On Fri, Jun 29, 2012 at 5:05 PM, Peter Duveen <email@example.com> wrote: > Joe, of the links you provided, most referred to either Cavalieri's principle, which I find a bit enigmatic, or list either s^2 or l x w is a postulate, which I have objections to. The winner, in my opinion, is http://www.beva.org/math323/asgn3/sep26.htm, which says: > "Axiom 1: Congruent polygons have equal areas." > That axiom seems self evident and reasonable to me. That makes sense.
Not to change the subject or anything, but "congruency" to me has been problematic in that it's not just a matter of translation and rotation, with superimposition (a kind of visual proof).
In Tetris, there's the left L and right L and they're not interchangeable. Left and Right is a real difference. The way congruency is taught, I see the beginnings of a campaign to submerge to importance of chirality in geometry.
Kids "drink the thalidomide" at this point (called that in that "drink the kool-aid" is a joke idiom for taking in the beliefs of a cult in a perhaps suicidal manner, whereas thalidomide had devastating effects because of one isomer, left or right I forget which).
Note how the above all writing invokes chemistry without apology or 2nd thought? That's STEM for ya. "Pure math" wastes a lot of bandwidth trying to make its story problems "meaningless" whereas what's needed is synchronization.