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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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