Calculating Numerical and Analytica Planar Evolutes

Introduction to planar parameterized curves: Derivatives, determinant, curvature and curvature radius. Calculating the evolute: the curvature factor. We emphasize that, while the curvature as well as the curvature ratio contains the rather 'ugly' cubic velocity factor, the curvature factor contains the simpler quadratic velocity factor. Numerical derivation. Numerical calculation of evolutes. Calculating analytical evolutes, verifying the expressions by comparing with the numerically calculated evolutes as well as drawing the resulting curves: Ellipsis, Folium of Descartes and Roses. Lissajous curves. Supercircles and Superellipsis. Cycloids and Trochoids. Epi and Hypocycloids and Trochoids. Roulettes: Rolling a circle on any curve. Arclength and natural parametrization.