[Edu-sig] Re: Euclid

[Arthur]

> How do you do Euclid's Elements in PyGeo?
> Can be done, yes?

Yes, and no.

PyGeo is really built to explore more modern notions of geometry.  Notions
of length, area, and to a good extent shape are not invariants in projective
space, or non-euclidan space - and so are not of the essence when studying
those kinds of geometries. So not a lot is done with those notions in
PyGeo - at least in how I use it.

Those notions are more significant in Euclian space.

Plus, no need to reinvent the wheel:

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

has the complete Elements up, with essentially all the constructions as
dynamic Java applets.

Using the applets are great to explore a construction *after* one has done
that construction by hand, IMO.  We can get into a whole discussion about
the use of technology in education.  To the extent it has been
scientifically studied, the evidence is that the heavy use of computers in
the classroom  = a slight detriment to student advancement. No evidence of a
major +.

I'm believing that it  is too easy for someone to slip into passive mode,
and out of learning mode - in front of a screen.

There is only one way to build a construction in PyGeo.  By the deliberate
act of writing a script.  The mental process is much closer to that of
building by hand - then for example it would be using a GUI. And that is how
I want it to be. The important thing is that it does things you can't do on
a piece of paper.  Like simulate the working in 3d space. In that way - by
doing something that it is hard or near impossible to do without it - it
employs technology for educational purposes.

The Euclidian constructions are generally simple enough to do on paper with
a ruler and compass.  I see no reason, really, to do them any other way.

Art