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From: Archimedes Plutonium on 24 Jun 2010 01:36


Archimedes Plutonium wrote:
> Archimedes Plutonium wrote:
> > 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
>
> That is misleading, and sorry to ever mislead, but the formulas for
> volume
> and area are identical to that of sphere and pseudosphere, but
> however, the
> pseudosphere is open and infinite whereas the sphere is closed and
> finite.
>
> But this perhaps is where an "Earth pseudosphere" may have a special
> number for 5,000 km. The Earth sphere is circumference of 40,000 km
> and 1/8 of that is 5,000 km
>
>
> > 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.
> >
>
> Consider the Earth-Sphere, and this is Earth idealized as a sphere
> with
> a circumference of approx 40,000 km. Now consider a Earth-Pseudosphere
> whose equitor is identical to Earth-Sphere equator and are
> superimposed as
> one. In that superposition of Earth-Pseudosphere inside that of Earth-
> Sphere,
> the ends of the pseudosphere go popping out through the poles. And the
> poles
> of the Earth sphere are points, but are cylinders in the Earth-
> pseudosphere at
> the moment they popp out of the Earth-sphere.
>
> Now I wonder, I just wonder if that cylinder that comes popping out of
> the
> Earth-pseudosphere nested inside Earth-sphere, I wonder if the
> circumference
> of that cylinder is 5,000 km or 1/8 the circumference of the Earth-
> sphere?
>
> I may have struck gold here. That the intersection of the nested Earth
> pseudosphere
> at the polar region is a cylinder that may have a circumference of 1/8
> Earth Sphere
> circumference. I have to explore that lead.
>

Wikipedia provides an excellent picture of a pseudosphere:

http://en.wikipedia.org/wiki/Pseudosphere

And one can immediately see the two poles cutaway. And if that
pseudosphere
were tucked inside the sphere the poles of the sphere would be two
points
but the poles of the pseudosphere would be two hollow cylinders or a
circle.

From the Wikipedia picture we can almost sense how large of a
circumference
those polar circles of the pseudosphere are. Now 1/8 of the
circumference of
Earth sphere is 5,000 km and picture a Earth pseudosphere stuffed
inside of
Earth. The question would be, how much of a distance are the two
circles of the
pseudosphere poles? Would they each be about 2,500 km for a total of
5,000 km?

From the Wikipedia picture it looks as though the circumference of the
total polar
circles is larger than 5,000 km.

One can always compute how large the circumference of these
pseudosphere
poles are, but I rather trust hands on, eyesight of direct models and
to measure
the length.

In the news recently was the world soccer games in South Africa with
their noisy
bugle toys and some are made of plastics. So I am ordering two of
those bugle
horns and then fold a sheet of paper to simulate an enclosing sphere
and find out
how much of a circumference for the two pseudosphere poles.

Now if it arises that these pseudosphere poles are 5,000 km or 1/8 of
Earth sphere,
then I am rather bewildered with this outcome. Bewildered because I
can logically
understand how a log spiral could be a measure of time versus the
meridian-strips
as length for the speed of light derivation. But how can a so called
"defect" of the
pseudosphere cutaway be the time element? The only logical sense I
could make of
that circumstance, is that time is a imaginary feature of physics. It
is measured by
"what is not present", namely, the rest of the poles of the
pseudosphere that goes to
infinity. This is a rather surprizing result, provided of course it is
1/8 the Earth sphere
circumference.


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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