The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.
Most of us have little trouble working out how many millilitres are in 2.4 litres of water (it’s 2,400). But the same can’t be said when we’re asked how many minutes are in 2.4 hours (it’s 144).
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