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From: Archimedes Plutonium on 14 Feb 2010 02:41


gudi wrote:
> On Feb 14, 1:01 am, Archimedes Plutonium
(snipped)
> > I do not seek any compression or strain or deflection. I seek only a
> > definition that 90% fits surface contact.
>
> What you seek in other words is in fact strain, be it for the surface
> or for the meridional lines. Bending,surface strains are defined in
> the mathematical Theory of Elasticity relevant to curved surfaces
> (shells).
>
> Narasimham

I disagree Gudi. A much easier and intuitive approach is via area
inside those graph-squares
where the great-circle splits a square apart and where the tractrix
splits the square apart.

Your approach is more from the engineering standpoint. Mine is more
from pure math.
Yours goes into elasticity and bending. Mine seeks just pure
relationships.

So in my approach, I want to examine all the graph-squares and see if
there is any
square which the arc of the circle is matched in area by the arc of
the tractrix as it
splits that square into two parts. If it matches exactly in area, then
the arcs are equal.
So I simplified my task and chore to finding where the area of the
tractrix square is
90% the area of the circle square. I think you would agree that I made
the problem far
more esthetically pure, rather than introduce a strain and bending
concept which would
be the only route for an engineer, since an engineer is not after the
pure-knowledge but
rather the practical.

By the way, I am after this, for the ulterior motive that 10% of the
tractric is equal or close
to equal to the great-circle, for the idea that Algebra is only good
for about 10% of all the
numbers and that Algebra is deaf dumb and silent over 90% of the
numbers that exist.

So, I have what I sought for, and time to move onwards.



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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