The Cissoid of Diocles is an effort by ancient greek mathematician Diocles to solve the problem of doubling the cube. Mythologically, this doubling was a challenge given by the gods to the Athenians to make an alter double the size of an original. The Athenians constructed an alter with length, width, and height twice the original – but the gods were unimpressed because, by size, they meant volume, not the dimensions. The volume of the resulting alter was actually eight times the original, and not the prescribed doubling. The gods are picky.

Anyway, Diocles’ effort to solve this problem, loosely with a nod to the Euclidian restraints of simply a straight-edge and compass, is a graph with a “ivy-shaped” set of curves (hence the name) that establish a relationship of two mean proportionals to a ratio.

Diocles was fascinated by conic sections, and his notes, “On Burning Mirrors”, he explores the focal points of parabolas in search of an optimal focus.