This demo includes two graphical display windows.

The window "Curve: X(t)" displays the curve X(t) (which is by default a planar curve), the point X(t0), the unit tangent and principal normal vectors T(t0) and P(t0), and the vector U(t0) obtained by rotating T(t0) 90 degrees counterclockwise, with the tails of these three vectors at X(t0). Note how U(t0) compares to P(t0).

The window "k(t)" displays the graph of the curvature k(t).

You can change t0 and X(t) in the control window. The control window includes a list of functions that you can use for X(t), along with parameters used to define those functions.