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About: Tangent indicatrix     Goto   Sponge   NotDistinct   Permalink

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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 be a closed curve with nowhere-vanishing tangent vector . Then the tangent indicatrix of is the closed curve on the unit sphere given by . The total curvature of (the integral of curvature with respect to arc length along the curve) is equal to the arc length of .