Swoopet

Meet Swoopet, a rolling ball who knows that the shortest path is not always the fastest.

In 1696 Johann Bernoulli challenged the best mathematicians of Europe. Which curve lets a bead slide from one point to a lower point in the least time, under gravity alone? The answer is called the brachistochrone, from the Greek for shortest time.

A straight line is the shortest path, but the bead starts slowly. A curve that drops steeply first builds speed early, and that speed carries it the rest of the way. The best curve is a cycloid, the path traced by a point on a rolling wheel.

For a cycloid made by a wheel of radius r, a bead released from the top reaches the lowest point in t = π√(r/g), and it takes the same time from any starting point on the curve. With r = 1 m the trip takes about 1.0 s.

Newton, Leibniz and the Bernoulli brothers all solved it. The problem helped launch the calculus of variations, used today in physics and engineering.