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MathGroup Archive 2001

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Number Rotation??(?)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30107] Number Rotation??(?)
  • From: edward.griffin at ireland.com (Edward Griffin)
  • Date: Sat, 28 Jul 2001 01:51:07 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Okay, you can laugh if you want, but not 'till you've read the whole
thing. This is something that's been bothering me for a while, and I'd
kind of like to get it cleared up.

Some time ago (Whilst a mathematics student in college)I toyed with
the idea of numbers (as whole and real values) being represented on a
cartesian plain as a point in space, and then being 'rotated' around
x=0 & y=0 to give a point representing the same value, but in another
position. If it's supposed that the observer is at x=0 & y=0, is it
fair to say that the value in it's 'rotated state' is still the same
value, but just seems to be different because it is being judged from
a different perspective. I guess what I'm trying to do is place a real
life object in the same situation as the point on the cartesian plain
which represents the real value of this object. 

Okay, here's what I really mean.


                           Y
                           |
                           |
                          5|
                          4|       *             
                          3|                     
                          2|
                          1|
                 ----------0---------- X
                 -5-4-3-2-1| 1 2 3 4 5
                         -2|
                         -3|
                         -4|       *1
                         -5|
                           |
                           |
 
 Above, * represents the value 16, and I get it's initial position on
the cartisian plain from x = root of 16 and y = root of 16, hence x =
4, y = 4.

 I now have a point that represents 16 on the cartesian plain (to my
mind anyway).

 If I rotate * through 90 degrees around the point 0, it will end up
in the position shown by *1. At this point x is still 4, but y is now
-4. To the observer at point 0, I have taken the value on the
cartesian plain (16) and rotated it around so that it represents -16
(x=4, y=-4, and to arrive back at the true value of the rotated value,
x*y = -16).

This can be performed with any value at any angle by using the
expression below..

{n} = nCos(2t)
   t

I think that we spend too much time thinking of numbers and values as
flat boring two dimensional objects, what if they could have sides, a
back and a front, and maybe on a three dimensional plain, a top and a
bottom.

Okay, the men in white coats are comming soon... but is any of this
valid?


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