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 . :-) - To get out of this list, please send email to majordomo@suse.com with this text in its body: unsubscribe suse-linux-e Check out the SuSE-FAQ at <A HREF="http://www.suse.com/Support/Doku/FAQ/"><A HREF="http://www.suse.com/Support/Doku/FAQ/</A">http://www.suse.com/Support/Doku/FAQ/</A</A>> and the archiv at <A HREF="http://www.suse.com/Mailinglists/suse-linux-e/index.html"><A HREF="http://www.suse.com/Mailinglists/suse-linux-e/index.html</A">http://www.suse.com/Mailinglists/suse-linux-e/index.html</A</A>>