[Edu-sig] Confused how teach geometry and importance of teaching geometry in 21st century.

[kirby urner]

On Thu, Mar 25, 2010 at 7:40 PM,  <chris at seberino.org> wrote:
> I'm teaching high school math to homeschoolers and I'm looking for how to make
> geometry year meaningful.
>

Most geometry taught in high school is flat, planar.

This is a problem in an age of HDTVs, LCDs.

If you wanna blow some time on a meandering meditation on
just this theme, 'Beyond Flatland', here's something I wrote
last night.  This takes off from a 1997 Math Summit held here
in Oregon, with Keith Devlin, Roger Penrose, Ralph Abraham
and other luminaries.

http://groups.yahoo.com/group/synergeo/message/58095

(maybe just scan the opening paragraphs, then decide
if it grabs ya -- I'm talking to an inner circle, using some
shoptalk, so probably a yawner).

> I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x
> more useful for future math and science work.
>

10th grade geometry distills just some of the Euclidean
stuff.  There's precious little topology, no V + F = E + 2,
no Descartes Deficit, no sphere packing, gnomon studies,
hardly much about polyhedra, their duals, little to nothing
about Phi...

I agree with ya, a big rip off.

Fortunately, the Internet is brimming with cool stuff, so
much to see and do.  Lots of great Java applets, no reason
to avoid them (we're not language bigots).

Geometry in the sense of events in space is about geography,
which (going big) includes astronomy and (going small)
internal organs, cells, molecules down to whatever particles.

In other words, geometry applies to the whole kit 'n kaboodle
so can't be "irrelevant to science" no matter how hard we try.

My advice:  remember to stay spatial, with planar as subset
(special case) of spatial.

Regarding Python in particular, I recommend getting into
VPython.  Also POV-Ray if you have the time, and VRML.
I've got lots of writings on this at my web site, complete
with source.

Recommended:  'The Book of Numbers' by Conway and
Guy.  Lots to program around.

> The only thing I can remember that was useful from geometry was a few volume
> and area formulas.  That can justify maybe a month but not a whole YEAR of
> geometry!?!?
>
> cs
>

I've spent many years with the Python + Geometry combo.

One pay-off is I generated most of the graphics at my web
sites and am therefore free to upload them to Wikipedia
and Wikieducator, where the authorities tend to be sticklers
about intellectual property.

Given all these cool graphics are mine, mine, mine, I feel at
liberty to spread them.  Thank you Python.  Thank you other
free tools.

> P.S. Yes yes I know that geometry is meant to teach logical reasoning.  Maybe
> one can get that from chess, debate club and other activities as well if
> not better?  People also say geometry is where you learn proofs.  Couldn't
> proofs be just as easily emphasized in all the other math classes?
>

If you're free to work in a home schooling setting, then you
can blend the topics a lot more, as student interest meanders.

'The Geometrical Foundation of Natural Structure: A Source
Book of Design' by Robert Williams would be a good title to
start with.  It's not a textbook.  Dover Press books tend to
be quite affordable though, this one not too hard to obtain.

If you're into lore or stories, which I consider central to any
credible curriculum, then maybe the Siobhan Roberts bio of
Donald Coxeter would be work getting and sharing with
students.

There are some juicy stories in there, gossip about Escher's
son I think it was, trying to break into the radome business...
radomes were those DEW line things across Canada, a
manifestation of the cold war....

Lots more to say, but since this is a topic I've worked on a
lot, I need to hold back, not open the floodgates.  Lots here
in the archive.

Thanks for joining us.

Oh, and if you get the Litvins text, Math for the Digital Age
and Programming in Python, then you'll find stuff on graphs
(in the sense of networks), mostly planar, but it's easy to
turn graphs into polyhedra with the wave of a magic wand.

Turtle Art / Turtle Graphics...

Springie.com.

Darwin @ Home.

Gregor helped me with getting Python turtle to draw the plane-net
for a T-module (back to my shoptalk), 120 of which build a rhombic
triacontahedron (an important shape with thirty 1 x phi diamond
facets).

Per Robert Williams, once you start jamming polyhedra
together, you're into lattices, and that's Linus Pauling style
chemistry, nanotechnology, crystallography -- no shortage
of relevant pages and projects.

Happy camping!

Kirby

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> Christian Seberino, Ph.D.
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