What Is So Mysterious About “Squaring The Circle”?

“Said the man about town, ‘I have a flair for Squaring The Circle, I swear.’ But he found that the strain was too great for his brain, so he’s gone back to circling the square.”

These quoted words were hand-scripted on the title page of Squaring The Circle, A history of the Problem by E. W. Hobson, published in 1913. Whoever penned the quote obviously came to the conclusion that squaring the circle was not possible. John Robinson in a commentary summed up the problem ever so simply: How can one geometrically construct a square equal in area to a given circle? This is considered one of the great mathematical mysteries of all time, argued since Aristophanes who in the Fifth Century concluded it was impossible, but he never really proved or disproved it,  irking mathematicians for over two thousand years until Lindermann verified that the circle cannot be squared using a compass and ruler because PI is transcendental.

Why do mathematicians, scientists and philosophers have to make everything so complicated?

Perhaps one way to solve it is by drawing a Celtic cross on the circumference of the circle, then connecting the endpoints to create a square, using a ruler to draw the straight lines, literally “squaring the circle.” Moving the square around its center proves the same circle, outlined without needing a compass. Even though the square initially looks diamond-shaped, it’s still a square, just a different perspective of the same thing created by rotation.

If you want to get technical about it, it’s really Cubing the Sphere, not Squaring the Circle, since we live in a three dimensional world. Extend the  center point of the circle into space and draw the four sided pyramid, which is one half of the cube. Continue the line in the opposite direction in space and draw the other pyramid not seen from a two dimensional perspective and you have the cube contained within the center of the sphere. The only way one could see the whole sphere at the same time is by being everywhere. Since that isn’t possible, the position one is viewing the object defines what is capable of being seen at any given moment, unless of course it’s invisible, than one wouldn’t see anything.

By rotating the square 360 degrees in space, where time is defined as the fourth dimension, the circle, outlined from the intersecting points on both geometric figures, proves that the square (cube) and the circle (sphere) are the same. The only difference is perspective. Area is insignificant since a circle is nothing more than the spherical revolution of an object around a center created by the pull of gravity, suggesting Particle Physics. Moving one’s position in space reveals that the circle is in fact a spiral from a bird’s eye view, unable to see the other levels because everything is superimposed in slinky formation. Forget PI. Don’t worry about infinity, non-rational integers, complex computations, or intricate algebraic formulas. All are unnecessary details used to promote insecurity in those illiterate in the ways of the scientific method and detracting from the philosophical nature of what the problem is meant to convey. That is the real mystery of “squaring the circle.”

Perspective will always be limited by finite consciousness requiring one to “think outside the box or the sphere” since appearances can be deceiving. In fact, moving farther away (in space) from the square one no longer sees the four-sided polygon, or the circumference of a circle. One only sees The Point. So, realistically speaking, it doesn’t matter whether you start with a circle or a square, since everything is an optical illusion anyway, said the man about town, “I’ve a flair for Squaring The Circle, I swear. But I found that the strain was too great for my brain, so I’ve gone back to circling the square.”

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