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From: Archimedes Plutonium on 31 Jul 2010 00:54


Archimedes Plutonium wrote:
> Archimedes Plutonium wrote:
> > Looks like I invented some new terms here of:
> > (a) ReCalculus to signify the strip-building rather than the
> > decomposition into picket-fences
> > of Calculus.
>
> I looked up the word "calculus" and surprized to find it is a Latin
> word that meant
> "a small stone used for counting". I have to check into that some more
> to see exactly
> what is meant by that.
>
> I also looked to see if the ancient Romans had a picket fence and a
> word for picket
> fence.
>
>
> > (b) Pseudocircle to signify the name of the object formed from the
> > circle inside a square
> > and which is put together as a 4 pointed star shape.
> >
>
> Now this is where it gets really interesting in that the pseudocircle
> and pseudosphere
> are derived from the surface of the circle or sphere from which they
> came from and so are
> involved with "pi", but if we tamper with the pseudocircle and
> pseudosphere in a unique
> tampering we convert the "pi form of pseudocircle" and the "pi form of
> pseudosphere" into
> a logarthmic form, an "e" form of pseudocircle and "e" form of
> pseudosphere.
>
>
> > But an interesting question is whether the 2D pseudocircle is related
> > to the circle by the
> > same percentage of area as the 3D pseudosphere formed from the nested
> > inside sphere
> > and the residue of the cube?
> >
> > So for a square of side equal to 2 and the circle inside of radius 1,
> > we have the square
> > as area of 4 and the circle of area 3.14... which means the total
> > residue area of 4-3.14
> > of 0.86. So the circle takes up 3.14/4 = 79% of the area.
> >
> > For the cube of side 2 would have a volume of 8, and the sphere would
> > have a volume of
> > 4/3 pi r^3 of approx 4.18. So the volume of the sphere is about 52% of
> > the volume of cube
> > leaving the residue which is the pseudosphere to be 48% of the volume
> > of the cube.
> >
> > Now the surface area of the cube is 6 x 4 = 24, and the sphere surface
> > area is 4 pi r^2
> > which is 12.56 and the surface area of the pseudosphere is also 12.56
> > for it is just the contours of the sphere surface area. So this leaves
> > us with an interesting question as to how we have more surface area,
> > and obviously surface area is not conserved. And tells us a bit about
> > conservation laws in physics. We have conservation of volume in 3D but
> > lose conservation of surface area in 3D.
> >
>
> This above is the major new mathematics of this millenium and the
> next. For here
> we have the actual assemblage of mathematics as a part of physics.
>
> In Physics, it is Quantum Mechanics that pulls together all of
> physics. And the essential
> aspect of QM is that existence is both particle and wave. Physics is
> duality and duality is
> both particle and wave. We have this idea or concept repeated in
> mathematics in that math in whole is both geometry and arithmetic. And
> inside geometry we have this duality also in that
> Geometry is both Elliptic and Hyperbolic and when the two are
> considered as one, it is
> Euclidean.
>
> So we have the famous formula:
>
> Euclidean Geometry = Elliptic geometry unioned with Hyperbolic
> geometry
>
> and this is also in physics:
>
> Quantum Mechanics = particle unioned wave
>
> Elliptic geometry is always a "closed" geometry and so it is a
> particle aspect
> of nature. Hyperbolic geometry is a "open ended" geometry and is thus
> the
> wave nature of reality.
>
> Given any closed Euclidean figure or object, we can see nested inside
> the closed
> figure such as a cube, we can see a sphere inside and what is not the
> sphere is
> the residue which when assembled so as to remove all straight line
> segments
> we have a Hyperbolic figure, but based on "pi". We must now convert
> that figure
> to be based upon "e".
>
> Now "pi" and "e" are related since they come from the fact that the
> Universe is one
> big atom of plutonium 231Pu, and this atom has 22 subshells inside of
> 7 shells and only
> 19 occupied subshells in any instant of time, so we have 22/7 and
> 19/7. If the Universe
> were an atom of helium then our values of "pi" and "e" would be closer
> to the values of
> 1 and 2 and not 2 and 3.
>
> Since "pi and e" are related, then we convert the residue of the cube
> and the residue
> of the square and the residue of all Euclidean closed objects from
> their "pi based residue"
> to their "e based residue".
>

Now as I described the above pseudocircle as the residue of the square
containing the
circle inside the square, that the four pointed star figure is a
pseudocircle. But there is one
thing remaining to be done to this pseudocircle in that two of the
pointy ends, the north
and south ends have to have a logarithmic curves rather than a
"circular curve" and where
the ends leave not a point in common but form a tiny gap. The other
two ends (the equator
ends) meet in a point.

Now maybe the circular curves are acceptable, but I rather think they
must be transformed.

And as for the cube with its three cuts of the residue to form a
pseudosphere, the curves of
it are also "circular curves" so that the north and south poles have
to be logarithmically adjusted. Now pi and "e" are not far off from
one another in terms of value: 3.14... and 2.71...
So the adjustment is not a huge one.

The famous formula still stands as

Euclidean Geometry = Elliptic unioned Hyperbolic geometries

For in 2D, the area remains the same and in 3D the volume remains the
same.

Now when we make the conversion of the hyperbolic part removing the
"pi base"
and converting to the "e base" obviously the logarithmic portion that
is changed
must have its end effect of keeping the area equal in 2D and keeping
the volume
equal in 3D. So the changes that occur on two points of the 4 pointed
star must
cause a change in the other 2 points so that the area of the
logarithmic curves
compensates for the area of the circular curves. Same thing goes for
the 3D
pseudosphere that the changes in the pole curves has to be compensated
by
changes in the equatorial curves so the volume is preserved in the
formula.

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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