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Tangent Indicatrix


Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix,

 tau=(sigma^.)/(|sigma^.|)

is another closed curve on S^2.

If sigma immerses in S^2, then so will tau.


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References

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

Referenced on Wolfram|Alpha

Tangent Indicatrix

Cite this as:

Weisstein, Eric W. "Tangent Indicatrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangentIndicatrix.html

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