Catenoid
A catenoid is a type of surface formed by rotating a catenary curve around an axis. It is a minimal surface, meaning it has the least surface area for a given boundary. Catenoids can be found in nature, such as in soap films stretched between two circular rings, demonstrating their efficiency in minimizing surface area.
Mathematically, a catenoid can be described using parametric equations involving hyperbolic functions. It is one of the few surfaces that can be classified as a minimal surface, alongside others like the plane and soap bubble. Catenoids have applications in various fields, including architecture and engineering, due to their structural properties.