```Date: Jul 30, 2005 12:02 PM
Author: Kirby Urner
Subject: Which Polynomial?

We'd likely consider it ludicrous were NCLB administrators to put out that they had a special polynomial in mind, for all school children of eligible age to solve beginning next school year.  Anti-NCLBers would scoff that you don't "solve" a polynomial because polynomials needn't equate to anything and therefore the matter of "solving for an unknown" (perhaps several) is moot.  Others would simply decry the dictatorial sound of "mandating a polynomial."However, *were we* to accept the above surreal development (the NCLB's mandating of an Official Polynomial), it'd be interesting to speculate just *which* polynomial (equated to zero) that'd be.  I have a candidate:p**2 - p - 1 = 0.Why?First, let's look at a solution.  Either completing the square or the quadratic formula suggest themselves.  Solve it both ways.  Your answers will be (1+pow(5,0.5))/2 and (1-pow(5,0.5))/2 [Python notation].  Only one of those is positive, so if looking for a geometric length, the positive root is the most relevant.  And that solves as a decimal to around 1.618, which some of you may recognize.  We're talking about phi ('fie' -- not 'pi' and not 'fee').So where does this polynomial come from?  From a diagram:        p             q |--------------|-----------|The goal here is to establish this relationship:(q:p) :: (p:(p+q))orq/p == p/(p+q)Set q = 1 and solve for p.phi is important as the ratio between a side and a diagonal of a regular pentagon.  It is known as the "golden mean" and has been called that since ancient times.  That should be your cue:  this number *is* important.  That's why the NCLB is on board.  Don't leave any child behind next year.  How 'bout it folks?Kirby
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