
 The Helen of Geometers 
  The curve traced out by a point on the rim of a rolling circle is called a cycloid, and we've seen that this curve described gravitational freefall, both in Newtonian mechanics and in general relativity (in terms of the freefalling proper time). 
  Mersenne publicized the cycloid among his group of correspondents, including the young Roberval, who, by the 1630's had determined many of the major properties of the cycloid, such as the interesting fact that the area under a complete cycloidal arch is exactly three times the area of the rolling circle. 
  Thus he had discovered that the cycloid is the tautochrone, i.e., the curve for which the time taken by a particle sliding from any point on the curve to the lowest point on the curve is the same, independent of the starting point. 
 www.mathpages.com /rr/s803/803.htm (1364 words) 
