Editing Maximum modulus principle (section)

===Using Gauss's mean value theorem===
Another proof works by using [[Cauchy's integral formula#Consequences|Gauss's mean value theorem]] to "force" all points within overlapping open disks to assume the same value as the maximum. The disks are laid such that their centers form a polygonal path from the value where <math>f(z)</math> is maximized to any other point in the domain, while being totally contained within the domain. Thus the existence of a maximum value implies that all the values in the domain are the same, thus <math>f(z)</math> is constant.