This demo includes a single graphical window that displays a curve
X(t) (which you may change in the appropriate textbox in the control
window), the point X(t_{0}), the unit tangent vector T(t_{0})
with base X(t_{0}),
the involute curve I(t) = X(t) + (c – s(t))T(t) for parameter c defined
in the control window, and, if the "String" box in the control window
is checked, a curve showing that one can interpret the involute curve
as the result of winding or unwinding a string around the curve X(t)
and having the end of the string trace out a curve. The control window
lists several curves that you may enter for X(t). For example, type
cardioid(t) in the textbox for X(t) to make X(t) a cardioid. The
control window also includes parameters used in defining these curves.
To change these parameters or t_{0}, use the following buttons:

[<]: 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.