Wavy Skirt Surface

Kim Horstman
George Mason University Math 401: Mathematics through 3D Printing
11/8/2020

In multivariable calculus, we learned about partial derivatives and their applications. The most notable of those was the use to locate critical points for a two-variable function. A critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero. The second derivative test is used to identify a critical point as a local maximum, local minimum, or saddle point. A saddle point is a point on the surface of the graph of a function where the slopes/derivatives in orthogonal directions are all zero (critical point), but which is not a local extremum of the function. The name comes from the fact that the example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a saddle or a mountain pass between two peaks.

There are many types of saddles ranging from the