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From: Archimedes Plutonium on 8 Feb 2010 03:48


Archimedes Plutonium wrote:
> Alright, I went to this website:
>
> http://en.wikipedia.org/wiki/File:Tractrix.png
>
> And then constructed a circle of equal radius to the picture shown.
> Then I moved the circle around on the tractrix to see if the arc of
> the
> circle matches the arc in the tractrix. It does not match very close
> to the cusp, but it does match about 1/2 ways from the cusp graph
> square
> into half of the next graph square. From the squares of 0,3.5 to 0,
> 2.5
> looks like an alignment of arcs of the tractrix with circle. But the
> problem
> with this method is that the lines are too wide to really see any
> precision.
> But this method does lend credence to the idea that an arc of the
> tractrix
> matches an arc of the circle (sphere).
>
> I have looked through the literature to see if there are any theorems
> in
> geometry that would immediately and automatically eliminate the idea
> of
> a arc of the tractrix never able to match an arc of the sphere
> involved.
> There is none.
>
> However, there is a fact or quasi theorem in math that suggests there
> is
> an arc to match in both tractrix and sphere. The fact is Euler's
> identity
> of sine and cosine that yields e^(i x 2pi) = 1 wherein the pi relates
> to the
> sphere and "e" relates to the tractrix. So this identity suggests
> there is
> a matching arc in both tractrix and associated great circle of sphere
> involved.
>
> The idea behind the matching is that the sphere has a constant-arc-
> curvature
> but that the tractrix has what can be called a collection of sequental
> varying arc curvatures wherein one of those arcs fits an associated
> arc on the circle.
>

Now the above technique is very amenable to computer aid in that the
computer can make those tractrix lines so very narrow and precise as
far as a computer drawing, better than a human instrument aided
drawing.

And then the computer can automatically lift up the circle and roll it
along the
tractrix to see if any arcs match up. Rather than any human
construction
and then superposition to see if a alignment occurs.

Archimedes Plutonium
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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