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> 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?

I don't see how pi would change. No matter how the disk is moving, it will either look like a circle or an oval... If you are seeing it under conditions when "pure" Lorentz contraction is visible, it will look like an oval, otherwise, it will look like a disc. Neither of these involve any magical geometry, like Terry Prachett's five-sided squares. Take a picture of the disk and it will either look like a circle or an oval. Become comoving with the disk, and you measure it as a circle. In either case, pi pops out as per normal.

> Curiouser and Curiouser.

Indeed.

Marc Taylor
Manager, Planetarium and Science Programs
Hudson River Museum
511 Warburton Avenue
Yonkers, NY 10701
914 963 4550 x223
Fax 963 8558
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www.hrm.org
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