The mosiacs from the Squared Circle group at Flickr tweaked my curiosity and I started wondering if a Mandala really does qualify as a "squared circle." My internet search for the meaning of this phrase landed me at Wikipedia from which comes the following explanation:
"Squaring the Circle is a problem proposed by ancient geometers. It is the challenge to construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.
In 1882, the task was proven to be impossible, as a consequence of the fact that pi (π) is a transcendental, rather than algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for some decades before then that if π were transcendental then the construction would be impossible, but that π is transcendental was not proven until 1882. Approximate squaring to any given non-perfect accuracy, on the other hand, is possible in a finite number of steps, as a consequence of the fact that there are rational numbers arbitrarily close to π.
The term quadrature of the circle is sometimes used synonymously, or may refer to approximate or numerical methods for finding the area of a circle."
Well, that started out simply enough, and then it went right over my head. Math was never my best subject.