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From: Archimedes Plutonium on 23 Jun 2010 14:02


Archimedes Plutonium wrote:
(all else snipped)
>
> --- derivation of speed of light out of pure math ---
>  Earlier I wrote how the speed of light in physics should be derived
>  out of pure math
>  as that of Stripe Geometry on the surface of Earth where I take all
>  the meridians
>  as stripes and where the circumference of Earth is 40,000 km so all
>  the stripes are
>  1 km wide and all of meridians distance would be 40,000 x 40,000 and
> the
> stripe
>  that represents
>  the Log-spiral would be 5,000 and this is the time in seconds

A Logarthmic spiral, whether golden spiral or not, and whose arclength
is
5,000 km becomes 5000 seconds is the representative spiral in this
derivation

> instead of distance,
> thus yielding a speed of light
> 40,000 x 40,000 / 5,000 is equal to 3 x
>  10^5 km/sec.
> --- end of derivation ---
>
> Now the above derivation is unitless, in other words it matters not
> whether we do in
> in km/second or meters/second or in miles/second because the band
> width of the
> stripe compensates for the different units.
>

I am backtracking for a moment. I am not an expert on log spirals and
that is why
it has taken me longer time to straighten this out. I call this log
spiral of 5,000 seconds
or 1/8 of Earth circumference as the *log spiral representative*.

The task for me is to find out what is so special about a particular
log spiral, if it be the
golden log spiral and what is special about the arc length of 5,000 km
on that
log spiral for Earth's circumference at 40,000 km.

So I need to find out if there is any log spiral that has something
special going on when
running from pole to pole and with a 5,000 km arc length.

So what I am going to do is experiment by getting pieces of bendable
wire and playing
around on a globe. I need to see it in practice rather than just ideas
floating in the mind.

If I find out that there is a special unique log spiral for Earth
(idealized as a sphere) and that
there is something special about arclength of 5,000 km for this log
spiral, then I will have
solved it.

By the way, I ran through some integer numbers for circumference of
Earth and 1/8
Earth circumference to see how close I could reach 314159 km/s.

39633 x 39633 = 1,570,774,689 and that divided by 1/8(39633) or 4954
is 317072

But all of that is meaningless pursuit, unless I find a unique log
spiral, whether it be
a golden spiral, but a unique log spiral for Earth that makes 1/8
circumference as
arc length on the spiral have special meaning.

SECOND OPTION: there is a second option, in case the above fails
completely. By
failure, I mean that there is no special log spiral where a Earth
metric of 5,000 arc
length is special. A second option is the pseudosphere, or the
hyperbolic geometry
analog of the sphere in elliptic geometry. So I have 40,000 x 40,000
and I need a time
factor of 5,000 divided into 40,000 x 40,000. Is there something about
a 5,000 km on
the analog pseudosphere that is unique and special? I recall that the
volume and surface
area of the pseudosphere is identical to the sphere. There are no
lines of longitude on
a pseudosphere, so I wonder if that the lines of longitude on sphere
is 40,000 km, there
are some special hyperbolic lines on the pseudosphere of arc length
5,000 km?

So if my log spiral option runs out into failure, I need to look into
the pseudosphere.


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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