The fastest way down is not a straight line
Quarx1 min read
Johann Bernoulli posed it as a challenge to the mathematicians of Europe. Newton solved it overnight and sent it back unsigned.
In June 1696 Johann Bernoulli asked a question that sounds trivial: given two points at different heights, what shape of ramp gets a ball from one to the other fastest? Not the shortest path — the fastest.
The answer is a cycloid, the curve traced by a point on the rim of a rolling wheel. It dips below the straight line, trading distance for early speed, and it wins every time.
Newton reportedly received the problem after a day's work at the Mint, solved it before morning, and published anonymously. Bernoulli is said to have recognised the author immediately — ex ungue leonem, you know the lion by its claw.