The Pi-angle

It has been assumed for eons that the universe could be explained as containing dimensions and that these dimensions were sequential. One dimensional space is an indivisible point, two dimensional space is at least two one dimensional points connected by a line and three dimensional space is at least three of these two dimensional lines on at least two planes. There may be other dimensions but they're too hard to explain so I'll just ignore them. There is a problem however: There is no two dimensional space, it's just a convenient abstraction.

The absence of a second dimension is only apparent with an object having some curved component, a circle for instance. We are taught that circles are derived by multiplying the diameter of a circle by pi which will give us that circle's circumference. Thing is, pi is ugly. It's an irrational number not only because the fractional portion of the number continues forever, but also because it makes no sense. The fractional part of pi assumes that there really are two dimensions when it actually comes from trying to render a two dimensional object in three dimensions. A circle starts to make sense when drawn on a curve where, depending on the curve, pi will equal three.


The constant, pi, is just an unnecessary complication. In reality it's a rendering error (RE) of just over 4% (4.7197551% to be fairly precise) that results from trying to render three dimensions as two dimensions. What this means is that the diameter of any circle actually 4% longer because it's really a curve that we insist on seeing as a straight line.

What happens is that we look at the diameter of a circle from above so it appears as a line. Rotate it 90 degrees and we can see its curvature. Since we don't think we can rotate a two dimensional circle in three dimensions, we never see the curve.

So why care? Will correcting this error really change anything? Consider that the standard circle using pi doesn't exist in nature, it's wholly artificial, a shortcut. This error is incorporated into everything we build having curved elements. This include machinery, architecture, bubble gum and sport equipment and pocket calculators.

(see this)

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