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From: Archimedes Plutonium on 9 Apr 2010 14:56


Archimedes Plutonium wrote:
> --- quoting from ---
> http://www.mathpages.com/home/kmath502/kmath502.htm
>
> This curve on the surface of a sphere is sometimes called a loxodrome,
> rhumb line, or spherical helix. A path beginning on the equator and
> maintaining a constant heading of K=0.2 is shown in the figure below.
> --- end quoting ---
>
> Trouble with alot of geometry is that few think about defining angles
> in Elliptic unioned
> with Hyperbolic geometry. Seems as though all of geometry falls back
> to a "default" of
> Euclidean. So when I want to know the Elliptic angle in which the
> Golden Rectangle
> Logarithmic Spiral cuts each and every longitude or meridian, it is
> not to be found.
> Because noone can define an angle in Elliptic geometry. Always have to
> throw in some
> Euclidean rigging to talk about an angle.
>
> So we say that Euclidean geometry is 180 degree triangles and Elliptic
> is greater than
> 180 and Hyperbolic is less than 180 but when we actually examine the
> loxodrome angle,
> we all revert to some Euclidean outrigging program.
>
> So what is the Rhumb line angle, the Loxodrome angle of the Golden
> Rectangle
> logarithmic spiral?
>

So what is the Loxodrome angle or the Rhumb line angle using a Golden
Rectangle
Log Spiral as it cuts each meridian at the same angle? Is it 71
degrees angle?

Now some are going to say, AP, how does your derivation get rid of the
units for
the speed of light? And my answer is that no matter what units you
want to throw
at me. Throw me 186,282 miles/sec or throw me some really obnoxious
made up stuff
for a speed of light, and have you thence put miles or made up stuff
into the
Planck units of Planck Length and Planck Time. So if you throw me
miles/sec, then it
is your burden to have to put miles into the Planck Length. And so,
what comes out
is that it all is equal to 3 x 10^8 m/sec.

And thus there is a pure math derivation of the speed of light. It
involves the Golden
Rectangle Logarithmic Spiral on a sphere surface. The spiral is time
and the longitude
is distance. The angle formed is a constant, or, is the speed of light
itself. So in the
forming of the angle, we divide distance by time and end up with
something like this
for meters and seconds, 10^44 / 10^36.

If someone complains that it does not look like miles/sec, well, put
miles into the conversion
so as to fit into the Planck length and Planck time equations.

Now if memory serves me on the history of the loxodrome, that the
Rhumb line was thought to
be the shortest distance between two points on the globe. But
obviously near the poles this is
false, and that near the equator one maybe tempted to think that the
rhumb line could be a
close call as the shortest distance, but we do know the great-circle
is the shortest distance.

I want to harp back to the anchor in this quest. The anchor is that of
Special Relativity, and
for Euclidean geometry alone, it is the number "pi" that is constant
to all observers and all
frames of reference since every circumference/diameter is pi in
Euclidean. But in the breaking
of symmetry of Euclidean we have Elliptic unioned Hyperbolic geometry
and that is the spacetime we live in and that the speed of light is
the Special Relativity of Elliptic unioned
Hyperbolic. The speed of light is not pi, since pi is a variable in
Elliptic and Hyperbolic, so
thence, what is the speed of light in Elliptic unioned Hyperbolic? The
answer is the angle
of a loxodrome with a golden-mean log-spiral. And the derivation of 3
x 10^8 for meters and
seconds is purely got from mathematics itself. Just as the derivation
of the mass ratio of
proton to electron or the inverse fine structure constant come out of
pure math in that the
Plutonium Atom Totality is 5f6 giving rise to 6(pi^5) and (pi^7)/22
giving rise to 137.

Likewise in a Plutonium Atom Totality, the Planck length/Planck time
yields a constant angle
in the loxodrome of the 5f6.

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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