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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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978-0-387-97743-0Springer Science+Business Media New York 1992
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Geometry of Surfaces978-1-4612-0929-4Series ISSN 0172-5939 Series E-ISSN 2191-6675
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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 this.
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The Hyperbolic Plane,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 this.
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Tessellations of Compact Surfaces, 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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The Euclidean Plane, properties of lines and circles as axioms and derived theorems from them by pure logic. Actually he occasionally made use of unstated axioms; nevertheless his approach is feasible and it was eventually made rigorous by Hubert [1899].
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