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Newsgroups: sci.math
From: Robert Israel <isr...@math.MyUniversitysInitials.ca>
Date: Wed, 04 Nov 2009 15:02:30 -0600
Local: Wed, Nov 4 2009 9:02 pm
Subject: Re: cos(pi/19)
master1729 <tommy1...@gmail.com> writes: Indeed, its minimal polynomial over the rationals is > > what do you know about cos(pi/19) ? > > nice expressions or properties ? > algebraic order is 9. -1+10*x+40*x^2-160*x^3-240*x^4+672*x^5+448*x^6-1024*x^7-256*x^8+512*x^9 which might look a bit nicer as -1+5*z+10*z^2-20*z^3-15*z^4+21*z^5+7*z^6-8*z^7-z^8+z^9 where z = 2*x. Thus 2*cos(pi/19) is an algebraic integer (which is also obvious from the fact that it is exp(i pi/19) + exp(-i pi/19), the sum of two roots of unity). Its conjugates are cos(3 pi/19), cos(5 pi/19), ..., cos(17 pi/19). You must Sign in before you can post messages.
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