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 osculating circle to X(t) at X(t0), the line segment from the center of the osculating circle to X(t0), which is normal to the curve and has length given by 1/kg(t0), and the evolute curve, which is traced out by the center of the osculating circle.
br>Change the value of t0 and other variables as in earlier demos. As in earlier demos, there are "Show entire curve" and "Show Color Spectrum" options. "Show Color Spectrum" also colors the osculation cirlce, its radius, and the evolute curve. "Show Parallel Curve" displays parallel curves at distance d. Note that as d changes, the cusps of the parallel curves lie on the evolute.