DART 发表于 2025-3-21 19:22:54
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https://doi.org/10.1007/978-3-642-98007-7In this chapter we discuss two mathematical formulations of the intuitive notion of a curve. The precise relation between them turns out to be quite subtle, so we shall begin by giving some examples of curves of each type and practical ways of passing between them.大漩涡 发表于 2025-3-22 08:01:56
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Curves in the Plane and in Space,In this chapter we discuss two mathematical formulations of the intuitive notion of a curve. The precise relation between them turns out to be quite subtle, so we shall begin by giving some examples of curves of each type and practical ways of passing between them.轻快带来危险 发表于 2025-3-22 16:52:12
,Gauss’s Theorema Egregium,One of Gauss’s most important discoveries about surfaces is that the gaussian curvature is unchanged when the surface is bent without stretching. Gauss called this result ‘egregium’, and the Latin word for ‘remarkable’ has remained attached to his theorem ever since.轻快带来危险 发表于 2025-3-22 19:08:52
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Lexikon der Wirtschaftsinformatikrface patch, is all that is needed for most of the book, it does not describe adequately most of the objects that we would want to call surfaces. For example, a sphere is not a surface patch, but it can be described by gluing two surface patches together suitably. The idea behind this gluing proceduSEED 发表于 2025-3-23 09:07:31
https://doi.org/10.1007/978-3-662-08371-0rface. Of course, this will usually be different from the distance between these points as measured by an inhabitant of the ambient three dimensional space, since the straight line segment which furnishes the shortest path between the points in .. will generally not be contained in the surface. The