Andrew the Orchid wrote:

>> Well, if it's the same as the first knot, below, and I think it is, 
>> then it's a "3,2 Torus Knot" (which I generated using KnotPlot -- 
>> http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html )
>>
>> In which case, using KnotPlot, I deformed it (continuously, so it 
>> should be topologically equivalent) to the second knot, below, which 
>> looks somewhat familiar ;-)
> 
> 
> OK, now I'm puzzled...
> 
> The first image does indeed appear to be the same knot - as far as I can 
> tell. And yet, you claim it's topologically equivilent to the trefoil 
> knot. And yet... I computed the Jones polynomial for it, and it's 
> different to either of the trefoil knots...
> 
> Well, one of us has fluffed up somewhere :-S Since the procedure you 
> undertook is simpler, I suspect it was me :-$
> 
> Andrew.

I noticed that, too, but, as you noted, I didn't do anything 
mathematical, just clicked "go" and let it tighten itself up (or is it 
loosen itself up?) and it quite apparently transformed without ever 
disconnecting.  I haven't calculated a Jones polynomial since grad 
school, which is too many years ago.  I best look it up.

Dave Matthews

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