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Topic: Is Geometry the first Inspirational Math class?
Replies: 7   Last Post: Apr 29, 2009 3:54 PM

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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Is Geometry the first Inspirational Math class?
Posted: Jan 22, 2009 2:13 AM
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Since computers (PC revolution, then FOSS), there's been
new interest in spatial renderings of polyhedra, putting
those on YouTube. Some geometry classes take this
approach (see some of my earlier posts to this archive,
just click on my name in the web interface @ Math Forum).

Also you may remember the explosion of interest around
fractals. Again, that's a topic, along with cellular
automata, that sometimes works its way into a pre-college
project, even if only in an extra-curricula context.
Some curricula are doing more to build those in, noticing
student interest, plus the complex plane is a pre-college
topic, at least in IB.

Book publishers have a hard time keeping up with these
practices, as theirs is a read-only medium, not
interactive, and not programmable. As a former
contributing editor for McGraw-Hill (publishers of BYTE),
I could see the writing on the wall back in the 1980s:
there'd be a fork in the road, with some schools taking
a more "place based" approach and producing most of
their own materials, value adding to downloaded booty.

This has come to pass, especially with the emergence of
of legally free software (FOSS) though again, we're
talking two cultures here, with "left behinders" sticking
with calculators and text books.

Those crossing to our brave new world get more involved
with ray tracers, game engines, other tools amenable
to formalized treatments, in terms of vectors, Euler's
Law for Polyhedra, Descarte's Deficit, symmetry groups,
spin axes, space-filling etc. I call this "Beyond
Flatland" as we're not confined to the plane, even as
we use Euclid's proof methods (his constructions weren't
always flat either, plus "left behind" texts bleep over
Euclid's Method for the GCD -- gotta have that). This
is still "schoolish math" in other words, with plenty
of theorem proving. Lots of figurate and polyhedral
number sequences, maybe you've seen...


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