(ex + e−x)/2: The Hanging Chain
Therefore, I have attacked [the problem of the catenary], which I had hitherto not attempted, and with my key [the differential calculus] happily opened its secret.—GOTTFRIED WILHELM LEIBNIZ, in Acta eruditorum (July 1690)
We are not quite done with the Bernoullis yet. Among the outstanding problems that occupied the mathematical community in the decades following the invention of the calculus was the problem of the catenary—the hanging chain (from the Latin catena, a chain). This problem, like the brachistochrone, was first proposed by one of the Bernoulli brothers, this time Jakob. In the May 1690 issue of Acta eruditorum, the journal that Leibniz had founded eight years earlier, Jakob wrote: “And now let ...