|
|
deriving speed of light from pure math alone; Tractrix ; Chapt 19
#198; ATOM TOTALITY
Posted:
Jun 25, 2010 2:09 AM
|
|
Wikipedia has a fine outstanding entry on "tractrix"
http://en.wikipedia.org/wiki/Tractrix
It runs hand in hand with this argument I am making. It shows a graph
of the
Tractrix with a radius of 4 units and it thus reveals the "defect" to
be about
2 units and a bit more.
Now by defect, I mean the fact that the enclosing of a sphere with
pseudosphere
inside has to deal with the cutting-off of the two infinite poles of
the pseudosphere.
So for Earth sphere of 40,000 km strips with 40,000 of these strips
making a total
distance of 40,000 x 40,000 km and then divided by time in seconds of
5,000 seconds.
How do I get 5,000 seconds?
A long time ago, I thought there was 5,000 km of a special important
log spiral,
perhaps the golden ratio log spiral. So that the speed of light is a
rivalry or a race
between light travelling through the 40,000 strips each 40,000km long
and the
log spiral is the timekeeper for the travelling through all the
strips.
And thus the speed of light would be 40,000km x 40,000/ 5,000 seconds.
Trouble is, I cannot find anything special about log spirals to give
me 5,000 km
to say it is 5,000 seconds. There is no log spiral with a 5,000
connected to it
that is special.
So that is why I now have turned to looking at the Hyperbolic geometry
for a
5,000 special number.
I think I may have found it, unlike the U2 song "found what I am
looking for".
Notice on that Wikipedia page of Tractrix, that the poles of the
pseudosphere
are cutaways. The poles go to infinity, but being enclosed inside the
Earth sphere
of 40,000 km circumference, the pseudosphere has its poles cut off,
and there
is this gap or breakage of continuity of the pseudosphere inside the
Earth sphere.
I think this gap is the specialty, where I find the special number of
1/8 of the
enclosing sphere circumference over the pseudosphere inside.
So if you look at that Wikipedia page of tractrix, the defect of the
tractrix or pseudosphere
pole is 1 unit in 8 units, or 1/8 circumference.
In the prior immediate posts, I was looking at the circumference of
the pseudosphere poles
and that is a far to big of a number. All I want of a defect number is
a "bridge number".
A bridge number so that as the light waves go around 40,000 times each
of a distance
of 40,000 km. That those light waves, so to speak, go over the bridge
of the
enclosed pseudosphere defect.
So how much length of this bridge during each circuit of the
circumference? If I am not
mistaken, the distance or length of the bridge that fills in the gap
of the pseudosphere
poles is a distance of 5,000 km, if the enclosing sphere circumference
is 40,000 km.
Now the way to think about this all, would be to reverse where the
light travels, since
Elliptic and Hyperbolic geometries are reversals of one another, or
inverses or duals of
one another.
So the way to think about this derivation of the speed of light is
that given a sphere,
and I chose the Earth sphere of 40,000 km circumference with the
pseudosphere inside
it. And the light wave travels down every 40,000 km strip, not of the
sphere but of the
pseudosphere, but when it reaches near the poles, there is a hole
there that is bridged
by the Elliptic sphere, and so the light wave disengages with the
pseudosphere track
inside Earth sphere when it gets close to the poles and takes the
bridge of the sphere
to get it back to where the pseudosphere inside leds the track
further.
Or, better yet, since elliptic is reverse of hyperbolic we shift the
poles of the pseudosphere
to be located at the equator of the Earth sphere and thus have the
cusp of the tractrix where
the poles of the Earth sphere is located. And now, as the light wave
travels on the Pseudosphere track, it naturally will take the bridge
at the equator as the sphere curve.
In this manner, speed of light is seen as a rivalry of a competing for
how long is the
pseudosphere circumference and since it has a hole or defect, the
competing of filling
or bridging that hole gap by the bridge of the sphere arc over the
hole gap.
And so we have 40,000 x 40,000/ 5,000
I think I am getting closer, but not fully satisfied with this. Still
feel some ad hoc in this.
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
|
|
