## Minimal Surfaces: Catenoid

Drag mouse to rotate model.

Hold *shift* key and drag (or use mouse wheel)
to adjust the separation between the two rings.
A soap film is formed between two parallel rings of radius separated by a
fixed distance. To minimize the surface-tension energy of the soap
film, its total area seeks a minimum value. The derivation of the shape of the
film involves a problem in the calculus of variations. When the separation
between the two rings gets too large, the film collapses to disks within the two
rings.

Click here
for an explanation/derivation of the shape of this surface.

LOQO was used to compute the minimal surface shown at right.
To get a better feel
for the surface, set it in motion by dragging and releasing the object.

Here are some other interesting minimal surfaces:

*Updated* 2012 Dec 2