A spherical indicatrix of a regular space curve is the curve traced on the unit
sphere by one of the unit vectors in its moving frame.
If 
,
,
and 
are the unit tangent vector, principal normal
vector, and binormal vector of a curve
parametrized by arc length 
, then their images on the unit
sphere are called the tangent indicatrix,
normal indicatrix, and binormal indicatrix, respectively. For example,
 |
so the speed of the tangent indicatrix is the curvature 
. Spherical indicatrices translate questions about curvature
and torsion into the geometry of curves
on a sphere.
