Stan Tenen – Squaring the Circle: The One & the Many, Mind & World

Stan Tenen – Squaring the Circle: The One & the Many, Mind & World

Published on Jun 26, 2012 by

http://www.meru.org/3220lecture/stpresrl.html

Here is an unexpected philosophical solution to the central mathematical riddle of the ancient world: Is there a way to express the transcendental – Pi – relationship between the radius and circumference of a circle (“squaring the circle”) using only a straight-edge and a compass? Mathematicians are certain this is not possible, because they’ve proven there can’t be an exact geometric construction for any transcendental number.

Scholars are not certain how the riddle of squaring the circle was understood in the ancient world. Most scholars, who read the riddle in an exclusively mathematical context, believe that the Greek mathematicians did not know that the problem wasn’t possible to solve exactly. These scholars believe that ancient mathematicians were speaking plainly about a real problem in geometry whose solution they were actually seeking.

Other scholars are not so sure. They believe that the riddle of squaring the circle was a way of teaching about important philosophical concepts that were based on geometric thinking. For these scholars the riddle is not seeking an exact geometric construction for its resolution. Unfortunately, even scholars open to a philosophical solution have not been able to propose one. [For more information on how the ancient world may have viewed this problem, see Background Information on Quadrature.]

Tenen reminds us that the letters of the traditional western alphabets, Hebrew, Greek, and Arabic, are claimed to be sacred, and that name implies an explicit way in which these alphabets are also, like the Pi relationship, transcendental.

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2 thoughts on “Stan Tenen – Squaring the Circle: The One & the Many, Mind & World

  1. Re: “Is there a way to express the transcendental – Pi – relationship between the radius and circumference of a circle (“squaring the circle”) using only a straight-edge and a compass?”

    Theoretically, “Yes”.

    Consider the geometry of these recent “Pi Corral” designs which display the unique scalene triangle that squares the circle: http://www.aitnaru.org/images/Pi_Corral.pdf

    The intrigue of this new perspective of Pi is that the perfect scalene triangle does exist somewhere in the transition from the smallest square of a circle to the largest square. When discovered, the bottom horizontal line of the scalene reflects the square root of Pi … regardless of the number of decimal digits!

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