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3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure?

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  3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure? Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-11-23 13:17 -0800
    Re: 3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure? Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-11-23 18:59 -0800
    Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-11-24 14:13 +0000

#714284 — 3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure?

3-With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure? 


On Thursday, November 22, 2018 at 7:26:02 PM UTC-6, Archimedes Plutonium wrote: 

With this definition of Geometry-Density, is it safe to say the torus is the most dense geometry figure? 

AP 

Newsgroups: sci.math 
Date: Thu, 22 Nov 2018 17:59:20 -0800 (PST) 

Subject: is the torus the most dense geometry object? Re: A new breakthrough 
 in Physics and Mathematics-- GEOMETRY DENSITY Re:  Where the 8 comes from, 
 intrinsic in Faraday Law 
From: Archimedes Plutonium <plutonium....@gmail.com> 
Injection-Date: Fri, 23 Nov 2018 01:59:20 +0000 

is the torus the most dense geometry object? Re: A new breakthrough in Physics and Mathematics-- GEOMETRY DENSITY Re: Where the 8 comes from, intrinsic in Faraday Law 

On Thursday, November 22, 2018 at 2:19:54 PM UTC-6, Archimedes Plutonium wrote: 
> Newsgroups: sci.physics 
> Date: Thu, 22 Nov 2018 12:11:57 -0800 (PST) 
> 
> Subject: A new breakthrough in Physics and Mathematics-- GEOMETRY DENSITY Re: 
>  Where the 8 comes from, intrinsic in Faraday Law 
> From: Archimedes Plutonium <plutonium....@gmail.com> 
> Injection-Date: Thu, 22 Nov 2018 20:11:57 +0000 
> 
> A new breakthrough in Physics and Mathematics-- GEOMETRY DENSITY Re: Where the 8 comes from, intrinsic in Faraday Law 
> 
> - hide quoted text - 
> On Thursday, November 22, 2018 at 12:11:11 AM UTC-6, Archimedes Plutonium wrote: 
> > Mass of real proton is 840MeV and real electron is 105MeV for a ratio of 8 to 1. 
> > 
> > Now i need that number 8 in Faraday Law 
> > 
> > The surface area of torus is 4(pi^2)Rr 
> > 
> > Volume of torus is 2(pi^2)Rr^2 
> > 
> > When we take Area times Volume for electricity-magnetism we end up with 
> > 
> > 8(pi^4)R^2r^3 
> 

Now with those constants of 8 and pi^4 = 97.21... we have 8*97.21... = 777.69.... 

And I cannot find another geometry object more dense than the torus density. Every other object will be to a 5th power. But the constant involved all seem to be smaller than the torus constant. 


> I have landed on a brand new concept of Physics, Mathematics and Chemistry. This concept would never work in Old Physics or Old Math because it requires Space be quantized, Space be discrete not a continuum. 
> 
> And the idea is that Space has a density. Now in chemistry they use density often, for the atoms of chemical elements have a density, where the most dense are the metals in the middle of the Periodic Table-- osmium, iridium etc 
> 

Sad that in Chemistry, none were bright enough to demand density of atoms. Sure, they found radii, and electronegativity and mass of atoms, but no-one had the forethought that density was crucial, also. 

AP 

On Friday, November 23, 2018 at 12:53:59 AM UTC-6, Archimedes Plutonium wrote: 
is the torus the most dense geometry object? Re: A new breakthrough in Physics and Mathematics-- GEOMETRY DENSITY Re: Where the 8 comes from, intrinsic in Faraday Law 

Now the cylinder area & volume match the torus so i need to investigate that for then we could say all toruses are just cylinders. 

AP 

Newsgroups: sci.math 
Date: Thu, 22 Nov 2018 23:51:00 -0800 (PST) 

Subject: is the torus the most dense geometry object? Re: A new breakthrough 
 in Physics and Mathematics-- GEOMETRY DENSITY Re:  Where the 8 comes from, 
 intrinsic in Faraday Law 
From: Archimedes Plutonium <plutonium....@gmail.com> 
Injection-Date: Fri, 23 Nov 2018 07:51:01 +0000 

is the torus the most dense geometry object? Re: A new breakthrough in Physics and Mathematics-- GEOMETRY DENSITY Re: Where the 8 comes from, intrinsic in Faraday Law 

Well, here, the density of the cylinder tells us directly the torus is never a remake of a cylinder— you cannot twist a tube into a curve. 

Cylinder area = 2(pi)rh + 2(pi)r^2 

Cylinder volume = (pi)r^2h 

Cylinder density = volume*area 

Density = 2(pi^2)r^3h^2 + 2(pi^2)r^4h 

Far short of the torus density. 

AP 

On Friday, November 23, 2018 at 1:56:46 AM UTC-6, Archimedes Plutonium wrote: 
is the torus the most dense geometry object? Re: A new breakthrough in Physics and Mathematics-- GEOMETRY DENSITY Re: Where the 8 comes from, intrinsic in Faraday Law 

Now of course, keep in mind that with big numbers the cube will have a greater density. But with small numbers of the size of atoms and molecules apparently the torus structure is the most dense. 

AP 

Newsgroups: sci.math 
Date: Fri, 23 Nov 2018 11:57:02 -0800 (PST) 

Subject: unifying principle that unifies Conic Sections with Regular 
 Polyhedra// why Topology is a error filled piece of mathematics junk// 
 conjecture if torus is maximum density is tetrahedron minimum density? 
From: Archimedes Plutonium <plutonium....@gmail.com> 
Injection-Date: Fri, 23 Nov 2018 19:57:02 +0000 

unifying principle that unifies Conic Sections with Regular Polyhedra// why Topology is a error filled piece of mathematics junk// conjecture if torus is maximum density is tetrahedron minimum density? 

- hide quoted text - 
On Friday, November 23, 2018 at 1:51:09 AM UTC-6, Archimedes Plutonium wrote: 
> Well, here, the density of the cylinder tells us directly the torus is never a remake of a cylinder— you cannot twist a tube into a curve. 
> 
> Cylinder area = 2(pi)rh + 2(pi)r^2 
> 
> Cylinder volume = (pi)r^2h 
> 
> Cylinder density = volume*area 
> 
> Density = 2(pi^2)r^3h^2 + 2(pi^2)r^4h 
> 
> Far short of the torus density. 
> 

The torus looks like it can come from a cylinder that is bent, but this reminds one of the case situation of the surface area of a sphere, in that we want to take a sphere surface and lay it flat, but in doing so, we have to make constant cuts and tears into the fabric to get it to lay flat. Same thing happens with a cylinder, we want to bend it so it forms a curved cylinder as ending up being a torus, trouble is, we cannot bent it into a curve for we need to add curvature (add material to one side and remove material from the opposite side). 

So the cylinder is not a torus. And topology of bending does not make for area or volume formulas. In fact, I raise the issue that the entire subject field of topology is a nuisance study and can be thrown out of mathematics altogether as a fakery subject field, much like the Reals as numbers is a fakery subject field, much like the Negative Numbers are fakery, much like the sinusoid wave is a fakery subject field, much like the ellipse as a conic was totally fakery. So, here, we say that the entire subject of Topology of mathematics is just a piece of error filled worthless junk. 

What is valid in area and volume is cut and paste. So that a parallelogram is the area of a rectangle as we cut one corner and adjoin it to the opposite corner forming a rectangle. So, can we form a torus from a cylinder by cut and paste? No, we cannot. Can we form a great-circle from a sphere lune (4 lunes = surface area of sphere) by cut and paste? No we cannot. 

Cut and paste is legitimate math technique. But bend is _not a legitimate_ math technique. 

Now the volume of a cylinder is found by the height times the area of one of its ends. This technique is called *summing up areas* and is a legitimate technique of mathematics. Bending is *not a legitimate* technique of mathematics. 

So we have two legitimate techniques of mathematics geometry: 

1) cut and paste 
2) summing up areas 

Now those of my readers who have been following me for decades now, know that I am after a Unification of Conics with Regular Polyhedra, and through the years, I have been tackling this unification, where I said in one post-- I need a unification principle. 

In this past week I believe I finally found the Unification Principle that will allow me to unify all geometry figures, and that principle is Density of Geometry. Now density of geometry is a bit different from chemistry density of mass/volume = density. Here, in mathematics, numbers and geometry have no mass. So the density in mathematics is about density = points/volume wherein in True Math, points have infinitesimal length, infinitesimal width, infinitesimal depth. We could also do density with line segments as this formula density = line segments/volume because line segments in True Math are slender thin rectangles. Lines in True Math have a length and infinitesimal width, infinitesimal depth. 

So, when I ask the question is the torus the most dense geometry figure possible, I am asking  if we can fit the most line segments into a given volume. This is made more clearly by thinking of physics electricity and magnetism. What geometry figure allows us to Maximize the Faraday Law? That would be a figure that allows us to pack the most wires into a coil closed loop, thus, that is a torus. 

But as a unifying principle for unification of Conic Sections and Regular Polyhedra, the principle of using DENSITY as the unifier. To do that I need density of Area*Volume = Density for 3rd Dimension figures, but I need also Perimeter*Area = Density for 2nd Dimension figures. 

So, in case of the square density and the cube density. The cube density is area*volume = 6s^5. And now the square density is perimeter*area. The perimeter of the square is 4s, and the area of square is s^2 so the density of square is 4s^3. 

Now, is there any geometry figure whose volume is 4s^3 ? Cannot think of one off the top of my head at this moment. 

What I am more concerned about is the Unifying Principle of Density. 

Notice I have placed a Conjecture out there-- the torus is the maximum density figure of geometry, for small numbers anyway (as the numbers are large, the cube has maximum density). So, is that conjecture true about the Torus, for small numbers-- the size of chemistry atoms and molecules, the torus is maximum density and the torus has that magical number 8. 

Another conjecture, if the torus is maximum density, that begs the question whether the inverse is the smallest density figure having a constant number prefix of 1/8. Now looking at the tetrahedron and thinking it must be the geometry figure in 3rd D of the smallest density of mathematics. Is the tetrahedron 1/8 prefix density? 

AP 

Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.       

Read my recent posts in peace and quiet. 

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium

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#714385

Newsgroups: sci.math
Date: Fri, 23 Nov 2018 18:31:07 -0800 (PST)

Subject: looking at tetrahedron density versus torus // conjecture if torus is
 maximum density is tetrahedron minimum density?
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sat, 24 Nov 2018 02:31:08 +0000

looking at tetrahedron density versus torus // conjecture if torus is maximum density is tetrahedron minimum density?

- hide quoted text -
On Friday, November 23, 2018 at 3:30:31 PM UTC-6, Archimedes Plutonium wrote: 
> Circle density is perimeter*area = 2(pi^2)r^3 
> 
> That does not remind me of any volume of some figure 
> 
> Unless perhaps some polyhedra come close to that 

Alright, so, let me apply this new found knowledge to look for the Smallest Geometry figure density. I would guess a regular tetrahedron. 

So the density of a tetrahedron would be (surface-area)*volume. That would be (sqrt3)s^2 times (sqrt2)(1/12)s^3 = (sqrt6)(1/12)s^5 

If the torus is a maximum density and the regular tetrahedron a minimum density, we do not see a inverse of a prefix factor. Tetrahedron prefix factor is .20.... and torus prefix factor is 777.69.... 

Torus density is 8(pi^4)R^2r^3 

If it were a inverse relation of 8 to 1/8 would be 8 to .125, although .2 is rather close to .125. 

Now as for Perimeter*Area density for equilateral triangle we have 3s * (sqrt3)(1/4)s^2 = 3(sqrt3)(1/4)s^3 = 1.299...s^3. 

So still looking for link-ups,,,, 

AP 

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#714415 — Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

X-No-Archive: yes

Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

>I have landed on a brand new concept of Physics, Mathematics and
>Chemistry.

> This concept would never work in Old Physics or Old Math because it
>requires Space be quantized, Space be discrete not a continuum.

>And the idea is that Space has a density. Now in chemistry they use
>density often, for the atoms of chemical elements have a density, where
>the most dense are the metals in the middle of the Periodic Table--
>osmium, iridium etc

>But Physics saw density concept as secondary not primary. Here we make
>density of utmost importance as a primary concept.
...
The sphere density would be 4(pi)r^2 * 4/3(pi)r^3 = 16/3(pi^2)r^5

The cube density would be 6s^2 * s^3 = 6s^5

So density is proportional to the fifth power of the length????

And the units don't match: Automatically WRONG. (real density is mass/vol)

And the mass isn't even a factor? So a helium balloon has the same density
as a lead balloon of the same size? Hey Uncle Al, have you ever heard of
*anything* as dumb and stupid as this???


"I cannot believe how incredibly stupid Archie-Poo is.  I mean rock-hard
stupid.  Blazing hot mid-day sun on Mercury stupid.  Surface of Venus
under 80 atmospheres of red hot carbon dioxide and sulfuric acid vapor
dehydrated for 300 million years rock-hard stupid.  Stupid so stupid that
it goes way beyond the stupid we know into a whole different sensorium of
stupid.  Archie-Poo is trans-stupid stupid. Meta-stupid.  Stupid so
collapsed upon itself that it is within its own Schwarzschild radius.  
Black hole stupid.  Stupid gotten so dense and massive that no intellect
can escape.  Singularity stupid. Archie-Poo emits more stupid/second than
our entire galaxy otherwise emits stupid/year.  Quasar stupid.  Nothing
else in the universe can be this stupid.  Archie-Poo is an oozingly
putrescent primordial fragment from the original Big Bang of Stupid, a
pure essence of stupid so uncontaminated by anything else as to be beyond
the laws of physics that define maximally extrapolated hypergeometric
n-dimensional backgroundless stupid as we can imagine it.  Archie-Poo is
Planck stupid, a quantum foam of stupid, a vacuum decay of stupid, a grand
unified theory of stupid.

Archie-Poo is the epitome of stupidity, the epiphany of stupid, the
apotheosis of stupidity.  Archie-poo is stooopid."

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