Catenoid

A catenoid is a type of minimal surface formed when a flexible, soap-filmed surface spans between two circular boundaries. It looks like a smooth, symmetrical, hourglass-shaped or saddle-like surface. Mathematically, it’s characterized by having the smallest possible surface area for the given boundary, meaning it’s a natural form of energy minimization. Catenoids appear in nature and engineering, such as in the design of bridges and architectural structures, demonstrating efficient and stable shapes. Their unique shape results from the balance of tension and curvature, embodying principles of both geometry and physics in a simple yet elegant form.