Re: Illusion and Forthrightness in Wikipedia

[Timothy Porter <t.porter@bangor.ac.uk>]

   The parametrisation given corresponds to the symmetric placing of the
trefoil on a torus, the fact that you get the `lumps' is an artifact of
that.  The knot parametrisation can neatly `turned around' changing the
role of p and q. That is also a trefoil!

Have fun,
Take care.  Don't tie yourself in knots :-)

Tim

On 13/09/2010 01:11, Fred E.J. Linton wrote:
> These somewhat off-topic remarks are at least almost as connected
> with category theory as the study of knots is, as they have their
> origin in my reliance on, and subsequent disillusionment with, the
> Wikipedia site for basic information about a certain knot.
>
> The knot? -- the familiar trefoil knot, aka (2,3)-torus knot.
> The offending Wikipedia page? -- http://en.wikipedia.org/wiki/Torus_knot .
> The problem?
>
> A reader might be forgiven for expecting that when a page of mathematical
> text offers a parametrization, in the form
>
> x = (2 + cos((q phi)/p))(cos(phi)) ,
> y = (2 + cos((q phi)/p))(sin(phi)) ,
> z = sin((q phi)/p) ,
>
> of each (p,q)-torus knot, and then offers an illustration dubbed
> (2,3)-torus knot, that said illustration might have been produced
> by means of the p=2, q=3 instance of the parametrization given.
>

...


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