randform

The above is a little applet from Tim and me, illustrating the associated family which interpolates between helicoid and catenoid. If you move the slider you can observe the interpolation. You can rotate the surface by dragging. Both geometric figures (and all interpolations in between) are socalled minimal surfaces, which means that they have mean curvature zero.

The applet was inspired by the fact that clowns usually wear red spheres on their nose, which are surfaces with constant positive mean curvature. We wondered how a variation of this kind of comic circus fashion may look like.

related:
-> the helical keyboard – a piano in a helicoidal shape (at least thats what i understood from the website) …where I indeed somewhat have the suspect that one could break ones hands if one would play on it for real.