Quickest Way Down

Can you predict which path will be the quickest? Test your prediction.

Why do you think this path is the quickest?

What happens if you release the ball at a different point?

The shortest distance between two points is a straight line, but thanks to gravity and acceleration, it is not the quickest way down. Instead, you will discover that the quickest way down is one of the curves.

The curve is called a brachistochrone, which means “shortest time”. This curve is quicker because it starts off steeply which allows the ball to accelerate quickly. The other curve is related. This curve will take the same time no matter where the ball is released.

This curve is called a tautochrone, which means “same time”. The two curves are related because they are both part of the curve drawn by a point on a circle as it rolls along the ground. This curve is called a cycloid.

A tautochrone can start at any point on the cycloid, but always ends horizontally. A brachistochrone can end at any point on the cycloid, but always starts at the top of the cusp.