Talk:Figure-eight knot (mathematics)

Regarding the statement:
 * The figure eight is also the hyperbolic knot whose complement has the smallest possible volume, 2.02988... by work of Colin Adams.

Colin Adams was not the one who showed it has the smallest volume. I can't remember who it was. I think maybe a pair of Japanese mathematicians.--C S 01:59, Sep 8, 2004 (UTC)

You are correct - Cao and Meyerhoff proved the stated theorem - Adams actually showed that the Gieseking manifold is the minimal volume non-compact hyperbolic manifold. The Gieseking manifold is double covered by the figure eight knot complement. I will fix the page. --sam Wed Sep 8 10:23:23 EDT 2004

Of course, Meyerhoff is not Japanese. Best, Sam nead 15:19, 6 August 2007 (UTC)

Primality
I guess the figure-eight knot is not prime... If so, of what knots is it the sum? Vectro (talk) 17:01, 9 December 2008 (UTC)
 * It is prime.--agr (talk) 21:38, 9 December 2008 (UTC)



Simpler form of equations
The plotting equations x=(2+cos(2t))*cos(3t) and y=(2+cos(2t))*sin(3t) actually produce the same curve as the simple polar coordinates equation r=2+sin(2θ/3), only rotated by 45° degrees. This curve is shown in the graphic File:Figure8knot-rose-limacon-curve.svg... AnonMoos (talk) 12:37, 4 November 2010 (UTC)


 * Substituted it in in place of squared version File:Figure8knot-math-square-alternate.svg ... AnonMoos (talk) 10:54, 19 May 2011 (UTC)