What shape does a chain hanging between two posts make? Galileo guessed wrong
Hang a chain loosely between two fixed points and let it sag under its own weight. Galileo Galilei claimed in 1638 that the resulting curve was a parabola, the same shape as a thrown ball's path. Decades later, Jakob Bernoulli publicly challenged other mathematicians to find the true equation. Was Galileo's guess correct?
Reveal the answer
No. In 1691, Gottfried Leibniz, Christiaan Huygens and Johann Bernoulli independently showed the true shape is a catenary, described by a hyperbolic cosine curve, which only looks similar to a parabola at a glance but has a distinct mathematical form. The curve's name comes from the Latin catena, meaning chain, and the same shape shows up today in the St. Louis Gateway Arch, built upside down for structural strength.