Squaring the Circle Revisited

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.

Mandala Mosaics at Flickr

From krazydad at Flickr, we have these wonderful mosaic images.

A Sufi Story

One day a neighbor found Mullah Nasruddin sitting in a tree in his garden, in the process of sawing off the limb on which he was sitting.

"Mullah, you'd better stop, otherwise you'll fall down," said the neighbor, then went back inside his house. Sure enough, Mullah kept sawing, the limb broke, and he fell. Mullah ran next door and pounded on his neighbor's door.

"O, great one, please forgive me," said Mullah, "I didn't know I had a psychic for a neighbor! Could you please predict what will happen to me tomorrow?"

The neighbor tried to deny that he could predict the future, saying that what he had told Mullah was just common sense. But Mullah wouldn't listen and kept after him. Finally, the neighbor became exasperated and said, "Mullah, for heaven's sake, for all I care you can drop dead tomorrow!"

The next morning, Mullah woke and said to his wife, "Our neighbor is a psychic and he told me that I would drop dead today, so I have to prepare." He took his donkey along for company and went to the graveyard, then dug a grave for himself and lay down in it. As the day ended, he was still lying there and thought, "I must be dead now. This isn't really so bad!"

Then a pack of dogs came by and started harassing his donkey. The donkey began to bray and make a racket. Finally, Mullah yelled from the grave, "You dogs - get out of here! If I weren't dead I'd get out of my grave and give you a thrashing!"