Inexpressible Number and the Secrets of the Erechtheion

Abstract

In the Classical period, the Erechtheion and the Parthenon were constructed opposite each other on the Acropolis of Athens. If the Parthenon represents perfection, what can be said of the Erechtheion? We are familiar with the idea that the perceived perfection of monuments such as the Parthenon is due in large measure to their proportional systems. Can such a system possibly be at work in the Erechtheion, a structure that otherwise seems the antithesis of the compositionally simple, perfectly pure Parthenon? Asymmetrical buildings closely configured to elaborate programmatic requirements are the norm in contemporary architecture, yet the Erechtheion continues to seem idiosyncratic, and the intentions of its designers obscure. Yet the exquisite beauty of its carving has always promised more. This paper will show that the Erechtheion does indeed follow a rigorous proportional scheme that is consistent down to its smallest details and which is located firmly within a Greek tradition as passed on to us by Vitruvius. The proportional apparatus of ancient Greek architecture, most often interpreted as relationships of rational numbers, will be shown to control the design of the Erechtheion through the rational approximations of irrational numbers as described by ancient authors. Keywords: Erechtheion, Vitruvius, Ionic order, irrational numbers, square root of two