This shows the shape of the brachistochrone from the origin to a variable final point. The circles indicate the position of the sliding point at equally spaced times.

More than 300 years after Johann Bernoulli published the "problema novum" in Acta Eruditorium in the summer of 1696, the new Manipulate feature of Mathematica 6 shows the solution curve, a brachistochrone, in an interactive way.