AbstractThe author raised the nature of the problem presented by the geometry and philosophy of quadrature in a letter to the Editor (Survey Review28, 221, pp. 372–373).This paper examines the background to the proven impossibility of the Quadrature of the Circle, offers methods for apparently achieving that quadrature, and poses questions concerning the validity of any proof of impossibility which is based upon a demonstration of the incommensurability ofπ.