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Mathematics

Calculus of Variations and the Brachistochrone Problem

Quick fact

The solution to the brachistochrone problem is a cycloid—the curve traced by a point on a rolling wheel—which is faster than a straight line and even faster than an arc of a circle.

Why this is interesting

What if the fastest path between two points isn't a straight line? In 1696, Johann Bernoulli challenged the world's best mathematicians with this very puzzle—and the answer reshaped physics.