As an art student, you’re hit over the head repeatedly with Renaissance art, so I’ve gotten a little tired of it, but something I’m not tired of is the seemingly impossible naturalistic detail attained from stone and a chisel back then.

This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.

If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?

Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.

Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.

MINNEAPOLIS (The Borowitz Report)—Historians studying archival photographs from four decades ago have come to the conclusion that the U.S. must have believed in science at some point. The New Yorker