[Edu-sig] Brute force solutions

[John Zelle]

> 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