|
|
Re: Alternative area postulate for geometry
Posted:
Jun 30, 2012 1:07 PM
|
|
On Fri, Jun 29, 2012 at 11:23 PM, Wayne Bishop <wbishop@calstatela.edu> wrote:
<< snip >>
> Kirby won't like the left=right implication of reflection on the line but?
>
What I don't like is me ordering 84 pairs of gloves in my electronic
shopping cart, and getting only right handed gloves in the mail.
When I complain, some lawyer tells me to read the fine print and lo
and behold the contract said the gloves only had to be "congruent".
They have some finger-angle-finger proof that all my gloves are
congruent, ergo I must fork over the dough or risk a lawsuit.
Fortunately, where gloves are concerned, the concepts of "left" and
"right" are somewhat engrained.
But with the invention of tube socks and other "doesn't matter"
garments, there's the danger of whittling at the important difference
"handedness" makes.
- -----------
I'm OK with the Euclidean nugget remaining embedded in the curriculum
for what it is, but not without critique.
Euclideanism is a fine belief system with its infinitely wide,
infinitely thin planes, a spooky Greek metaphysics that has done much
for our civs (civilizations).
But lets not artificially dumb ourselves down like they did in the
Middle Ages, and treat ancestor sources as somehow setting the
boundaries of all that might be usefully thought and/or propagated.
That's to fight against a next generation's right to innovate and go
its own way.
[ I encourage people to inwardly / nonviolently rebel against "father
knows best" reflexing among the graying, and to pick and choose their
teachers across the age spectrum. And yes, I'm plenty gray myself. ]
In the liberal arts, we encourage ancestor worship of a kind in that
you're encouraged to delve deeply into the works of the long gone,
sure by all means, why not?
But discrimination and judgement should be exercised. Life is short.
There are lots of dead people to spend time with not to mention the
living, way too many for any one judge (I'm imagining David
Feinstein's science fair judges).
Maths and philosophies are like bottles of wine. A lot of the stuff
you'll get in school is just glorified grape juice in a box, only
barely psychotropic (i.e. able to alter gestalts, provide deep
insights). School should help you develop / cultivate your tastes and
give you the tools to pursue and develop them.
For example, I'm really into the Mandelbulb (not a typo) lately and
have been sharing the Youtube fly-throughs at retreats and meetings,
propagating that research (not taking credit for any of it -- I've got
my little L-Systems thing and my simple fractal generator in Python,
but the Mandelbulb is just something I stumbled upon).
Role model teachers are really into pet topics and will be happy to
share about them.
How to best educate is itself a pet topic and it's not too shabby to
made pedagogical / andragogical technique a front and center focus.
But then a lot of the most skilled in those realms aren't classroom
teachers at all. They work for Disney or comic book companies. A lot
of our unit-volume tetrahedron stuff is coming from the manga / anime
folks.
STEM owes a lot to its software engineers as well, for its increasing
sharability. Google, Facebook... major players in STEM, more so than
most publishers.
Of course some schools block Youtube or put up posters about the
limitations of the "free Web". Some of my Facebook friends and I have
been ridiculing this one, a photo by me from a local high school:
http://www.flickr.com/photos/17157315@N00/5236269713/sizes/l/in/photostream/
(file under "lies they tell children" series)
Hah hah.
Anyway, back to work,
Kirby
> BTY: Lou likes geometry and knows a lot. I'm surprised he hasn't chimed
> in. On vacation?
>
> Wayne
>
>
> At 05:05 PM 6/29/2012, Peter Duveen wrote:
>
> Joe, of the links you provided, most referred to either Cavalieri's
> principle, which I find a bit enigmatic, or list either s^2 or l x w is a
> postulate, which I have objections to. The winner, in my opinion, is
> http://www.beva.org/math323/asgn3/sep26.htm, which says:
> "Axiom 1: Congruent polygons have equal areas."
> That axiom seems self evident and reasonable to me. That makes sense.
|
|
