Thanks so much, James. Never expected the solution to look like this, but this is exactly what I wanted. :) Warut On Tue, Aug 18, 2009 at 10:12 PM, James Buddenhagen<jbuddenh@gmail.com> wrote:
On Tue, Aug 18, 2009 at 8:05 AM, Warut Roonguthai<warut822@gmail.com> wrote:
James Buddenhagen associated the polynomial:
x^3 - sqrt(7)*x^2 + x + 1/sqrt(7)
to the identity:
tan(3*pi/14) + cot(pi/7) - tan(pi/14) = sqrt(7).
Is there a polynomial that we can associate to the fact that
tan(3*pi/11) + 4*sin(2*pi/11) = sqrt(11)?
Warut
I'm not sure this helps, but tan(3*pi/11) is a root of:
x^5-3*x^4*sqrt(11)+22*x^3-2*x^2*sqrt(11)-11*x+sqrt(11)
and 2*sin(2*pi/11) is a root of:
y^5-y^4*sqrt(11)+3*y^2*sqrt(11)-11*y+sqrt(11)
and the relationship x + 2y = sqrt(11) transforms either polynomial into the other.
James
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