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Tangent indicatrix

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 .


  • Solomon, B. "Tantrices of Spherical Curves." Amer. Math. Monthly 103, 30-39, 1996.