> 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 [EMAIL PROTECTED] (319) 352-8360 _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
