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 2
Plane Curves: Global Properties
Most of the properties of curves we have studied so far are called local properties. By definition, a local property of a curve (or surface) is a property that is related to a point on the curve based on information contained just in a neighborhood of that point. By contrast, global properties concern attributes about the curve taken as a whole. In Chapter 1, the arc length of a curve was the only notion introduced that we might consider a global property.
Analytically speaking, local properties of a curve at a point involve derivatives of the parametric equations while global properties deal with integration along the curve and topological properties and geometric properties of how the curve lies ...
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