1. A three-dimensional surface of revolution formed by rotating a catenary curve around a horizontal axis; the only minimal surface of revolution.
Usage: mathematics; geometry; technical

Examples

• The catenoid is one of the most important minimal surfaces studied in differential geometry.
• A soap film stretched between two circular rings naturally forms a catenoid shape.
• The catenoid was discovered by Leonhard Euler in the 18th century.
• Unlike a sphere, a catenoid has zero mean curvature at every point.
• The catenoid can be parametrized using hyperbolic functions.