you wrote about synthetic geometry:
However, my considered view is that this approach is
> a pedagogical dinosaur. Students generally hate it, and I've begun
> to see in my old age that the Greek approach to geometry was ponderous
> and clumsy.
I have notice that H. S. M. Coxeter loves to present projective geometry
synthetically, and he generally avoids the analytic approach as much as he
can. Notice how elegant his presentations are. Of course, in the analytic
approach the notation does often does away with most of our thinking.
Isn't the true problem that your students don't love mathematics and can't
be bothered with beauty and elegance. That makes me very sad. Why don't
they study something else?
I would hate it if I didn't know analytic techniques, and if I have no
other way to get there, I'll go that way. Your first thoughts were the
best thoughts, but second thoughts are best says the nurse in the
Hippolytus of Euripides as she proceeds to lead Phaedra into disaster, and
you must do what has some chance of working.
If this is over-opinionated, ignore it.
Best wishes from Annapolis for a fine '99,
Sam Kutler