Steiner's calculus problem

Steiner's problem, asked and answered by Steiner (1850), is the problem of finding the maximum of the function It is named after Jakob Steiner.

, where e denotes the base of the natural logarithm.

One can determine that by solving the equivalent problem of maximizing Applying the first derivative test, the derivative of

and negative for

, which implies that

– is increasing for

is the unique global maximum of