It is impossible to construct circles and squares of equal areas or perimeters precisely, for circles are measured by the incommensurable value pi (π) and squares by rational whole numbers. But from early times, geometers have attempted to reconcile these two orders of geometry. “Squaring the circle” can represent the union of opposing eternal and finite qualities, symbolizing the fusion of matter and spirit and the marriage of heaven and earth. In this column, we consider various methods for squaring the circle and related geometric constructions.