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Tangent Indicatrix

Let the Speed $\boldsymbol{\sigma}$ of a closed curve on the unit sphere $S^2$ never vanish. Then the tangent indicatrix

\boldsymbol{\tau}\equiv{\dot\boldsymbol{\sigma}\over \vert\dot\boldsymbol{\sigma}\vert}

is another closed curve on $S^2$. It is sometimes called the Tantrix. If $\boldsymbol{\sigma}$ Immerses in $S^2$, then so will $\boldsymbol{\tau}$.


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

© 1996-9 Eric W. Weisstein