The window "Curve: X(t)" in this demonstration displays the curve X(t)
= (cos(t), sin(t), cos(2t)/c), the point X(t0), and the
normal, and binormal vectors T(t0), P(t0), and B(t0),
with their tails
at that point.
The window "Spherical Images: T, P, B" displays the same
three vectors with their tails at the origin, the sphere on which their
heads are constrained to lie, and the tangential indicatrix.
length of the tangential indicatrix, displayed in a readout in the
control window, is called the total curvatuve of
the curve X(t). From Fenchel's theorem, this quantity is
always greater than or equal to 4π. It is possible to
change c, t0, and X(t) in the control window. It is also
possible to set X(t) equal to circle(t) or spacecardioid(t), listed in
the control window.