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

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 Robert Hansen Posts: 9,688 From: Florida Registered: 6/22/09
Re: Alternative area postulate for geometry
Posted: Jun 29, 2012 12:33 PM
 att1.html (2.1 K)

Yeah, I got that, I was almost there to, now I am saying that is flat out wrong. Why do you say that 1 x 1 = 1 is conventional? That doesn't look like convention, unless you are saying that 1 + 1 = 2 is also convention. I don't think anyone decided that the unit square was a unit of area. It just so happened that 1 x 1 = 1 looks like a unit square and the name stuck. And the definite integral of S over the interval (0,S) ends up to be S^2 which for a unit square is also 1.

So far I am seeing silliness, but I certainly can be persuaded. Show me the formula for area of an equilateral triangle with sides of length 1 that computes to an area of 1. And then show me the calculus solution of the same area. And then explain where the heck some constant came from out of thin air. I say that if you introduce such a constant then you are inventing a unit where there was none. The problem with this thread is the assumption that the unit square is a unit of area, it is not, and never was.

Bob

On Jun 29, 2012, at 11:51 AM, Joe Niederberger wrote:

> But, more to your point and apparent consternation, Kirby, Wayne, myself, realize that this taking of the unit square as the unit of area *is* conventional, and *can* be taken to be other things, like setting a equilateral triangle of side 1 to be the unit area.

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