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:
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?
