Tautochrone

The tautochrone, or inverted cycloid curve, was discovered by Galileo in the 17th Century. The word itself is derived from the Greek words tauto, meaning the same; and chronos, meaning time.

To picture what an inverted cycloid curve looks like, imagine the line traced in the air by a chalk mark on the wall of a tire as the wheel rotates. It's like an arch, right? Now, invert the arch to get a trough-like shape. The interesting property of this curve is that a ball-bearing, placed anywhere on the wall of the "trough", will always take the same amount of time to reach the bottom of the curve.

The tautochrone came to the attention of 17th Century Dutch scientist and mathematicican Christiaan Huygens whilst pondering the periodic accuracy of a pendulum as a function of the size of the arc it described. He discovered that using an inverted cycloid as part of the regulatory mechanism of a pendulum greatly reduced the influence of the size of the pendulum swing on its period.

Tau"to*chrone (?), n. [Gr. , for the same + time: cf. F. tautochrone.] Math.

A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone.

 

© Webster 1913.