The fun part here is we can use numerator/denominator syntax with
open-ended
precision integers, to like express sqrt of 19 as some humongous fraction
(as many digits as memory will allow). This lets us far surpass the
floating point barrier.
For example, the sqrt of 19 is rougly:
n = ((pow(orig,0.5) + addterm)/denom)**2
H, this may be the Achilles heal of my project, to not use any sqrt
finder in the process of finding a sqrt using continued fractions. Back to
the drawing board?
Kirby
[EMAIL PROTECTED] wrote:
The fun part here is we can use numerator/denominator syntax with
open-ended
precision integers, to like express sqrt of 19 as some humongous fraction
(as many digits as memory will allow). This lets us far surpass the
floating point barrier.
OK, here we go:
def
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
On 22 Sep 2005 at 12:00, (Kirby Urner) wrote:
Some lessons that might be learned from this approach:
(1) when working with floats, you want to compare differences, not check for
equalities, e.g. looking for when b/a == 1/b would be a bad idea.
(2) you get greater accuracy in
-Original Message-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Daniel Ajoy
Sent: Thursday, September 22, 2005 10:07 AM
To: edu-sig@python.org
Subject: Re: [Edu-sig] Brute force solutions
My approach to teaching about phi is by asking kids to draw
construction
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
I'm sorry, but I couldn't help taking Kirby's findphi() function as a
personal challenge.
At the cost of roughly doubling the complexity of the code (19 lines instead
of ten lines in the function body), I was able to improve the performance by
a factor of more than 6500, while basically still
At 14:33 21/09/2005, you wrote:
At the cost of roughly doubling the complexity of the code (19 lines instead
of ten lines in the function body), I was able to improve the performance by
a factor of more than 6500, while basically still using the same
brute-force approach of guessing a number,
On Wed, Sep 21, 2005 at 06:44:01PM +0100, Peter Bowyer wrote:
At 14:33 21/09/2005, you wrote:
At the cost of roughly doubling the complexity of the code (19 lines instead
of ten lines in the function body), I was able to improve the performance by
a factor of more than 6500, while basically
On Wed, Sep 21, 2005 at 09:31:41AM -0700, Kirby Urner wrote:
Mine original draft makes sense to set the stage, cuz the reasoning is so
dang primitive. Yours adds a layer of sophistication more reflective of how
real world programmers learn to squeeze the most out of their cycles.
Your
David Handy wrote:
On Wed, Sep 21, 2005 at 09:31:41AM -0700, Kirby Urner wrote:
Mine original draft makes sense to set the stage, cuz the reasoning is so
dang primitive. Yours adds a layer of sophistication more reflective of how
real world programmers learn to squeeze the most out of their
Per my 'Pentagon math' thread, I think the golden ratio (phi) is an
important one to explore in K-12.[1] It's one of those key nodes in our
curriculum network.
Given a regular pentagon, the ratio of a diagonal to an edge is phi. In
other words, that famous pentacle pattern is phi-edged,
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