发表于 2025-3-22 02:46:24

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Injunction 发表于 2025-3-22 05:55:05

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 ℝ. when extended indefinitely, even if small parts of it matched small parts of ℝ. with absolute precision. Indeed, we ma

牢骚 发表于 2025-3-22 08:49:58

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适宜 发表于 2025-3-22 15:23:26

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

适宜 发表于 2025-3-22 17:19:19

,Die Größenordnung der Kardinalzahlen, function . such that each . ∈ . has an ε-neighborhood isometric to a disc of ℍ.. The proof of the Killing-Hopf theorem (Section 2.9) carries over word-for-word (provided “line”, “distance” etc., are understood in the hyperbolic sense), showing that any complete, connected hyperbolic surface is of t

Fallibility 发表于 2025-3-23 00:01:32

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

有毛就脱毛 发表于 2025-3-23 03:51:11

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污点 发表于 2025-3-23 07:19:41

Einleitung in die griechische Philologie sides of II according to the side pairing, is also an orbit space .Γ. Here . = . is S., ℝ., or ℍ.—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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查看完整版本: Titlebook: Geometry of Surfaces; John Stillwell Textbook 1992 Springer Science+Business Media New York 1992 Area.Fractal.curvature.differential geome