
Re: Which Polynomial?
Posted:
Jul 30, 2005 7:42 PM


> Well, if we are going to split hairs, it's "phee", > but who cares! >
In English we say fie, as in fee FIE foe fum.
> The two roots (actually, halves of the two > roots, if I recall correctly) generate the Fibonacci > sequence.
The phi sequence is both geometric and recursively additive.
The usual thing we do with the Fibonacci sequence is show how the ratio (F[n+1]/F[n]) > phi as n > infinity, where F[n+1] and F[n] are successive terms in this series.
Makes for a fun computer programming experience.
> I'll leave you with this point as an exercise. > > But back to Kirby's question, my answer would simple. > We could just as well take another polynomial to > establish some sort of a special or classical > relationship. The question really should be, "How is > the application of this polynomial important to the > student's learning progress?" The issue should not be > of the importance of the particular piece in the > *history* of mathematics, but its importance in the > learning process.
Maththroughstorytelling: part of what we're doing is passing on a history, a "where we've been" story. It's not like history is irrelevant. On the other hand, phi to this day has geometric importance  its value undimished with time (like gold).
If you've got other polynomials with deep histories to share, by all means do so. Let's add to our list.
> There are no irreplaceable parts in the curriculum, but > many of the ideas we want students to learn may well be > irreplaceable.
phi is an idea and is irreplacable.
> The trouble is, we cannot agree on which ideas these > are.
I'd think phi, pi and e we could at least agree on, though we might take different approaches in introducing them. > Kirby, if you want to use a particular polynomial as > the cornerstone of some part of the curriculum, more > power to you. But it does not mean that everyone (or > anyone) should follow your example. > > VS)
It's implicit in writing curriculum that one is saying something like "follow me"  and then only some do, maybe none. That's a given.
However, within the rhetorical conceit of offering leadership, it behooves me to be persuasive, to exercise whatever leadership experience and qualities I possess.
So: NCLB people, listen up, we're going to push Phi (FIE) and we're going to do it in connection with solving a Polynomial. This will provide positive reinforcement for (a) the quadratic formula (b) completing the square, plus it'll lead to connected topics such as: Fibonacci numbers, sequences, and fivefold symmetry ala pentagons.
Remember, Computer Programming for Everybody (CP4E) was a DARPAfunded initiative. So *of course* we're interested in our Pentagon's geometry.
Tenhut! March!
Kirby

