This is a collection of several animations that involve the Frenet frame and the osculating circle. For most of these, a curve is shown in \(\Re^2\) or \(\Re^3\) and a point moves along the curve along with the unit normal and unit tangent vectors and osculating circle. The binormal vector is shown for the curves in \(\Re^3\). The user can stop the animation and control the motion of the point, zoom in and out, and change the perspective for the 3D examples. The last applet demonstrates how parametric surfaces are a mapping from \(\Re^2\) to \(\Re^3\). The user drags a small rectangle in the domain and the mapping of the rectangle onto the surface is shown.