Optimization

Least, most, greatest, best, worst, biggest, smallest, fastest, coolest, maximization, minimization, optimal, etc.

From Wikipedia:

"In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set."

• the optimal shape for free soap bubbles is the sphere;
• the optimal shape for fencing the greatest area with the least perimeter is the circle;
• the shortest path between two points is a straight line (at least in Euclidean geometry!).
• the most beautiful (most elegant) proof of the Pythagorean theorem is ....

Avoiding waste in a complicated water system is obviously to be desired, and the optimal system might be defined as the one in which there is zero waste (a minimum of a function, the waste function!).

Ideas related to optimization:

• Symmetry
• Using the right tool for the job (the "best" tool).
• Solving multiple problems at once (e.g. "multi-tasking"; getting the "biggest" bang for the buck; killing the most birds with one stone).
• Buffering -- why adding a buffer into a system smooths out performance.

As an example of a non-standard example of mathematical optimization, I needed to create a four-hole latrine in a market in Kabou, Togo, West Africa. The group I was working with wanted to put the toilets in a line, but I had: a better idea (the middle picture -- view from the top). Even though one may have a better, it doesn't mean that anyone will pay any attention -- my group didn't!;)

Question: why do I believe that I could save material costs using this "back to back" design?