Titlebook: Exploring Curvature; James Casey Textbook 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996 Gaussian curvatu

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Surfaces,on to the geometry of surfaces, which is even more fascinating. We will proceed in our usual manner, moving from intuitions to concepts, and exploring the geometrical phenomena by means of simple experiments. Our discussion of surface geometry begins with a search for a good definition of the concep

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Intrinsic Geometry of a Surface,e also, they are preserved under all deformations. (Some examples of deformations of surfaces were studied at the end of Chapter 11.) There is a broader class of properties that are intimately bound up with the geometry of the surface and that are preserved under a large subclass of homeomorphisms.

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Gauss (1777-1855),ly intellectual activity, but it should not be regarded as an elitist one. Even those of us who have never created a song, or a story, or a piece of mathematics, can still experience much pleasure from playing or listening to music, or from reading a book or attending a play, or from doing a calcula

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https://doi.org/10.1007/978-1-4684-6536-5duced in earlier chapters. Our aim is to proceed from intuitive notions about curves to a clear, abstract definition. This process - the clarification of ideas - is really one of the most important activities of the mathematician.

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