A surface that has the least surface area among all surfaces with a given boundary i...

A surface that has the least surface area among all surfaces with a given boundary is called a minimal surface. Soap bubbles are naturally occurring examples of minimal surfaces. It is a fact that minimal surfaces having equations of the form z = f (x, y) (where f is of class C²) satisfy the partial differential equation

Exercises 31–33 concern minimal surfaces and equation

One way to describe the surface known as the helicoid is by the equation x = y tan z.

(a) Use a computer to graph a portion of this surface.

(b) Verify that the helicoid is a minimal surface.