
Thoughts about Pi - wkoszek
http://www.colorforth.com/pi.htm
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agjacobson
Diameters might appear in drawings. But they NEVER appear in physics. (The
distance between particles determines forces. Diameters are a boring parameter
about the size of something.) Machine tool programming is mostly radii in the
paths, and diameters in the setup parameters.

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avmich
> Diameters might appear in drawings. But they NEVER appear in physics.

Even as a characteristic size in, say, Reynolds number definition?

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sebastos
The statement about the diameter being the interesting parameter is kind of
exactly wrong. This is true for all the same reasons Tau is a better constant
than Pi.

For example, how does one derive the area of a circle? The most natural way is
to integrate with respect to radius. When using Tau and radius, you get A =
(1/2) _Tau_ r^2, which is nice since it looks a lot like the integral of, say,
momentum, which gives you kinetic energy. If you use Pi or diameter or both,
then weird factors of 2 start to creep in. It's also much more natural to
think about defining the radial extent at each angle, rather than the
diameter, especially if you're dealing with something other than a circle that
has changing radius.

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gaze
Tau is not happening.

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delish
I'll echo what gp said to help make tau happen:

 _tau_ : the circumference (perimeter) of a circle.

(1/2) _tau_ ^2 : the area of a circle.

Beautiful. To go from one to the other, you integrate or take a derivative.
Like gp said, there's no weird factor of two. Just the power rule in action.

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drdeca
You seem to have left out the r in both of those expressions.

Tou r. .5 tou r^2 .

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cmiller1
Nope, all circles have a perimeter of 19.7392088022.

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agjacobson
Yeah but the radius of the moon's orbit is sure interesting.

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alimw
Your conjecture as to the surface area of a hypersphere embedded in 4
dimensions (a "3-sphere") is not borne out :) The answer is in fact d^3 pi^2 /
4\. See
[https://en.wikipedia.org/wiki/N-sphere#Volume_and_surface_ar...](https://en.wikipedia.org/wiki/N-sphere#Volume_and_surface_area)

