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From: Archimedes Plutonium on 30 Jul 2010 01:44
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.
(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.

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.

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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