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the relationship of the surface of a sphere to its center point is equidistant from any point on the surface, which means that a radius drawn between the center and the surface will always be the same for all points on the surface of the sphere. and the circumference is always 2piR. Does that help?

The problem with the earth is, aside form not being a perfect sphere (it is slightly oblate so the radius will be longer at the equator than the poles, but not the circumference which should remain constant since it is a transform, not a reshaping), it is in motion, which gets to your next math problem. Anything moving changes its relative length (meaning relative to perspective on it from something either not moving--technically impossible--or moving differentially form the object being observed), even if it is not a significant fraction of the speed of light, its just that it is so slight as to be insignificant. 

Whenever I venture forth to areas in which I have incomplete knowledge (I know very little about relatively) I run the hazard of mischaracterizing something. I was told by a high end physicist once that no one really knows much about relatively and that if you think you know what it is, you don't know what it is.

Happy Pi Day!



Stephen Miles Uzzo, PhD.
VP, Science & Technology
New York Hall of Science
47-01 111th Street
Flushing Meadows Corona Park, NY 11368 USA
V +1.718.595.9177
F +1.718.699.5227








On Mar 14, 2013, at 5:07 PM, Eric Siegel wrote:

> A couple of pi questions on pi day:
> 
> 1) on a curve the ratio of the radius of a sphere to its circumference varies.  A line running from the north pole to the equator along the surface of spherical earth is 1/4 the length of the circumference at the equator.  Right?  Or am I missing something.
> 
> 2) even in planar geometry, I seem to remember reading that pi is variable depending on frames of reference.  Imagine a disk spinning at a significant fraction of the speed of light.  It gets shorter along the line of direction, in other words the circumference shrinks.  But a radius, which is not moving along the line of direction approaching the speed of light, doesn't shrink.  I think in Einstein's little book called Relativity this is an example he gives of how the "laws of nature" appear to change as you approach the speed of light.
> 
> Again, am I missing something?
> 
> Curiouser and Curiouser.
> 
> Eric


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