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From: Archimedes Plutonium on 30 Jul 2010 13:26


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".

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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