Revisiting the Squinch: From Squaring the Circle to Circling the Square

“Squaring the circle,” constructing a square that has the same area in a given circle using compass and straightedge, has long been a subject for intellectual investigations among mathematicians and philosophers from antiquity to the pre-modern era. The search for this unattainable ideal articulation found its way into Persian architecture with a different approach: circling the square. This architectonic approach, complementing the philosophical view, started from the square at hand, the chamber, to the circle of the vault. The transformation of the cubic to the domical space is mediated through the squinch, intermediary structural element that unifies the two structures. The two seemingly opposite directions of transforming of one form to another (i.e., square to circle or vice versa) allude to the metaphysical and material attributes involved in this process. This paper discusses the mutual relationship between the intellectual and material transformations and the intermediary role of the squinch.