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Topic: Alternative area postulate for geometry
Replies: 141   Last Post: Jul 18, 2012 9:39 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Alternative area postulate for geometry
Posted: Jun 29, 2012 9:15 PM

On Fri, Jun 29, 2012 at 5:05 PM, Peter Duveen <pduveen@yahoo.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.

Kirby

Date Subject Author
6/25/12 Peter Duveen
6/25/12 Robert Hansen
6/25/12 Gary Tupper
6/25/12 Robert Hansen
6/25/12 Gary Tupper
6/25/12 Robert Hansen
6/25/12 kirby urner
6/25/12 Peter Duveen
6/25/12 kirby urner
6/26/12 Robert Hansen
6/26/12 Gary Tupper
6/28/12 Gary Tupper
6/28/12 Robert Hansen
6/29/12 Wayne Bishop
6/29/12 Gary Tupper
6/29/12 Wayne Bishop
6/26/12 Joe Niederberger
6/26/12 Joe Niederberger
6/26/12 Peter Duveen
6/26/12 Robert Hansen
6/27/12 Wayne Bishop
6/28/12 kirby urner
6/28/12 Wayne Bishop
6/28/12 kirby urner
6/26/12 Joe Niederberger
6/26/12 Peter Duveen
6/26/12 Peter Duveen
6/27/12 Robert Hansen
6/26/12 kirby urner
6/27/12 Wayne Bishop
6/27/12 Robert Hansen
6/27/12 Peter Duveen
6/27/12 Peter Duveen
6/27/12 Joe Niederberger
6/27/12 kirby urner
6/27/12 Joe Niederberger
6/27/12 Robert Hansen
6/27/12 Joe Niederberger
6/27/12 Joe Niederberger
6/27/12 Peter Duveen
6/27/12 Joe Niederberger
6/28/12 Peter Duveen
6/28/12 Joe Niederberger
6/28/12 Wayne Bishop
6/28/12 Joe Niederberger
6/28/12 Joe Niederberger
6/29/12 Wayne Bishop
6/29/12 Peter Duveen
6/29/12 Joe Niederberger
6/29/12 Robert Hansen
6/29/12 Wayne Bishop
6/30/12 kirby urner
6/30/12 Robert Hansen
6/29/12 Joe Niederberger
6/29/12 Robert Hansen
6/29/12 kirby urner
6/29/12 Wayne Bishop
6/29/12 Joe Niederberger
6/29/12 Robert Hansen
6/29/12 Robert Hansen
6/29/12 Joe Niederberger
6/29/12 Robert Hansen
6/29/12 Robert Hansen
6/29/12 Joe Niederberger
6/29/12 Joe Niederberger
6/29/12 Robert Hansen
6/30/12 Louis Talman
6/30/12 Robert Hansen
6/30/12 Wayne Bishop
7/1/12 Louis Talman
7/1/12 Louis Talman
7/1/12 Louis Talman
7/1/12 Wayne Bishop
6/30/12 Robert Hansen
7/1/12 Robert Hansen
7/1/12 Louis Talman
7/2/12 Robert Hansen
7/2/12 Wayne Bishop
7/3/12 Gary Tupper
7/3/12 Robert Hansen
7/2/12 kirby urner
7/2/12 Robert Hansen
7/2/12 kirby urner
7/2/12 Robert Hansen
7/2/12 kirby urner
7/2/12 Robert Hansen
7/2/12 Wayne Bishop
7/3/12 kirby urner
6/29/12 Peter Duveen
6/29/12 kirby urner
6/30/12 Wayne Bishop
6/30/12 kirby urner
6/30/12 Wayne Bishop
7/1/12 kirby urner
7/1/12 Wayne Bishop
7/2/12 kirby urner
7/2/12 Wayne Bishop
7/3/12 kirby urner
6/30/12 Joe Niederberger
6/30/12 Joe Niederberger
6/30/12 Peter Duveen
7/1/12 Robert Hansen
7/1/12 Wayne Bishop
7/1/12 Joe Niederberger
7/2/12 Peter Duveen
7/3/12 Joe Niederberger
7/3/12 Wayne Bishop
7/4/12 Wayne Bishop
7/4/12 Robert Hansen
7/4/12 kirby urner
7/3/12 Joe Niederberger
7/3/12 Joe Niederberger
7/18/12 kirby urner
7/4/12 Peter Duveen
7/4/12 kirby urner
7/4/12 Louis Talman
7/4/12 Robert Hansen
7/4/12 Louis Talman
7/4/12 Robert Hansen
7/4/12 Wayne Bishop
7/4/12 Peter Duveen
7/5/12 Robert Hansen
7/4/12 Joe Niederberger
7/5/12 kirby urner
7/5/12 Wayne Bishop
7/5/12 kirby urner
7/6/12 Robert Hansen
7/6/12 kirby urner
7/6/12 Wayne Bishop
7/6/12 Robert Hansen
7/6/12 kirby urner
7/4/12 Joe Niederberger
7/5/12 Robert Hansen
7/5/12 Wayne Bishop
7/5/12 kirby urner
7/5/12 Robert Hansen
7/5/12 kirby urner
7/4/12 Joe Niederberger
7/6/12 Joe Niederberger
7/6/12 kirby urner
7/6/12 Joe Niederberger
7/7/12 Wayne Bishop