Dictionary.net

(Math.) The problem of finding the side of a square equal in area to a circle of given radius. It is understood that the solution is to be obtained either by elementary geometry, or is to be expressed arithmetically by commensurable numbers : under these conditions the problem is insoluble. Two squares can, however, be determined, one greater and the other less than the circle, whose areas differ by less than any assigned quantity, however small -by a quantity bearing, for instance, a ratio to one of the squares less than the ratio of one square inch to a million square miles.