[Edu-sig] thought re graphing calculators ...
Edward Cherlin
echerlin at gmail.com
Thu Oct 1 02:39:02 CEST 2009
On Wed, Sep 30, 2009 at 3:04 AM, Brian Blais <bblais at bryant.edu> wrote:
> On Sep 28, 2009, at 16:30 , Gregor Lingl wrote:
>
> Brian Blais schrieb:
>
> However, as I think
> about it, I can not think of a single problem where I *needed* the
> graphic calculator, or where it gave me more insight than I could do
> by hand.
>
> I think I have a counterexample.
> Run the script, that you can find here:
> http://svn.python.org/view/*checkout*/python/branches/release26-maint/Demo/turtle/tdemo_chaos.py?revision=73559&content-type=text%2Fplain
> What do you think?
The Logistic Map x-->rx(1-x) for varying values of r is easy to
examine on a calculator, but excessive by hand. Feigenbaum discovered
its periodicities on a calculator without any graphing capability, but
having graphs makes insight much easier, in the same way that the
Mandelbrot set was discovered mathematically in the 1920s, but became
of major interest only after computers permitted it to be visualized.
Of course, with a computer, you can visualize the entire bifurcation
diagram in a few seconds.
http://en.wikipedia.org/wiki/Logistic_map
http://en.wikipedia.org/wiki/Bifurcation_diagram
The bifurcation diagram of the logistic map is related to the Mandelbrot set,
http://www.math.lsa.umich.edu/mmss/coursesONLINE/chaos/chaos6/index.html
and has applications in physics, such as a dripping faucet.
--
Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://earthtreasury.org/
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