Hi, just to get more off-topic... ;-)
On Mon, 8 Nov 2010 20:01:19 +1100 (EST) Ian Smith <smi...@nimnet.asn.au> wrote: > And while a square enclosing a circle, it's hardly squaring the circle: > http://en.wikipedia.org/wiki/Squaring_the_circle .. but an interesting > read nonetheless for unrequited seekers of pi-foo :) In our case, it is as possible/exact as computing pi. When computing pi, you resolve to the same problem as you have when 'squaring' a circle: Transcendental numbers over the given field. Just having rational numbers, you can just approximate pi, and as a human or computer, one doesn't have the power to imagine pi or give it an exact value. And I don't know, but doubt there's someone who can imagine anything else than rational or at least over Q algebraic numbers. The same with the squared circle: You can approximate it, but over the the field of the constructible numbers, the length is transcendental, so you cannot exactly draw it without further assumptions. Regards, Julian
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