Our goal is to show how graphics can assist in studying the geometry of a surface in R3. Of course, a picture of the surface itself is often helpful, but there are other possibilities. Sometimes a graphic may actually constitute a proof, but its more common functions are to suggest what can and should be proved, or to verify the reasonableness of an analytical proof.
We consider two cases:
Kummer's surface is a simple, highly symmetrical surface, and the problem is to completely describe its Gaussian curvature K. This is not entirely trivial. For example, it is clear by inspecting a plot of the surface that K is never positive, but does K take on minima or maxima? and if so, where?
By contrast, Kuen's surface is a quite complicated surface, whose Gaussian curvature could not be simpler: it has constant value -1. The surface is made of smooth pieces welded together along creases and edges. The problem is to see what the individual pieces are like and exactly how they fit together. So this case might better be described as Geometric-Assisted Graphics.