catenoid

The surface of revolution produced when a catenary rotates about its central axis. The catenoid was first described by Leonhard Euler in 1740 and is the oldest known minimal surface (a shape of least area when bounded by a given closed space). It is the minimal surface connecting two parallel circles of unequal diameter on the same axis; soap film between two circular rings takes this form (see bubbles).

The catenoid is the only known minimal surface that is also a surface of revolution, and is one of only four minimal surfaces that have the topological properties of being unbounded, embedded, and non-periodic; the others are the simple plane, the helicoid, and Costa's surface.

Related category

• SOLIDS AND SURFACES

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