A tautochrone curve is the curve for which the time taken by a particle sliding down it under uniform gravity to its lowest point is independent of its starting point. The time is equal to the Pi times square root of the radius over the gravitation contant. Gravitation is the tendency of masses to move toward each other. ...

The tautochrone problem, the attempt to identify this curve, was solved by Huygens in 1659. He proved geometrically in his Horologium oscillatorium (The Pendulum Clock, 1673) that the curve was a cycloid. However this Pendulum Clock due to high friction. This solution was later used to attack the problem of the brachistochrone curve. Christiaan Huygens Christiaan Huygens (pronounced in English ( IPA): ; in Dutch: ) ( April 14, 1629– July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. ... Events May 25 - Richard Cromwell resigns as Lord Protector of England following the restoration of the Long Parliament, beginning a second brief period of the republican government called the Commonwealth. ... Events The English Test Act was passed. ... Cycloid (red) generated by a rolling circle A cycloid is the curve defined by a fixed point on a wheel as it rolls, or, more precisely, the locus of a point on the rim of a circle rolling along a straight line. ... A Brachistochrone curve, or curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and passes down along the curve to the second point, under the action of constant gravity and...

Later mathematicians such as Lagrange and Euler looked for an analytical solution to the problem. Joseph Louis Lagrange Joseph Louis Lagrange (January 25, 1736 – April 10, 1813) was an Italian mathematician and astronomer who later lived in France and Prussia. ... Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler [oilər] (April 15, 1707 - September 18, 1783) was a Swiss mathematician and physicist. ...