![[identity profile]](https://www.dreamwidth.org/img/silk/identity/openid.png) kaet.livejournal.com |
Thu 2002-11-14 11:32 |
I accuse you, Mr Tatham, of being a Mathematician. Dishonourable indeed, :)! I suppose you're going to say that taking the result and looking it up in a large database of common constants and then checking if it works anlytically with the nearest entry is dishonorouble true? :)
As a mathematician, though, can I ask you a topology question? I'm just starting to learn topology, and aren't sure I've got the axioms sorted in my head.
I've heard a rumour that given an Euler number and whether something is orientable or not, then you precisely determine a topological solid. Furthermore, upon closer questioning, I've hear that there are only two non-orientable solids, the projective plane and the Klein bottle, modulo extra handles and, more importantly only one kind of orientable solid, the sphere (modulo extra handles). So if you take your average sphere and dig an 'ole through it, you've clearly got a torus. But what if you tie a simple knot in the 'ole? Clearly, because of the eminent folks, this is still a torus (it'll have the same Euler number and is still orientable). But how do you squidge it about? I can think of two possible answers. The first is that my mind isn't yet warped enough and there is a perfectly plausible way of deforming a sphere with a knotted hole into a torus in three dimensions. The second is that if the going gets tough you're allowed to invent extra dimensions to help you undo your knots.
Which, in your expert opinion, is it to be?
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