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Chapter 10.3

MATH 2400 Chapter Notes - Chapter 10.3: Osculating Plane, Osculating Circle, Plane Curve

Course Code
MATH 2400
Markus Steindl

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Anna Pyle
University of Colorado Fall 2016
MATH2400 Calculus 3
Textbook: CALCULUS concepts & contexts 4 James Stewart
Chapter 10: Arc Length and Curvature
Arc Length
oThe length of a space curve is defined below:
oIt is useful to parametrize curve with respect to arc length because arc length arises naturally
from the shape of the curve and does not depend on a particular coordinate system
oA parametrization r(t) is called smooth on an interval I if r’ is continuous and r’(t) is not equal to
0 on I. It is also called smooth if it has a smooth parametrization. This means it has no sharp
corners or cusps.
oIf C is a smooth curve defined by the vector function r, recall that the unity tangent vector T(t) is
given by the equation shown below and represents the direction of the curve
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