Polyhedra = Graphs

kirby urner kirby.urner at gmail.com
Mon Nov 29 16:21:11 EST 2010


The subject line is non-controversial however
serves as a reminder of how we're to shoehorn
spatial geometry topics into discrete math,
which has historically sometimes bleeped
over the polyhedrons (not for any good reasons).

This link provides more context:
http://mathforum.org/kb/thread.jspa?messageID=7317443

Yes, there's still an OO flavor to some of this, but
I've dropped the word "paradigm" in favor of "notation"
in many contexts (i.e. dot notation is still the hallmark,
even if Perl isn't using it).  "Paradigm" is over-used.

A recent tour of the University of Washington, the
business school in particular, reveals high def LCDs
even in the intimate study rooms seating only 4-5.
Keeping the geometry "flat" in such technologically
endowed settings is inherently disturbing and frustrating
to students.  The trend is in the other direction, like
in the movie 'Avatar' (more spatial, less flat).

Today's introductory geometry must be spatial by
default and planar only when zoomed in for special
case demos and proofs (like when zooming in to some
junkyard on Google Earth).  This is of course the reverse
order from early last century, when the sequence was
Kiselev's Planimetry first (Book 1), then Stereometry
(Book 2).  The USA's 10th grade likewise gave the
polyhedrons "back of the book" treatment, meaning
many classrooms never got that far.

Today, walk into any classroom and hold up a cube.
Count how many students call it a "square" and say
it has four sides.  You may be astounded.

That's why we must insist that graph theory embrace
the polyhedrons.  Discrete Math needs to take full
advantage of those LCDs, other projection tools, or
fall by the wayside as "too dino" (i.e. "too retro").

However, making this connection is pretty easy to
do so I'm not seeing any obstacles at this point.

Full STEAM ahead! **

Kirby

** re STEAM:  adding "anthropology" to STEM to keep
the human focus and form a stronger bridge to the
humanities (some curriculum writers are doing this).

Of course STEM stands for Science Technology Engineering
and Mathematics, which the Obama administration assures
us includes Computer Science:

http://www.ncwit.org/news.newsletter.php?action=detail&year=&newsletterID=20

Computing in the Core
In a perfect world computer science courses would count towards high school
graduation; computer science teachers would all have the knowledge and
professional development they need; and computer science would be offered as
part of the "core" curriculum in every high school. A new cooperative
effort, Computing in the Core, has just launched to help create that perfect
world.

http://blog.acm.org/archives/csta/2010/01/its_a_great_day.html
(more good news)


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