The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Education » math-teach

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kirby urner

Posts: 3,242
Registered: 11/29/05
Re: Alternative area postulate for geometry
Posted: Jun 29, 2012 9:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
Read Alternative area postulate for geometry
Peter Duveen
6/25/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/25/12
Read Re: Alternative area postulate for geometry
Gary Tupper
6/25/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/25/12
Read Re: Alternative area postulate for geometry
Gary Tupper
6/25/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/25/12
Read Re: Alternative area postulate for geometry
kirby urner
6/25/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/25/12
Read Re: Alternative area postulate for geometry
kirby urner
6/26/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/26/12
Read Re: Alternative area postulate for geometry
Gary Tupper
6/28/12
Read Re: Alternative area postulate for geometry
Gary Tupper
6/28/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/29/12
Read Re: Alternative area postulate for geometry
Gary Tupper
6/29/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/26/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/26/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/26/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/26/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/27/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/28/12
Read Re: Alternative area postulate for geometry
kirby urner
6/28/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/28/12
Read Re: Alternative area postulate for geometry
kirby urner
6/26/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/26/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/26/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/27/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/26/12
Read Re: Alternative area postulate for geometry
kirby urner
6/27/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/27/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/27/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/27/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/27/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/27/12
Read Re: Alternative area postulate for geometry
kirby urner
6/27/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/27/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/27/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/27/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/27/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/27/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/28/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/28/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/28/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/28/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/28/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/29/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/29/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/30/12
Read Re: Alternative area postulate for geometry
kirby urner
6/30/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
kirby urner
6/29/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/29/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/29/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/29/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/30/12
Read Re: Alternative area postulate for geometry
Louis Talman
6/30/12
Read Re: Alternative area postulate for geometry
Robert Hansen
6/30/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/1/12
Read Re: Alternative area postulate for geometry
Louis Talman
7/1/12
Read Re: Alternative area postulate for geometry
Louis Talman
7/1/12
Read Re: Alternative area postulate for geometry
Louis Talman
7/1/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/30/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/1/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/1/12
Read Re: Alternative area postulate for geometry
Louis Talman
7/2/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/2/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/3/12
Read Re: Alternative area postulate for geometry
Gary Tupper
7/3/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/2/12
Read Re: Alternative area postulate for geometry
kirby urner
7/2/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/2/12
Read Re: Alternative area postulate for geometry
kirby urner
7/2/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/2/12
Read Re: Alternative area postulate for geometry
kirby urner
7/2/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/2/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/3/12
Read Re: Alternative area postulate for geometry
kirby urner
6/29/12
Read Re: Alternative area postulate for geometry
Peter Duveen
6/29/12
Read Re: Alternative area postulate for geometry
kirby urner
6/30/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
6/30/12
Read Re: Alternative area postulate for geometry
kirby urner
6/30/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/1/12
Read Re: Alternative area postulate for geometry
kirby urner
7/1/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/2/12
Read Re: Alternative area postulate for geometry
kirby urner
7/2/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/3/12
Read Re: Alternative area postulate for geometry
kirby urner
6/30/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/30/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
6/30/12
Read Re: Alternative area postulate for geometry
Peter Duveen
7/1/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/1/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/1/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/2/12
Read Re: Alternative area postulate for geometry
Peter Duveen
7/3/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/3/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/4/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/4/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/4/12
Read Re: Alternative area postulate for geometry
kirby urner
7/3/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/3/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/18/12
Read Re: Alternative area postulate for geometry
kirby urner
7/4/12
Read Re: Alternative area postulate for geometry
Peter Duveen
7/4/12
Read Re: Alternative area postulate for geometry
kirby urner
7/4/12
Read Re: Alternative area postulate for geometry
Louis Talman
7/4/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/4/12
Read Re: Alternative area postulate for geometry
Louis Talman
7/4/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/4/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/4/12
Read Re: Alternative area postulate for geometry
Peter Duveen
7/5/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/4/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/5/12
Read Re: Alternative area postulate for geometry
kirby urner
7/5/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/5/12
Read Re: Alternative area postulate for geometry
kirby urner
7/6/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/6/12
Read Re: Alternative area postulate for geometry
kirby urner
7/6/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/6/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/6/12
Read Re: Alternative area postulate for geometry
kirby urner
7/4/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/5/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/5/12
Read Re: Alternative area postulate for geometry
Wayne Bishop
7/5/12
Read Re: Alternative area postulate for geometry
kirby urner
7/5/12
Read Re: Alternative area postulate for geometry
Robert Hansen
7/5/12
Read Re: Alternative area postulate for geometry
kirby urner
7/4/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/6/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/6/12
Read Re: Alternative area postulate for geometry
kirby urner
7/6/12
Read Re: Alternative area postulate for geometry
Joe Niederberger
7/7/12
Read Re: Alternative area postulate for geometry
Wayne Bishop

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.