Rufus Bowen: Difference between revisions

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In [[differential geometry]], the '''tangent indicatrix''' of a closed [[space curve]] is a curve on the unit sphere intimately related to the curvature of the original curve. Let <math>\gamma(t)\,</math> be a closed curve with nowhere-vanishing tangent vector <math>\dot{\gamma}</math>. Then the tangent indicatrix <math>T(t)\,</math> of <math>\gamma\,</math> is the closed curve on the unit sphere given by <math>T = \frac{\dot{\gamma}}{|\dot{\gamma}|}</math>.
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The [[total curvature]] of <math>\gamma\,</math> (the integral of curvature with respect to arc length along the curve) is equal to the [[arc length]] of <math>T\,</math>.
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==References==
* Solomon, B. "Tantrices of Spherical Curves." Amer. Math. Monthly 103, 30-39, 1996.
 
{{geometry-stub}}
[[Category:Differential geometry]]

Latest revision as of 18:20, 30 October 2014

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