What is the maths behind tautochrone?

The type of tautochrone's mathematics, in general, depends on the particular time in the history of our civilization. read more

Using the first method you may say, e.g., that the point [math]P[/math] is the point you arrive at when, starting at [math]P_0[/math], you travel along the circle counter-clockwise a distance of [math]1.678823[/math]. read more

There is a lot of history behind the study of the cycloid, as noted from the wikipedia article cited above shows, so there is an endless supply of interesting applications of math and a lot of unsolved math mysteries for those who want to make a difference. read more

Such curve is called `tautochrone', which means `same time' in Greek. This curve turned out to be a cycloid, and later John Bernoulli and Euler independently proved the converse statement: every tautochrone is a cycloid. This was one of the earliest applications of differential equations. read more