A ball rolls from a high point to a lower one. What curved path gets there fastest?
In 1696, Johann Bernoulli challenged the best mathematicians in Europe with this problem: given two points, one higher than the other but not directly above it, what shape of frictionless slide lets a ball roll between them in the least possible time? Most people's first guess is a straight line. Is that actually the fastest route?
Reveal the answer
No — the fastest path is a cycloid, the curve traced by a point on the rim of a rolling wheel, which dips down steeply at first to build speed before leveling out, beating the straight line despite being a longer path to travel. Isaac Newton reportedly received the challenge, solved it overnight, and submitted his solution anonymously, though Bernoulli is said to have recognized the author immediately, remarking he could tell the lion by its claw.
— Johann Bernoulli, Problema novum ad cujus solutionem Mathematici invitantur — Acta Eruditorum, 1696