> > .... ... > > Do we really need a full year of geometry, anyway? >
ACK..URGHHH..OOoooo ... (the sounds of a teacher of university mathematics majors barely surviving an apoplectic fit)
Common scenario (senior level abstract algebra class):
Prof: Ok, today we're going to see some of the power of the field theory we've been discussing, by showing how it has been used to solve some classical geometrical problems that eluded the best mathematical minds for millenia. Namely, the problems of "doubling a cube" and "trisecting an arbitrary angle."
P: You recall how you learned to bisect angles using a compass and straightedge ...
S2: No way man, use a retractor?
S3: What's a compass?
S4 (to S2): That's reFRACtor, nimrod!
P: C'mon you guys. You remember doing Euclidean constructions in high school geometry ...
Students (in unison): Huh??
S2: No way! Geometry is just like proof stuff, you know angle-side-angle like.
P: ACK...URGHHH ...OOOoooo
Hmmmm...come to think of it, why not just ditch it altogether! :>