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## August 8, 2017

### The shortest time between two points is NOT a straight line

From Curiosa Mathematica:

The BrachistochroneThis animation is about one of the most significant problems in the history of mathematics: t

he 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

timehappens when the ramp curve is the one shown: acycloid.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.

August 8, 2017 at 12:01 PM | Permalink