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Re: Brainstorming about STEM (was About Functions)
Posted:
Dec 24, 2011 6:38 PM
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On Sat, Dec 24, 2011 at 9:56 AM, Joe Niederberger
<niederberger@comcast.net> wrote:
<< snip >>
> So why is this so much easier than finding a proof given a proposition that wants a proof (derivation)? Given a proposition, the sought for derivation may be very long, or it may not exist at all.
>
Which doesn't exhaust the possibilities.
Perhaps the proposition has a trivial yet non-computable proof,
followed by any number of derivations.
I suppose that might sound like an heretical notion to your offended
sensibilities but to my ears it's mundane.
I'm glad you cited Euler's V + F == E + 2, though, if recent
scholarship is to be believed, was also discovered by Descartes.
The story is he was too paranoid to put it out there (not saying
without reason -- tough times), not knowing what would be the reaction
of then church authorities.
Leibniz played a role in deciphering the notebook he encoded the result in.
http://reasonsociety.blogspot.com/2011/10/descartes-secret-notebook-3.html
Re this remark by Geometric Mean:
"Tellingly, Aczel gives no citation for his claim, which he uses to
bolster his questionable theory that Euler somehow learned his theorem
that F+V=E+2 from Descartes' lost notebook."
Is that the thesis, that Euler got it from the notebook, or came upon
it independently, as another great mind surely would. I admit to
having gotten the gist of this recent scholarship through Glenn, a
fellow teacher one floor down (I'm in the chairman's suite temporarily
and part time).
> This is why the two seemingly closely related activities turn out to be so very different computationally.
>
> M Xmas,
> JoeN
Or they might be closely related while being non-computational.
We're still getting our feet wet with these computational processes
and their limitations.
That Ramanujan thing might eventually have a proof I should think, and
maybe computers will play a role.
But I keep thinking it'll be seen as a derivation, as the result has
already been verified.
I held a contest last Pi Day to extend it 1000 places, which sounds
trivial but couldn't be done in the high school classroom at the
height of the TI era. Intel was not yet a household word (even less
so AMD).
Regarding another thread in this thread:
I'm in favor of going over Euclid's stuff and learning from those proofs.
I especially like that old color classic **:
http://www.math.ubc.ca/~cass/euclid/byrne.html (1847)
I also don't mind (highly encourage) having alternative axiom /
definitions handy, more accessible ones than usual.
Drawing on the work of Vienna Circle member Karl Menger, I follow his
suggestion to define a non-Euclidean "geometry of lumps".
Then there's just more shop talk about geometry generally,
independently of the scaffolding.
We have reason to talk about the rhombic triacontahedron and rhombic
dodecahedron having to do with chemistry and crystals.
This is STEM after all, so not just the needs of the geometry teachers
matter -- we have geography to think about too.
Kirby
** the availability of this wonderful reference counters that meme
virus infecting public schools, a poster / media campaign in libraries
about "the Free Web" and how it doesn't have any really good reference
materials, hyping the unfree web as having all the serious
scholarship. When I saw those cowardly posters, I knew the public
schools had gone over to the dark side for sure. Everything good
about democracy is being snuffed out in these daycare prisons.
High school / prison: Lying to Children
http://www.flickr.com/photos/17157315@N00/5236861850/in/set-72157625538952986/
http://www.flickr.com/photos/17157315@N00/5236269713/in/set-72157625538952986/
http://www.flickr.com/photos/17157315@N00/5236862304/in/set-72157625538952986/
How might we rescue them? Start small, spread out, occupy and vacate.
Keep 'em guessing.
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