  If A and B are two points in the plane, with B lower and to the right of A,
then we may consider the trajectory of an object travelling from A to B under
the influence of gravity. The search for the trajectory minimising the time
taken by the object gives rise to a mathematical optimisation problem involving
an indefinite integral. Although the solution of this problem is known, a full
detailed handling of the problem does not seem to be available. The aim of this
article is to provide such a detailed study.
