Collection: d'Alembert's Formula

While he made great strides in mathematics and physics, the French polymath Jean-Baptiste le Rond d’Alembert (November 1717 – 29 October 1783) is also famously known for incorrectly arguing in Croix ou Pile that the probability of a coin landing heads increased for every time that it came up tails. In gambling, the strategy of decreasing one’s bet the more one wins and increasing one’s bet the more one loses is therefore called the D’Alembert system.

Nevertheless, D’Alembert’s formula for obtaining solutions to the wave equation is named after him. The wave equation which provides a solution to the one-dimensional wave equation, was derived in 1747 as a solution to the problem of a vibrating strings that proceeded along new and very different lines. His innovative work was made possible by two advances. First, the proportionality of force to the time rate of change of momentum had come to be recognized as a general principle that could be applied to a wide range of physical problems. Second, during the 1730s researchers gained experience with partial differential equations as they investigated such mathematical problems as the construction of orthogonal trajectories to families of curves.