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From: Archimedes Plutonium on 10 Mar 2010 01:44
Sorry I do not have a interpretation of (i) as a 90 degree rotation.
To me it looks more
like a 180 degree rotation.

--- quoting Wikipedia on (i) ---
In this representation, multiplication by -1 corresponds to a rotation
of 180 degrees about the origin. Multiplication by i corresponds to a
90-degree rotation in the "positive" direction (i.e. counter-
clockwise), and the equation i^2 = - 1 is interpreted as saying that
if we apply two 90-degree rotations about the origin, the net result
is a single 180-degree rotation. Note that a 90-degree rotation in the
"negative" direction (i.e. clockwise) also satisfies this
interpretation. This reflects the fact that -i also solves the
equation x^2 = - 1
--- end quoting Wikipedia ---

I need to have an interpretation if the number for (i) is of the
3162...pattern.

sqrt9 = 3
sqrt99 = 9.94
sqrt999 = 31.60
sqrt9999 = 99.99
sqrt99999 = 316.22
sqrt999999 = 999.99
sqrt9999999 = 3162.27

I would instantly have a beautiful interpretation of 3162.... were a
point on the Equator
where 0000.... is the North Pole and 09999.... is one unit short of
the South Pole and
90000..... was the South Pole (formerly written as 1000....0000) and
where 9999.... = -1
is one unit short of the North Pole.

So as you can see for the 10^500 Algebra Wheel of Numbers that there
is no number
3162..... Since one hemisphere contains 0 to 10^500 minus one, and
the second hemisphere
contains the negatives of the first hemisphere written with a 9
preface for frontview.

The number 3162.... as (i) has a 3 preface for frontview. So where is
it? Is it a point on
the Equator that is 270 degree radian?

Is it perhaps on a different longitude line that is a 90 degree
rotation from the wheel I am
starting with?

So I do not know how to interpret 3162..... pattern.

But there is a good sign in this, for Wikipedia entry talks about -1
being a 180 degree rotation
and (i) being a 90 degree rotation. So that is just 1/2 X or half
times the magnitude that I am
comfortable with. For as I see it, a rotation of -1 is from 0 all the
way around to 9999...999 and
stopping short by one unit of the North Pole. And so I would think
that if -1 is a 360 degree rotation (less one unit distance) then (i)
would be a 180 degree rotation.

Now in binary, -1 is 1111...1111 but that the last and largest Finite
is 01111....1111 which is
one unit short of the South Pole. And a rotation from the South Pole
to the North Pole is
180 degrees. So here a question popps up. Is the South Pole the
imaginary number (i)??
Can we have the South Pole as (i) whether it is 9999.... pattern or
3162..... pattern?

Now in Hyperbolic geometry, the poles have to be imaginary in order to
have more than one
line parallel to a given starting line.

Now the pattern of 1111.....11111 versus 01111....11111 in binary look
almost similar except for that lonesome "0" digit meaning it is one
unit short of the South Pole versus 1111....111 one
unit short of the North Pole. So is 01111....1111 in binary the (i)??

Also, while I will be ruminating over these questions, in the geometry
of the Luminet-Poincare
Dodecahedral Space there is a twist of 36 degrees or 10% of the sphere
circumference. The
number 3162.... pattern could have some tie into 36 degrees of a
circumference.

Let me ruminate.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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