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Unformatted text preview: [Return HW; hand out time sheets] Prof. Tibor Beke will substitute for me on Thursday and Friday of this week. Another perspective on the | v ( t )| = | v ( t )| for all t problem we discussed last time: What values can the left hand side take? What about the right hand side? Section 10.8: Arc length and curvature Three formulas for the curvature of a space curve: = | d T / ds | (the definition; requires the arc-length parametrization) ( t ) = | T ( t )|/| r ( t )| (any parametrization will do) ( t ) = | r ( t ) r ( t )| / | r ( t )| 3 An intuitive description of = | T ( t )|/| r ( t )|: Since the length of T ( t ) is constant, | T ( t )| is the rate of change of direction, or turning, of the unit tangent, and | r ( t )| measures the speed along the curve. So is the rate of turning of the unit tangent divided by the speed along the curve. For a circle in the plane parametrized in the standard way, r ( t ) = a...
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- Fall '11