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Re: Geometric Algebra



Jane Jackson wrote:

The wedge product is a fundamental concept in geometric algebra. Read about
it on David Hestenes' web site:
http://modelingnts.la.asu.edu/

That site is complex and a bit hard to navigate.
There is some excellent stuff there, along with some
slightly sloppy and muddled stuff.

...
David Hestenes' Oersted Lecture on GA will be published in AJP.

It's available now at:
Abstract etc.:
http://modelingnts.la.asu.edu/html/overview.html
Paper:
1) http://modelingnts.la.asu.edu/pdf/OerstedMedalLecture.pdf

I recommend it. Figure 11 is particularly nice; I haven't
seen that elsewhere. Note: you might at first think that
the vectors a,b,c lie on or near the surface of the sphere,
but they don't. Each one has its tail deep down at the center
of the sphere, and its tip on the surface.

Other references include:

2) http://www.mrao.cam.ac.uk/~clifford/introduction/intro/intro.html

This is a good starting point. It is fun to read, and
does a good job with the motivation. It is more explicit
about some of the details than item (1) above. OTOH it
is unnecessarily incomplete and/or sloppy sometimes. For
instance it says "multiplication by scalars is obvious".
Well, maybe obvious to experts, but not to students; see
Harke's equation (18b).

3) http://www.harke.org/ps/intro.ps.gz

I really liked this. It doesn't talk too much about the
motivation, but if you're already motivated it's great.
It is a little more thorough, more careful, and more
general than some of the other treatments (but doesn't
suffer from rigor mortis).

Intuitive insight is nice, and rigor is nice, but the best
thing is to have both of them working in tandem.

BTW if your searching for Geometric Algebra, you might also
want to search on Clifford Algebra. GA is pretty much a
modernized CA emphasizing applications to geometry and physics.