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From: Archimedes Plutonium on 24 Jun 2010 14:53


Archimedes Plutonium wrote:
>
> 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.
>

Playing around with some of the algebra of the setup. It works if I
use
only one pseudosphere-pole and where 1/2 circumference of pseudosphere
pole equals 1/8 circumference of sphere.

So this relationship is starting to materialize as true:

Earth Sphere = 40,000 km circumference
Earth Sphere 1/8 circumference = 5,000 km
Earth Pseudosphere Pole = 10,000 km circumference and both
pseudosphere poles
would be 20,000 km

If it were 1/2 of a single pseudosphere pole circumference then I
would have
the 5,000 km but that seems awfully ad hoc.

But there maybe some mathematical relief in my favor. If we apply a
generality,
not just restricted to the sphere but to all ellipse containing the
pseudosphere
of a given diameter, then I think this relationship holds:

circumference of both pseudosphere poles when added together, the sum
equals
1/8 of the circumference of the diameter of the sphere.

P.S. I did note that in the tractrix curve that the defect from the
tractrix to the
circle of same radius is a linear defect of 8 to 1. What I mean is
that you go 8 units
of the Tractrix and you have 1 unit missing to the circle. The circle
is finite and closed,
yet the tractrix is infinite and open. Starting at 0 or the origin or
center of circle, that
you go 8 units of the circle, 4 on Y-axis and 4 on -Y, and you have a
defect of 1 unit
of the tractrix. So if I can better define this defect, maybe the
answer to 1/8 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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