I've Eliminated 'irrational' numbers
kpaulc at [remove]earthlink.net
Thu Apr 15 07:10:42 EST 2004
While Working with the other stuff that I've
posted recently, I Totally-Busted Incommens-
And it's Easy to see.
Given a Circle, having =any= radius, construct
1. having the Circle's radius as it's hypotenuse,
call it C,
2. one side as a semi-chord, with one end shar-
ing a point with the circle-end of the hypotenuse,
call it A,
3. and the other side drawn from the center of
the Circle, to meet the semi-chord, forming a
right-angle, and sharing a point with the 'dangl-
ing'-end of the semi-chord, call it B.
4. The Pythagorean Theorem applies, and
A^2 + B^2 - C^2 = 0,
5. and is =ALWAYS= Equals Zero.
6. As one varies the angle that the hypotenuse
make with the X axis, A and B adjust their
lengths continuously, and
A^2 + B^2 - C^2 = 0, always,
7. even when A or B becomes Equal to
8. at which point, either the semi-chord, A,
or the center-pinned line, B, becomes Equal
to the hypotenuse, C.
9. This seems, to me, to be quite "astounding",
because "Incommensurability" is nowhere to
10. Since the radius can be of =any= length,
this Circle operation scales from zero to
Infinity, which covers =any= plane, and does
so, Continuously, without a hint of "Incom-
11. It does this be-cause when A and B go-
Irrational, they balence each other =Exactly=!
12. Which means that Irrational Numbers
are no longer a "Problem" - just construce
a Circle with the necessary radious, and, voilà,
there's your "Conjugated"-pair of Irrationals,
ready to do anything that you want to do with
13. Of course, you cannot measure these
Numbers, but you can "address" them, Exactly,
through the Circle-Geometry, given above. You
know, pick your favorite Greek symbol, and
its, "Bye-bye, 'Irrationals'.
Q. E. D.
K. P. Collins
(c) 2004-04-15, by K. P. Collins
More information about the Neur-sci