A wine merchant's lazy pricing trick turned out to be nearly impossible to cheat
Austrian wine merchants priced a barrel by pushing a measuring rod diagonally through the bunghole to the far bottom rim, and charging purely by that one length -- never mind the barrel's height or width. A mathematician, annoyed at being charged this way at his own wedding, wondered: could a barrel-maker exploit this rule to cheat the merchant, just by choosing the barrel's proportions cleverly?
Reveal the answer
Not easily -- Kepler found that the traditional wine-barrel shape sits remarkably close to the volume that actually maximizes for a given diagonal rod length, so the lazy rule turns out to be nearly fair. He worked this out in Nova Stereometria Doliorum Vinariorum (1615), using proto-calculus decades before Newton and Leibniz, sparked by a real wine purchase at his own 1613 wedding.
— Johannes Kepler, Nova Stereometria Doliorum Vinariorum — 1615