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.