From the text: The golden mean is often naively seen as a sign of optimal beauty but rarely does it arise as the solution of a true optimization problem. In this article the authors present such a problem, demonstrating a close relationship between the golden mean and a special case of Newton’s aerodynamical problem for the frustum of a cone. Then, they exhibit a parallel relationship between the general case of this problem and a general family of means called POEM’s (for \(p\)th order extreme means). The POEM’s share with the golden mean certain algebraic and geometric properties, and also a remarkable minimizing physical property. Sadly, here is yet another situation in which an interesting property of the golden mean is not unique but is matched by the other means.