## Quick Reference

Suppose that *A* and *B* are points in a vertical plane, where *B* is lower than *A* but not vertically below *A*. Imagine a particle starting from rest at *A* and travelling along a curve from *A* to *B* under the force of gravity. The curve with the property that the particle reaches *B* as soon as possible is called the brachistochrone (from the Greek for ‘shortest time’). The straight line from *A* to *B* does not give the shortest time. The required curve is a cycloid, vertical at *A* and horizontal at *B*. The problem was posed in 1696 by Jean * Bernoulli and his solution, together with others by * Newton, * Leibniz and Jacques Bernoulli, was published the following year.

*Subjects:*
Mathematics.