[Edu-sig] Algebra 2

[kirby urner]

On Mon, Oct 6, 2008 at 1:28 PM, Ivan Krstić <
krstic at solarsail.hcs.harvard.edu> wrote:

> [Kirby, I find it very difficult to follow your messages; they tend to be
> long and meandering. I'm certain I'm not the only one. Please try to be more
> directly on-topic and succinct.]
>

[ they have been lately, yes, though if you go back in the archive you'll
find more succinct ones ]


>
> On Oct 6, 2008, at 10:56 AM, kirby urner wrote:
>
>> What passes for "pure math" would be something to study in college, after
>> getting a broad sampling ahead of time, good overview, the job of a
>> pre-specializing curriculum.
>>
>
>
> Speaking with no experience teaching mathematics, only learning it, this
> statement strikes me as sheer nonsense. It's like saying "what passes for
> painting would be something to study in college, after getting a broad
> sampling of brushes, stroke techniques and paint chemistry ahead of time,
> all without ever seeing an actual painting."


More I'm saying mathematics has a long and proud history outside of Ivory
Tower specialties, a johnny come lately invention, whereas Leibniz, to take
an example, was what we'd today call a polymath.  Pre-college we do
polymath, until you're old enough to make your own choices and maybe not get
suckered by folks who talk a brave talk, but seem to dish out the same
crufty / stale pablum year after year, left to their own devices, despite
tremendous advances in the literature.


>
>
> This isn't a discussion that's particularly on-topic for Python's edu-sig,
> so I won't belabor it much. I share the views expressed at some length in
> Paul Lockhart's excellent "A mathematician's lament" (<
> http://radian.org/~krstic/LockhartsLament.pdf<http://radian.org/%7Ekrstic/LockhartsLament.pdf>>).
> In summary, if you don't show kids that mathematics is something beautiful,
> how are they supposed to have anything but bored disregard for the seemingly
> meaningless mechanics they're taught for 8 years before college? Fractions
> don't qualify as beauty. Many aspects of pure mathematics do.


Continued fractions do, especially:

IDLE 1.2.1
>>> from __future__ import division
>>> 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1))))))
0.61904761904761907
>>> 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1))))))
0.61538461538461542
>>> 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 +
1)))))))))
0.6179775280898876

[ much easier when you have color-coded parentheses checking, like in IDLE ]

Better in Akbar font.  We appear to be approaching something, from above and
below.

Kirby



>
>
> --
> Ivan Krstić <krstic at solarsail.hcs.harvard.edu> | http://radian.org
>
>
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