The Historical Timeline of Minimal Surfaces and the Mathematics behind its Defining Property
A photo of a catenoid. Image from Catenoid Minimal Surface What is a Minimal Surface? As one might think, a minimal surface is a surface that minimizes its surface area for given boundary conditions. Moreover, the more mathematical definition of a minimal surface is a surface with zero mean curvature ( Weisstein) . In this post, I will not only expound the mathematical definition of a minimal surface, but I will also provide a brief history of curvature and minimal surfaces. The Study of Curvature and Minimal Surfaces Throughout the Years The history of curvature goes back a long way, but for this post I will begin telling its story in the 18th century. Leonhard Euler (1707-1783), being the first to study curvature of surfaces, provided the world of differential geometry the formula for normal curvature in 1760 (Schreck, 2016, p.120). This was seen as a huge breakthrough. Adding to the study of curvature in 1771 was Gaspard Monge (1746-1818) who studied space curve