ABSTRACT
The origins of minimal surface theory can be traced back to 1744 with Euler’s paper [Euler2], and to 1760 with Lagrange’s paper [Lag]. Euler showed that the catenoid is a minimal surface, and Lagrange wrote down the partial differential equation that must be satisfied for a surface of the form z = f (x, y) to be minimal. In 1776, Meusnier 1 rediscovered the catenoid and also showed that the helicoid is a minimal surface [Meu]. The mathematical world had to wait over 50 years until other examples were found by Scherk. These include the surfaces now called “Scherk’s minimal surface,” “Scherk’s fifth minimal surface,” and a family of surfaces that includes both the catenoid and the helicoid.
