If you claim that because π is transcendental, the circle cannot be squared, I can respond

        In fact, there is no geometric operational difference between rational, irrational and transcendental numbers.  Mathematically they are all absolutely precise, with no fuzziness in the least.  Transcendental numbers occupy mathematical points on the number line that are exactly as determinate as points occupied by rational numbers and natural numbers.  The length of a line π meters long is no more or less fuzzy than the length of a line 1 meter long. But physically, all numbers of all sorts are limited in accuracy by the operation of measurement.  And they are limited to the same extent.  The number 1 measured to an accuracy of ± .0001cm is no different than the number π measured to that accuracy.  If you claim that because π is transcendental, the circle cannot be squared, I can respond that although the number 1 is natural and rational, and although your circle has a radius of 1, you cannot copy that circle.  You cannot precisely copy that circle for the same reason I cannot square it precisely, the reason being that neither one of us can make real measurements to zero-width points--or measure to an infinite precision.  http://milesmathis.com/square.html

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       “Squaring the circle” is the alchemical process of transferring an airy concept from the mental (or etheric) plane to the physical dimension so that objective conception and birth become a demonstrative reality.    –   Dr. John Mumford    https://joedubs.com/squaring-the-circle/

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Steps 5, 8, 10 below are shown in context at     http://www.themushroom.net/2011/06/squaring-the-circle-or-rather-circling-the-square/

(The ratio of the little square at lower left to the square with circle inside is close to 1 in 7, perhaps 1 in 6.9, as measured by me.  -r)

(Perhaps the real issue is:  why does one move toward top of paper a triangle by one small square's length?  What is the rationale of taking triangle a single square-step toward top of paper?  -r)

(There is this effect anyway:  the triangle's apex and the large square's center allow for a circle to be drawn with that radius. Suppose it was an "accidental" motive to move the triangle toward top of paper; pure sport, say--just wondering what would it look like.  Okay. -r)  Thanks to Cavan McLaughlin who apparently found this geometry about 2001 A.D.   -r