\begin{definition}[Definition:Brachistochrone]
Let a point $A$ be joined by a wire to a lower point $B$.
Let the wire be allowed to be bent into whatever shape is required.
Let a bead be released at $A$ to slide down without friction to $B$.
The shape of the wire so that the bead takes least time to descend from $A$ to $B$ is called the '''brachistochrone'''.
\end{definition}