April 2016
Intermediate to advanced
430 pages
8h 58m
English
Content preview from Differential Geometry of Curves and Surfaces, 2nd Edition
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CHAPTER 3
Curves in Space: Local Properties
The local theory of space curves is similar to the theory for plane curves, but differences arise in the richer variety of configurations available for loci of curves in ℝ3. In the study of plane curves, we introduced the curvature function, a function of fundamental importance that measures how much a curve deviates from being a straight line. As we shall see, in the study of space curves, we again introduce a curvature function that measures how much a space curve deviates from being linear, but we also introduce a torsion function that measures how much the curve twists away from being planar.
3.1 Definitions, Examples, and Differentiation
As in the study of plane curves, one must take some ...
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