Fine Shambles – Code. Juggling. Baking. Or not.
No matter how you slice it and dice it, you get out the same information. Well, that's not exactly true. But I'll show you one way you can look at individual slices of a shape in order to determine its overall topology.
This is basically a hollow donut with legs. Said differently, it's a shell of a sphere with a hole in it (so it's like a torus), with the lower bits stretched out. This three-dimensional shape has six total local minima and local maxima, which are called critical values. They are labelled as \(a_1\) through \(a_6\) .
We are going to look at one particular strategy we can use to slice this shape into smaller pieces. We'll then look at each piece individually and determine what shape it is. For example, each piece could be a point or a circle or a sphere or something else. We'll also take note of how many consecutive slices contain each particular shape.
Fine Shambles – Code. Juggling. Baking. Or not.