This demo includes three graphical display windows.

The window "X(t)" displays the circle given by X(t) = R*(cos(t), sin(t)), the point X(t0), and the unit tangent and unit normal vectors T(t0) and U(t0) with X(t0) as their base.

The window "Position and Velocity Vectors, Normalized" displays the unit vectors X'(t0)/|X'(t0)| and X(t0)/|X(t0)|, showing that the angle between X(t) and X'(t) is constant for the exponential spiral.

The window "T(t) and U(t)" displays the unit tangent and unit normal vectors with their base at the origin and the unit circle on which the heads of those vectors must lie.

The window "Graph: kg(t)" displays a graph of the curvature of X(t).

To change t0 or R, use the following buttons in the control window:

[<]: Decrease variable by one step.
[>]: Increase variable by one step.
[<<]: Decrease variable until it reaches its minimum value.
[>>]: Increase variable until it reaches its maximum value.