[Edu-sig] Brute force solutions
John Zelle
john.zelle at wartburg.edu
Thu Sep 22 15:31:48 CEST 2005
> On Wed, Sep 21, 2005 at 09:31:41AM -0700, Kirby Urner wrote:
>
>Of course all of this requires temporarily ignoring the fact that algebraic
>methods give us a way to compute phi as simply (1 + math.sqrt(5))/2.0.
I've been considering this a bit. The closed form here begs the
question, what is math.sqrt(5)? Sure, we have a built-in function that
computes this, but someone had to write the algorithm that computes
sqrt. That calculation makes use of numerical techniques similar to what
we are discussing w.r.t. phi (much more efficient ones, of course).
In a sense, you could view your discussion as a look under the hood at
possible implementations. In fact, I would think a good problem to
tackle in a math class is to develop some algorithms for approximating
square roots. Various "guess and check" techniques can be successful.
Newton's method is vary good, and can easily be "derived"/motivated
without actually looking at any of the calculus.
--John
--
John M. Zelle, Ph.D. Wartburg College
Professor of Computer Science Waverly, IA
john.zelle at wartburg.edu (319) 352-8360
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