The parametric form of this curve is given by x equals r times quant.
A pendulum constrained by inverted examples of this curve will have a path that follows a congruent, inverted example of this curve, which can be used to create isochronous pendulums for clocks. Roberval derived the area under this curve by using the method of indivisibles due to Cavalieri. The parametric form of this curve is given by x equals r times quant. t minus sine t and y equals r times quant. one minus cosine t. This figure is the fastest path by which a body can travel from one point to another under the influence of gravity, making it the solution to the brachistochrone problem. For 10 points, name this curve traced out by a point on a rotating circle traveling along a line.
A pendulum constrained by inverted examples of this curve will have a path that follows a congruent, inverted example of this curve, which can be used to create isochronous pendulums for clocks.
cycloids