Hubert Mantel wrote:
> On Mon, Feb 08, J-L Boers wrote:
>
> > / PPS: Want some challenge? Find the formula that gives you a torus ;-)
> >
> > It's pretty neat.The flat torus formula:
> >
> > [u,v] -> [cos(u + v), sin(u + v), cos(u - v), sin(u - v)]/sqrt(2)
> >
> But that's too easy. The question was meant to be: Find an equation
> f(x,y,z)=0 so that all solutions of the equation form the surface of a
> torus. To be honest: I don't know the solution. I even don't know if this
> equation exists ;)
Well I havn't looked at my Vector Calculus books in about 20 years, but
I found a set of formulas in "toroidal coordinates" for a torus.
They are quite complicated:
I will give the x equation only, but there are y, and z ones also.
x = ((a)sinh(v)cos(w))/((cosh(v)-cos(u))
where "a" is a constant, and u,v,w are the toroidal coordinates,
w is actually an angle theta.
If you want, I could scan the page with the full formula set,
including a cartesian coordinate graph , and email it to you.
But it would probably delay work on Suse 6.0 . :-)
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