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

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 Joe Niederberger Posts: 1,737 Registered: 10/12/08
Re: Alternative area postulate for geometry
Posted: Jun 29, 2012 10:05 AM
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Yes, well, being "interested in" and "being in a position to unduly influence" are quite different, in my experience.

You say you are dissatisfied with the "area postulate generally in use" and yet, when you go searching for a
definitive reference to said postulate on the internet, you come up empty handed. Something fishy here. Furthermore, you seemed not to realize that you can't derive A=LxW from your alternate "postulate" alone.
In your "derivation" you say "Naturally, the area of a square follows as a special case in which the sides of the rectangle are of equal length." Truthfully I'm not going to go through your steps one by one but I think if you dwell on that statement and rethink what "follows as a special case" means (as in logic) you've mis-stepped here. You are choosing to *make* it the special case so that you will agree with 99.9% of the rest of the world. I hope you're convinced by now that it is in fact a choice and does not "follow as a special case".

Being the internet searching maven that I am, I tried typing "area postulate"and "area axiom" into Google, (as well as consulting wikipedia on "area", which I've covered before.)

Try it yourself - if you go through several pages of results, you will turn up many results.
For example:

(My favorite, this one includes Cavalieri as a postulate)
http://academic.brcc.edu/ryanl/modules/geometry/area/area_axioms.pdf

http://www.beva.org/math323/asgn3/sep26.htm

http://library.thinkquest.org/20991/geo/area.html

http://per6.tripod.com/index-3.html

http://dlc.k12.ar.us/pat.%20laster/PDF%27s/Geometry/Postulates.pdf

http://www.math.uga.edu/~clint/2008/geomF08/axioms/area.htm

There are many more, some just slapdash lists without context, some from courses at the college level, etc.
For the slapdash, Wayne's cautions are most appropriate.

I get the distinct impression that the world is divided into those who take the "unit square = area 1" as fundamental, and those who take the rectangle formula A=LxW as fundamental. I hope everybody agrees that A=LxW
can be decomposed a bit, but one must still choose a unit.

So, rather than reinvent the square, why not just find a
nice solid course that teaches the unit square = area 1 approach?

Joe N

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

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