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Re: torus?

I dunno about the flatness, but Martin Gardner blew my mind back in
the '60's when he said that a torus could be 'turned inside out'.
(thru a small slit)

If you paint a RED stripe around the hole of the torus on the INNER
surface and a GREEN stripe perpendicular to it on the OUTSIDE
surface, they are topologically linked. (clearly)

Turn that sucker inside out (a legal operation) and take a peek at the rings.

This sent me to my mom's cloth scrape box and the sewing machine.

I STILL have to get my hands on something to be able to begin understanding it.

As any topologist knows, a doghnut is equivalent to a coffee
cup, so why get excited about ANY of this.


I suspect that the 'ideal' torus is an 'idea' cylinder with it's ends
joined in a particular way. Join 'em the OTHERway to get your basic
Klein Bottle.

Since the ideal cylinder isn't really curved, then the doughnut isn't either.





At 10:43 PM -0700 on 10/16/01, Bernard Cleyet wrote
Does one have to cut it to lay it flat?

Is the above the test?

bc



"RAUBER, JOEL" wrote:

If I remember correctly:

An ordinary torus, (the ideal donut), T2 = S1XS1, has a surface that is two
dimensional and the surface has intrinsic curvature.

Is this correct?

Joel R

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