Tangent indicatrix explained
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 . Bruce . January 1996 . Tantrices of Spherical Curves . The American Mathematical Monthly . en . 103 . 1 . 30–39 . 10.1080/00029890.1996.12004696 . 0002-9890.
