This is a slight thing that crossed my reading yesterday. You might enjoy. The question is a silly one: what’s the “optimal” way to slice banana onto a peanut-butter-and-banana sandwich?
Here’s Ethan Rosenthal’s answer. The specific problem this is put to is silly. The optimal peanut butter and banana sandwich is the one that satisfies your desire for a peanut butter and banana sandwich. However, the approach to the problem demonstrates good mathematics, and numerical mathematics, practices. Particularly it demonstrates defining just what your problem is, and what you mean by “optimal”, and how you can test that. And then developing a numerical model which can optimize it.
And the specific question, how much of the sandwich can you cover with banana slices, one of actual interest. A good number of ideas in analysis involve thinking of cover sets: what is the smallest collection of these things which will completely cover this other thing? Concepts like this give us an idea of how to define area, also, as the smallest number of standard reference shapes which will cover the thing we’re interested in. The basic problem is practical too: if we wish to provide something, and have units like this which can cover some area, how can we arrange them so as to miss as little as possible? Or use as few of the units as possible?
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