# Tangent indicatrix Redirected from **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 .

## References

- Solomon, B. "Tantrices of Spherical Curves."
*American Mathematical Monthly*103, 30–39, 1996.

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