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AP's 308th book of science// Conjecture, Sphere is maximum volume given
From
Archimedes Plutonium@21:1/5 to
All on Sat Nov 25 22:58:03 2023
Now I am sure the sphere is maximum volume given a specific surface area is proven a long time ago, and have to see how that proof goes.
But I am conjecturing that AP is the first to notice that the counterpart to a sphere of volume to surface area is the Torus. Which is inverse or reverse of sphere so that the Torus when given a specific volume, that the torus figure maximizes the
Surface Area from that volume.
It is the torus I make this conjecture and make this my 308th book of science, if not already proven true.
I have plenty of time to research this as my queu line of book writing is currently at 263, so sometime next year in 2024 will get to this idea.
AP, King of Science
AP's 308th book of science// Conjecture, Sphere is maximum volume given specific surface area, while Torus is reverse-- maximum surface area given specific volume.
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From
Archimedes Plutonium@21:1/5 to
All on Sat Nov 25 23:05:32 2023
Immediately I can recognize what is going to hold this conjecture up or even defeat it.
In my living room I have a electric space heater shaped like this ||||||| with ribs. So the volume inside this heater is a small number but the surface area with all those ribs are enormous in comparison to volume.
So unless I can well define a torus opposed to a space heater, I have no conjecture.
What can I say about a torus that eliminates the space heater as a figure of contention??
AP
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From
Archimedes Plutonium@21:1/5 to
All on Sun Nov 26 00:53:48 2023
Yes, ribs are a minor problem easily dispensed with by a well defined definition of Solid Figure versus Ribbed Figure. So my electric space heater is a ribbed rectangular box with 7 ribs and so I define the Solid Rectangular box that the heater can fit
into and then I define a ribbed rectangular box. Same thing for Sphere-- the solid sphere and a ribbed sphere. But then what happens is the ribbed Torus beats out the other ribbed figures. So no problem with ribs.
And I should detail some special ribbed figures, the Saddle shaped figure is actually the intersection of two ellipsoids or ovoids or a mixture of ellipsoids and ovoids that are then ribbed. None of this fancy Lobachevsky and negative curvature need be
applied or thought of.
But having solved the rib problem and dismissing it be saying the ribbed Torus beats out its rivals, I have a new problem to tackle. And I wonder why I never tackled this before. I need to well define the associated sphere to a given torus. I suppose it
is to enclose a torus inside a sphere and then pick off what the torus r radius and R radius are from the enclosing sphere. There should be ample new insights and new discoveries here in this undertaking.
So yes, this conjecture is going to be new and sweet.
AP
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From
Archimedes Plutonium@21:1/5 to
All on Sun Nov 26 13:23:08 2023
The problem of a unique enclosed in a sphere is easily solved when we demand the torus be 840 rings each separated from its neighbor rings by an angle of 360degrees/840 = 0.42 degrees.
--- quoting from my 205th book of science ---
Faraday Law is inverse projective-geometry of Coulomb-gravity Law//Physics-Math by Archimedes Plutonium
Preface: This book discusses the symmetry of the 4 differential laws of Electromagnetic theory, the Faraday law, Ampere-Maxwell law, Coulomb-gravity law and the Transformer law. This book also dives into the numbers of importance of physics and math, the
1/137, the pi, the pi subtract 2.71... and much more.
Cover Picture: Is my iphone photograph of 840 windings of slinky toy to form a torus that is the proton torus of physics of its 840MeV with a muon stuck inside at 105MeV doing the Faraday law.
--------
If true, my conjecture then places the meaning of the Fine Structure Constant, -- its meaning is geometrical, in that the fine-structure-constant is a measure of how many windings you need to make a torus, that allows the Faraday law to be carried out as
freely in a torus, as the Faraday law is carried out in a cylinder.
The 840 windings is t
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From
Archimedes Plutonium@21:1/5 to
All on Sun Nov 26 13:37:22 2023
In my 205th book of science I discover a way of producing four important constants of physics and math-- pi, Fine Structure, 840, and 360. One of those is a angle measure-- the 360 for a full revolution.
In an experiment described in that 205th book, I took 840 identical circles and crafted them into a perfect torus. To find the angle of separation I did a 360/840 and found an angle of 0.428 degrees. Look up what 0.428 degrees is in radians-- for it is
the Fine Structure constant of physics 0.0072. Then in that experiment I measured the diameter and radius of the torus I constructed from 840 identical circles placed with a angle 0.428 degree separation. Measuring the diameters of circles and of the
donut hole, the diameter of the donut hole of 840 circles forming a ratio which is pi = 3.14159....., specifically, in my experiment --
--- quoting my book ---
Alright, well it is easy to see that 210/65 is 3.230... So I went back to the lab and measured again and it was actually 205mm to 65mm. That gives me 205/65 = 3.15 and compared to pi 3.15/3.14 is a 0.3% sigma error, so close that it is automatic we
announce that given any circle, and if you have 840 of those circles wound around into a torus, that the donut hole diameter divided by given circle diameter is pi number.
--- end quote ---
This is amazing for in a torus construction of precisely 840 circles, specifically 840, it cannot be any other number. That in the construction of 840 falls out pi = 3.1415... falls out that a full circle revolution must be the number 360 degrees and
falls out the Fine Structure Constant in radians 0.0072.
My 205th published book of science.
Faraday Law is inverse projective-geometry of Coulomb-gravity Law//Physics-Math
by Archimedes Plutonium (Author) (Amazon-Kindle edition)
Preface: This book discusses the symmetry of the 4
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From
Archimedes Plutonium@21:1/5 to
All on Sun Nov 26 20:09:46 2023
Now that is an interesting question and one of the problems solved in this book. The question of the horse saddle shaped geometry of Old Math geometry. Of course they thought it to be an example of hyperbolic geometry, or Lobachevsky geometry of negative
curvature.
But the big problem is-- how do you pin a Volume quantity to a saddle shaped figure????
In New Math there exists not 3 geometries in the world, just 1 and that Euclidean is the only geometry, but you can separate Euclidean into two parts, a positive curvature along with a negative curvature, only because you separated them. A circle
enclosed in a square, and cut out the circle and what remains is 4 pieces of what is called hyperbolic triangles. This is not a separate new geometry but cut-aways of Euclidean geometry.
Back to the horse saddle shape. A true geometry would have volume, not just area. But you cannot place a volume into a saddle shape.
And this then brings our attention to the idea that the Saddle Shape Geometry is merely the intersection of 2 ellipsoids or 2 ovoids and to make ribs of those 2 ellipsoids or combinations of ellipsoids and ovoids.
The Ribs are at a perpendicular to one another.
And then the question of the volume of the Saddle Shape is the volume of the 2 ellipsoids or ovoids.
AP
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From
Archimedes Plutonium@21:1/5 to
All on Sun Nov 26 21:54:08 2023
Alright, time for some calculations, and I harken back to a experiment I did in 2022, where I bought enough slinky toys to sort of guide me in what a 840 windings of a torus geometry produces in numbers. Here is a view of that experiment. What I want to
do is given a sphere of radius 10, diameter 20 compute the radius and diameter of a torus composed of 840 windings inside the sphere and tangent at the equator line. Compute the r radius, not the big R radius, and diameter of this smaller circle that
composes the torus of 840 windings, being sure the ratio of donut hole diameter is that of 3.14159....
On September 17, 2022 in sci.math,sci.physics, plutonium-atom-universe, I wrote a corrected copy:
A fabulous discovery of science physics.
Alright, curiosity in my lifetime has been indefatigable. I wanted to get a rough estimate of the donut hole of 840 windings so I bought 9 more slinky toys to combine with my 2 already owned ones. And I measured what a 840 winding torus donut hole was.
My torus of 840 windings has a donut hole diameter of 205 mm and has a slinky toy diameter of 65mm. That would be a total diameter of torus as 65 + 205 +65 = 335mm with the donut hole diameter 205mm.
Now I play with those numbers and see what becomes of them for the Conjectures I placed so far. The most important being the idea that 840 windings is the physical geometry of the Fine Structure Constant as a torus the produces Maximum Electricity in the
Faraday law.
Alright, well it is easy to see that 205/65 is 3.15... And I went back to the lab and measured again and it was actually 205mm to 65mm. That gives me 205/65 = 3.15 and compared to pi 3.15/3.14 is a 0.3% sigma error, so close that it is automatic we
announce that given any circle, and if you have 840 of those circles wound around into a torus, that the donut hole diameter divided by given circle diameter is pi number.
Now also, looking at the angle which 840 circles create in a torus is 360/840 = 0.428 degree.
Amazingly a angle of 0.428 degree is in radians that of 0.0072 or the physics Fine Structure Constant. Here I have an angle for a torus which allows for a free thrusting of a muon inside the torus, as if the muon is in a cylinder in the Faraday law. And
this angle of 0.428 allows the muon to freely thrust without bumping into the torus walls.
But the amazement does not stop there, for where is the number 0.42 degree angle come up in Physics constants? Well if you take pi 3.14 and subtract from "e" 2.71 you get 0.42.
AP
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