Titlebook: Elementary Differential Geometry; Andrew Pressley Textbook 20011st edition Springer-Verlag London 2001 Curves and Surfaces.Euclidean Geome

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Global Properties of Curves,e ‘global’ shape of the curve. In this chapter, we discuss some global results about curves. The most famous, and perhaps the oldest, of these is the ‘isoperimetric inequality’, which relates the length of certain ‘closed’ curves to the area they contain.

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Curvature of Surfaces,t (see Theorem 10.4) that a surface patch is determined up to a rigid motion of .. by its first and second fundamental forms, just as a unit-speed plane curve is determined up to a rigid motion by its signed curvature.

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Meander

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死貓他燒焦

Surfaces in Three Dimensions, proofs in a section at the end of the chapter; this section is not used anywhere else in the book and can safely be omitted if desired. In fact, surfaces (as opposed to surface patches) will be used in a serious way on only a few occasions in this book.

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