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#509 AP book of science--- The best circle possible in Decimal 10 Grid, the true numbers of mathematics, not the foul smelling Reals and its fetid continuum// math-physics by Archimedes Plutonium

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Archimedes Plutonium

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Jul 6, 2026, 5:00:12 PMJul 6
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I am going to have to tone down the title when ready to publish this book. But for now that is a good title, for many people in academics often are too absent minded and foolish in what to understand and accept.

So in year 1900 with Max Planck in Germany starts a most profound Science Adventure called Quantum Mechanics. Soon other physicists pick up on this, but not the idiots who called themselves mathematicians. No, that mindless group went along more and more with the Continuum and its fetid Reals. They are stupid and absent minded. They learned nothing, nothing at all from Planck and quantum mechanics. For quantum means discrete, the opposite of continuum.

And then there were magnanimous fools like Cohen digging ever deeper into a continuum.

But worse than Cohen are the millions of math professors who not only cannot admit the truth that a slant cut of cone is actually a Oval, never a ellipse.

Of course these Egg-headed Ellipse Math Professors, not only cannot admit the truth on conic sections, but their blindness crosses over into Calculus. They all knew, even the fools like Terence Tao or Andrew Wiles, they all knew Calculus is geometry, yet not a single one of them with a 1/2 marble of logic intelligence offering a Geometry proof of the Fundamental Theorem of Calculus. No, all that these failed losers of math can offer is some stupid silly Wiggle Waggle Dance called the Limit Analysis.

So, when the World of Mathematics has its true numbers--- discrete numbers, then its smallest Grid is the 10 Grid. The 10 Grid is the set of numbers 0, .1, .2, .. 1, 1.1, 1.2, ...9.9, 10. Not counting 0 there are exactly 100 numbers on the x-axis in Decimal 10 Grid. Naturally in the xy plane there are 100 numbers not counting 0 on the y axis.

In total there are 100 x 100 = 10,000 coordinate points, not counting (0,0).

The Decimal 10 Grid is the smallest of all math grids and this book is about the question of how fine of a circle is possible in this Grid.

Well, if we make the size of 10,000 coordinate points be small as the computer type such as the letter O, then we of course can match that smoothness.

I say match that smoothness for our eyes can  no longer see that they are tiny straight line segments of a 200 Regular Polygon.

I have at home with me graph paper is 100 by 80 unit squares. I could attach two pieces together to make 100 by 100. Or, I could just work on a quarter of that, 1/4 of that to tell me the rest of the circle formed from a 200 Regular Polygon.

So what are the sides of this 200 Regular Polygon???

Well, it may not be a Regular Polygon for it may include diagonals of unit squares and sometimes sides of unit squares.

I will first do this on a 50 by 50 unit squares for the 1/4 circle.

And I start with a compass at circle center of (5,5) for Decimal 10 Grid. To draw a Quarter Circle, then I look to see how to make a pattern of straightline segments.

Now I stop to look for the best pattern.

AP

#509 AP book of science--- The best circle possible in Decimal 10 Grid, the true numbers of mathematics, not the foul smelling Reals and its fetid continuum// math-physics by Archimedes Plutonium


Archimedes Plutonium

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Jul 7, 2026, 2:57:17 AMJul 7
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Stunning, and absolutely beautiful math experiment. It teaches me that preconceptions can be extraordinarily wrong.

I went into this game thinking a Regular Polygon will form the most perfect circle from straightline segment. Not true, the outcome is a Irregular Polygon.

One of the rules of this game-experiment of geometry, is you can only connect coordinate points. Each square has 4 coordinate points and so a diagonal or a side line segment can be connected.

What I had not foreseen in my mind, and which the paper graph, pencil, compass, straightedge made quite clear to me--- is that a Irregular Polygon will come the closest in forming the circle.

I have trouble with my graph paper as the squares are not that uniform. I thought first it was my compass swing was not correct. Anyway, I get a 12 sided Irregular polygon for a 1/4 circle. Which would mean a 48 sided Irregular Polygon.

But I have to double check this 12 number, for it maybe 13 or 14.

And before I started this Experiment, I was thinking it was a 200 Regular Polygon for end result, how so wrong I was.

AP, King of Science

Archimedes Plutonium

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Jul 7, 2026, 3:26:36 AMJul 7
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Now, before I repeat the Exeriment with more accurate graph paper, better compass, more due diligence. I am going to look for some Physics or Math Constant that is Geometrical and which is for a semicircle is 2 x 12 or 2 x 13 or 2 x 14. Or, for a full circle would be 4 x 12, or 4 x 13, or 4 x 14.

Some important constant which predicts what the replacement of a semicircle or full circle with straight line segments Must be

Here I would look for what is called a Gradient in math or physics, a gradient constant. It would be extremely lovely to connect up with a already known theory of physics or math which will predict what My Experiment, is precisely going to end up, before I repeat the Experiment.

Now, already I noticed something of vital concern. I was thinking of doing the 1/4 circle because it is easier than doing full circle. But there is a Minimum Amount of the Circle that will give me the full answers to all these questions. It is the 1/8 of a Circle. At minimum. I need do Only 1/8 of a circle to answer all the questions of this Experiment.

Now, let me momentarily pause in my writing and go and check if 1/8 of the circle ends up on two coordinate points. I do know that both ends of the 1/4 circle end up or start on a coordinate point, but not certain if 1/8 of a circle ends up and starts on two coordinate points.

Let me verify----- Yes, indeed, 1/8 of the circle starts at a coordinate point and ends at a coordinate point. 

Now let me see if in the 1/8 circle I can get 8 vertex coordinate points which would mean I was wrong with 12, 13, 14 but is in fact 16 for the 1/2 circle.

No, sorry, I get 12 vertex coordinate points for the 1/8 circle would then be a 96 Irregular Polygon.

So tomorrow I need to look for a larger graph paper for my current paper is too small of unit squares. A larger unit square would be more accurate.

But the number 96 comes up in some physics or math constant, for which at this moment in time I have a lapsed memory.

See you tomorrow in this topic.

AP, King of Science

Archimedes Plutonium

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Jul 7, 2026, 3:50:55 AMJul 7
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Yes, it is the number 96 as the best you can form a circle in a grid.

--- from Internet---
Archimedes' Polygon: Archimedes famously used a 96-sided polygon to closely approximate the value of π by iteratively doubling the sides of a hexagon.



pp
--- quoting Wikipedia---
From Wikipedia, the free encyclopedia
The first five octagonal numbers illustrated.

In mathematics, an octagonal number is a figurate number. The nth octagonal number on is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to n dots, when the octagons are overlaid so that they share one vertex. The octagonal number for n is given by the formula 3n2 − 2n, with n > 0. The first few octagonal numbers are

1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936 (sequence A000567 in the OEIS)

The octagonal number for n can also be calculated by adding the square of n to twice the (n − 1)th pronic number.

Octagonal numbers consistently alternate parity.

Octagonal numbers are occasionally referred to as "star numbers", though that term is more commonly used to refer to centered dodecagonal numbers.[1]


--- end quoting Wikipedia---

Archimedes Plutonium

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Jul 7, 2026, 4:06:28 AMJul 7
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One of the most important characteristics of 96 is it is the next Atom Totality after 94 for Plutonium Atom Totality. They go in even number jumps. So we are in a Atom Totality growing and positioning itself to become 96 Atom Totality which  the physics makes the number 96 more special. In a plutonium atom, it has 22 subshells in 7 shells which is why pi is 3.14.... and only 19 subshells occupied at any one time and thus "equiangular spiral" is 19/7 = 2.718... for exponential constant.

What catches my attention below is 96 as the difference between two squares is utterly fascinating.

pp
--- quoting Wikipedia---
From Wikipedia, the free encyclopedia


← 95 
96
97 →
← 90 91 92 93 94 95 96 97 98 99 →
← 0 10 20 30 40 50 60 70 80 90 →

Cardinal
ninety-six
Ordinal
96th
(ninety-sixth)
Factorization
25 × 3
Divisors
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Greek numeral
ϞϚ´
Roman numeral
XCVI, xcvi
Binary
11000002
Ternary
101203
Senary
2406
Octal
1408
Duodecimal
8012
Hexadecimal
6016

96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when turned upside down.

In mathematics
96 as the difference of two squares (in orange).

96 is:

The number of divisors of 96 is 12.[6] As no smaller number has more than 12 divisors, 96 is a largely composite number.[7]

Skilling's figure, a degenerate uniform polyhedron, has Euler characteristic 

Every integer greater than 96 may be represented as a sum of distinct super-prime numbers.


--- end quoting Wikipedia---
ppp

Let me look up where 96 prefix digits are a constant in physics.

AP, King of Science

Archimedes Plutonium

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Jul 7, 2026, 4:31:17 AMJul 7
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The prefix digits of Faraday constant is 96. Now the onus is on me to relate that constant to the fact that a circle, a full circle is a 96 Irregular Polygon as straightline segments in Decimal Grid Numbers graphs.

The Faraday constant can be thought of as the proportionality factor between the Magnetic Monopoles (charge) in coulombs(used in physics and in practical electrical measurements) and the amount of substance in moles (used in chemistry)--- So I write that as the proportionality factor of 96 in taking a straightline segments Forming a circle.

--- quoting Wikipedia---

Wikipedia, the free encyclopedia
Not to be confused with farad.

Faraday constant
Michael Faraday, the constant's namesake

Common symbols

F
SI unit
coulomb per mole (C/mol)
In SI base units
s⋅A⋅mol−1
Derivations from
other quantities

F = eNA
Value
96485.33212 C/mol[1]

In physical chemistry, the Faraday constant (symbol F, sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge (q) by the amount(n) of elementary charge carriers in any given sample of matter: F = q/n; it is expressed in units of coulombs per mole (C/mol). As such, it represents the "molar elementary charge", that is, the electric charge of one mole of elementary carriers (e.g., protons). It is named after the English scientist Michael Faraday. Since the 2019 revision of the SI, the Faraday constant has an exactly defined value, the product of the elementary charge (e, in coulombs) and the Avogadro constant (NA, in reciprocal moles):

F = e × NA = 9.64853321233100184×104 C/mol.
Derivation

The Faraday constant can be thought of as the proportionality factor between the charge in coulombs(used in physics and in practical electrical measurements) and the amount of substance in moles (used in chemistry), and is therefore of particular use in electrochemistry, particularly in electrolysiscalculations. Because the elementary charge is exactly 1.602176634×10−19 C,[2] and there are exactly NA = 6.02214076×1023 entities per mole,[2] the Faraday constant is given by the product of these two quantities:

F = e × NA  = 1.602176634×10−19 C × 6.02214076×1023 mol−1  = 9.64853321233100184×104 C/mol.

The value of F was first determined in the 1800s by weighing the amount of silver deposited in an electrochemical reaction, in which a measured current was passed for a measured time, and using Faraday's law of electrolysis.[3] Until about 1970, the most reliable value of the Faraday constant was determined by a related method of electro-dissolving silver metal in perchloric acid.[4]

Faraday – a unit of charge

Related to the Faraday constant is the "faraday", a unit of electrical charge. One faraday is the amount of charge in one mole of electrons:

1 faraday = F × 1 mol = 9.64853321233100184×104 C = N0e = 6.02214076×1023 e.

Where N0 is Avogadro's number.[5] A faraday will electrodeposit one mole of silver metal atoms.[6]




--- end quoting Wikipedia---

That is the best picture of Faraday I have ever seen. In my mind, Faraday is likely to be more famous as a scientist than is Maxwell, for if Google would count how many times AP had to use the name Faraday in all of my writings, it would likely be tops, far far more times I needed to say Faraday law structure than mention of any other scientist. Far more than Newton, or Maxwell or Dirac or Bell or Feynman or Archimedes I or Democritus.

Faraday's work and discoveries in physics makes him exceptionally outstanding. His Faraday law-structure is probably the very most singular Law-structure in all of Physics. How electricity is formed from magnetism and so much more.

All stars and our Sun shine from Faraday law-structure, not from fusion. Sun shines 95% from Faraday law structure as the muons go round and round perpetual motion inside proton toruses. Fusion contributes 5% or less in starshine. And we better move out to Europa before the Sun extincts life on Earth and sends Earth into oblivion.

AP


Archimedes Plutonium

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Jul 9, 2026, 5:34:08 AM (13 days ago) Jul 9
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Alright, I am hoping the third one of these pictures takes a hold, because it is graphed onto a graph paper itself.

p

pp
--- quoting a Google search of 96 sided regular polygon---
--- end quote---

ppp

Archimedes Plutonium

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Jul 9, 2026, 5:48:01 AM (13 days ago) Jul 9
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Yes, my hope was fulfilled, but will it remain there.

The reason I want to pick on that third picture because it has a 96-regular-polygon graphed onto graph paper.

The 96 regular polygon begins to really look like a circle itself.

Now if I remain in say the 10 Grid alone the best circle like polygon I can produce is an Irregular Polygon.

And we can see that because if you look at that 3rd picture, Our Rule is we can only draw straightline segments from vertex to vertex. And you can well see that some of those vertices do not match a square vertex.

And here is a very long old time question that has bugged me for decades. The question is--- how many grids do I have to borrow from to make a circle look alike when starting in 10 Grid???? You see, if I stayed with 10 Grid my circle is a Irregular Polygon, but say I borrowed from the 100 Grid, 1000 Grid and finally the 10,000 Grid. Then ----- would all 96 vertices of the 96 regular polygon coincide with a one of the square vertices of 10,000 Grid??????

You see the question I am asking, for it is a difficult question to understand. If you start out in any one specific Grid, and use the rule that you can only draw straight line segments from one vertex to another vertex, then I cannot get a 96 Regular Polygon, but a 96 Irregular Polygon to be my Best Circle. However, If I am allowed to borrow the 100 grid, 1000 grid, and finally 10,000 Grid, those extra vertex points of tiny squares ends up giving my a Full 96 Regular Polygon.

I would need a proof of that assertion.

AP, King of Science

Archimedes Plutonium

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Jul 9, 2026, 6:01:49 AM (13 days ago) Jul 9
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Alright, here is a start in a Proof of that Claim.

Statement:: Starting in 10 Grid with its 100 points on x axis and y-axis, not counting 0.

We draw a circle from center (5,5).

We abide by the rule that you can only use straightline segments and those segments have to connect one coordinate point in 10 Grid with another coordinate point.

I know for sure that there will be 4 coordinate points that match square coordinate points as that of (0,5), (5,0), (10, 5), (5,10). I am confident but not sure that 4 more coordinate points intersect square vertex, making a total of 8, if true.

Now I add the 100 Grid vertex points giving me more intersections. We can think of this as the 100 grid spinning freely from the center (5,5) and thus we spin the 100 Grid to add more points to the existing 8. Add the 1,000 Grid then the 10,000 where the symmetry now gives us 96 intersections of 96 regular polygon with tiny square vertices.

Come to think of it, probably the 1,000 Grid gives me the 96-regular polygon.

AP

Archimedes Plutonium

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Jul 9, 2026, 4:32:17 PM (12 days ago) Jul 9
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Alright that was a start of the proof, to get me thinking along the lines of a proof.

But, here is the PROBLEM, PROBLEM, and big Problem. 

A Static Grid is where you cannot borrow from higher grids. 

A Dynamic Grid is where you can borrow from higher grids.

Old Math was smart enough to know ----- It is impossible to have a Equilateral Triangle using only lattice points. A isoceles triangle is possible but not a equilateral triangle.

Old Math was too dumb to understand that a Equilateral Triangle is Possible in a Dynamic Grid where you start out in 10 Grid and borrow from 100 to 1,000 Grid to retrieve a vertex point that fills in your Equilateral Triangle.

In the same manner, if we start out with a Static Grid say 10 Grid and want to construct a 96 regular-polygon--- impossible if we have to stay in 10 Grid or any other starting out initial Grid, but if you can borrow from higher Grids, the 96 Regular-Polygon is Constructable.

Let me get some pictures to show you these ideas.

AP, King of Science





 

Archimedes Plutonium

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Jul 9, 2026, 5:24:10 PM (12 days ago) Jul 9
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You see, much of Old Math is half-marbled brain math--- they cannot see nor understand slant cut of cone is Oval, never ellipse, nor can they see that calculus is geometry and the Fundamental Theorem of Calculus requires a geometry proof, not a dipship limit analysis wiggle waggle dance.

Knowing that about math professors, it is no wonder that they do come upon the idea that a static-graph does not allow for a equilateral triangle nor does it allow for a 96 regular polygon. But, but, if you have more marbles in the brain than a math professor you quickly can see that a Dynamic Graph that allows you to borrow from higher grids, quickly gives you a Vertex point of smaller squares of the lattice that then Allows the Construction of a Equilateral triangle, plus a 96-Regular Polygon.

--- quoting a Google search for equilateral triangle on graph paper---
p
It is impossible to draw a mathematically perfect equilateral triangle with all three vertices strictly on the intersections (lattice points) of standard square graph paper. This happens because the height of an equilateral triangle involves an irrational number (e.g., \(\frac{\sqrt{3}}{2}\)), while the grid intersections are rational numbers. [1, 2, 3]
To verify this, you can look at the coordinate math:
If you place one corner at the origin \((0,0)\) and another at an integer coordinate \((x, y)\), the third corner must be calculated using a factor of \(\sqrt{3}\), which makes its coordinates irrational. Therefore, it can never land exactly on a grid point. [1, 2, 3]
However, you can easily bypass this depending on your goal:
  • The "Eye-Balled" Fix: Draw a nearly perfect triangle by making the side length large; the vertices will get arbitrarily close to the grid dots without ever perfectly touching them. [1]
  • The Origami Alternative: You can create a flawless physical equilateral triangle using an ordinary Paper Folding technique. [1, 2]
  • The Isomteric Solution: To draw one on a grid, switch from square grid paper to Isometric Dot Paper, which uses a triangular lattice perfectly suited for \(60^{\circ }\) angles. [1]
If you'd like to explore this further, let me know:
  • Are you trying to draw this on the computer or by hand?
  • Is this for a math proof or an art/design project?
5 sites
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    Feb 17, 2018 — According to a post on r/mathriddles, it's impossible to draw an equilateral triangle with vertices on a square grid that has hori...
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  • Bonus - UCLA Math Circle
    Feb 24, 2014 — ... impossible: there is no equilateral triangle with its vertices on the lattice points of a piece of graph paper with square til...
    Olga Radko Math Circle
  • Can you draw a perfect equilateral triangle on a piece of grid ...
    Dec 3, 2018 — 10. Ian Carmichael. Former Teacher, Religion, Mathematics, Computing at. · 7y. Originally Answered: Can you draw a perfect equilat...
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pp

So, in a Equilateral Triangle all three interior angles are 60 degrees.

I pull out several sheets of 10 Grid Graph paper, and select the one in which one side fits closest to 2 lattice points. The third vertex of the triangle falls in between two lattice points. Here I start to borrow from the 100 Grid. And if it falls on a lattice point I have my equilateral triangle, if not, I break that square down into the 1000 Grid, and continue the process until the triangle vertex is within Available Precision. Math professors never learned that math is Practical, not Idealism.

Concept of Available Precision
------------------------------------------------

The obnoxious personality of almost every math professor, is that they believe mathematics is --- exacting perfect. This is true when they multiply say 2 x 3 and the answer is exacting perfect. But, when the little minded math professor from Pythagorean Theorem obtains a number like square-root of 2 or square-root of 3, their little mind will never understand that sqrt2 or sqrt3 are Imprecise numbers. They are muddy, foggy numbers and not at all are they exact.

The process of using a number like sqrt2 by a physicist or engineer is that whatever the application of using sqrt2 stops somewhere down the line of digits 1.41421356..... The physicist or engineer wants to be as precise as possible. All the mathematician can do is offer 1.41421356.... because the number itself sqrt2 is a foggy, muddy imprecise number. So somewhere down the line of this messy foggy number the physicist will stop and grab the digits because going further is impossible with the tools the physicist has. So he stops at 1.41421 for that is the limit of his experiment and tools of the experiment.

Same thing with AP constructing a Equilateral Triangle on Graph paper. I start in 10 Grid, I borrow from 100 Grid and stop at 1000 Grid. I select the lattice point of 1.414 as the vertex of the Equilateral triangle. Now if it were sqrt3 =1.7320508.... I would stop at the 10,000 Grid with that 0 digit.

You see, the great lesson that all Math Professors of Old Math need to learn and learn fast, is that Math in total is imprecise, with only a few spots of math that are Exact Precision. They deal mostly in the swathes of mathematics that is Exact Perfect like 8 divided by 4 or 5 x 10 where they have exact precise numbers and solutions. And they are too stupid to realize most of math is not in this swathe of Exact Perfect but in the patch that takes up most of mathematics the swathe of dirty, messy, foggy, muddy. When mathematics fall into the dirty patches of math, their tiny marbled brains then runs for Symbols to cover up the fact that they are neck deep in foggy muddy crap. That is why so much of mathematics is a dumb math professor at the blackboard, filling up the blackboard with nothing but mindless stupid symbols and is the reason most students Hate math, because they are bombarded with teachers who are muddy and foggy of what they teach.

I myself was and still AM a teacher of math, and I know the First Principle of teaching math---- teach so the student Understands and can Understand what you are saying.

AP, King of Science

Archimedes Plutonium

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Jul 9, 2026, 5:46:05 PM (12 days ago) Jul 9
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On Thursday, July 9, 2026 at 4:24:10 PM UTC-5 Archimedes Plutonium wrote:

Same thing with AP constructing a Equilateral Triangle on Graph paper. I start in 10 Grid, I borrow from 100 Grid and stop at 1000 Grid. I select the lattice point of 1.414 as the vertex of the Equilateral triangle. Now if it were sqrt3 =1.7320508.... I would stop at the 10,000 Grid with that 0 digit.

You see, the great lesson that all Math Professors of Old Math need to learn and learn fast, is that Math in total is imprecise, with only a few spots of math that are Exact Precision. They deal mostly in the swathes of mathematics that is Exact Perfect like 8 divided by 4 or 5 x 10 where they have exact precise numbers and solutions. And they are too stupid to realize most of math is not in this swathe of Exact Perfect but in the patch that takes up most of mathematics the swathe of dirty, messy, foggy, muddy. When mathematics fall into the dirty patches of math, their tiny marbled brains then runs for Symbols to cover up the fact that they are neck deep in foggy muddy crap. That is why so much of mathematics is a dumb math professor at the blackboard, filling up the blackboard with nothing but mindless stupid symbols and is the reason most students Hate math, because they are bombarded with teachers who are muddy and foggy of what they teach.

I myself was and still AM a teacher of math, and I know the First Principle of teaching math---- teach so the student Understands and can Understand what you are saying.

The great great problem of Old Math professors too stupid to understand that all of mathematics is imprecise, with only a small tiny patche that is perfect-precision, is the concept of math proof.

Math proof can lull even the brightest of Old Math professors, like Andrew Wiles, like Terence Tao none of whom can admit the truth that slant cut of cone is Oval, not ellipse, nor can any of these three do a geometry proof of Fundamental Theorem of Calculus, far too stupid to explain calculus as geometry. 

When you are weaned and suckled on math proofs throughout your career, it is hard to make a about face, a 180 degree turn and say that Math overall is mostly imprecise study. The numbers are mostly imprecise for most of them are root numbers (irrational). So when you do all these proofs, the small minded math professor comes away thinking that All of Mathematics is this Precision Perfect enterprise.

But examine carefully the foundation of a Math Proof. The foundation is axioms. Stupid agreed upon ideas forms the foundation of mathematics proof. One of the axioms is a point has no length, width, depth. But would physics agree to such silliness?????? In physics, the smallest entity has rest mass and having rest mass, means you have length, width, depth. The 0.5MeV particle which is the Magnetic Monopole, not the electron of atoms, has length, width and depth.

So, well, all of a sudden, every math proof that uses the axiom of "What is a point" is in question, and its proof no longer is precise-perfect but in the zone of imprecision.

And the only real reason Old Math professors keep pretending their subject is Precise Perfect is because they psychologically feel powerful with the pretense and make students fearful.

AP, King of Science

Archimedes Plutonium

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Jul 9, 2026, 6:17:44 PM (12 days ago) Jul 9
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So, now, getting back to this challenging question of what Grid system, starting out in 10 Grid, do I have to keep borrowing to make a Regular Polygon of 96 sides??

Say I wanted to make a Regular Polygon of 3 sides = equilateral triangle. Say I wanted to make the sides so that square root of 3 comes up. Sqrt3 =1.7320508..... Then if I made the rule to go by, that I stop at the first 0 digit would tell me that on Graph paper I need to borrow from 100 grid, from 1000 grid, from 10000 grid and can stop there.

And in a sense, we can look up and examine our silly stupid axiom that a Point has no length, width, depth and say that a Point has at least a length of 0.508......... In that manner, our Equilateral Triangle drawn in a Dynamic Graph, not the stupid Static Graph of 10 grid only.

Using the same techniques we examine drawing a 96 Regular Polygon starting in the 10 Grid. How much borrowing do we have to need?? 100 Grid, 10^3 Grid, 10^4 Grid, 10^5 Grid??? So 360 divided by 96  is 3.75 degree. In a regular octogon
360/8 =45 degree versus the 135 degree. In a 3-gon, angles 60 versus 120, in a 4 gon (square), angles 90 versus 90, in a 5-gon angles 72 versus 108.

In a 96-gon, angles 3.75 versus 176.25.

Now, here an interesting math calculation results, as we can see a 4 gon needs not borrow from higher grids to have lattice point intersections. And 4 divided into 100 is even. with a 3 gon we need to borrow and 3 divided into 100 is not even. Can we say that when the number of sides divides evenly into 10, 100, 1000, 10000, that we can graph in a single grid and not need to borrow???

96 divided into 100, 1000, 10000, etc always ends in ....6666.... Does this mean that 96 always needs to borrow from higher grids to be graphed on graph paper????

AP

Archimedes Plutonium

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Jul 9, 2026, 6:36:04 PM (12 days ago) Jul 9
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And this raises a more alarming question. That numbers like 1/3 or 2/3 are more messy and imprecise than most irrational numbers which has the chance of having a 0 digit such as sqrt3 is 1.73205....... In a sense, we can call numbers like 1/3 and 2/3 are far more messier and imprecise than most irrational numbers.

We could say 2/3 is worse of a number than is sqrt2 or sqrt3.

Archimedes Plutonium

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Jul 9, 2026, 9:21:45 PM (12 days ago) Jul 9
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So I am going to have to build a book on what I call the Sigma Error of Mathematics knowledge. Physics is never precise-perfect and always has Sigma Error in experiments and even in its law structures. Since math is a subset of Physics, that math also has Sigma Error where as a science it is never 100% precise perfect.

The main idea of this imperfection in mathematics is that the very axioms of math are formed from common sense agreement, and we can easily recognize what a axiom of a thousand years ago is shown in quantum mechanics to be a silly stupid axiom due to recent findings in physics--- a point has no length, width, depth.

But more easy yet is the large sigma-error found in numbers. Math has an infinity borderline at 1*10^604 and for a number like 1/3 =0.333..... endlessly is false for it can only go to 10^-604 and then dissolve into meaningless. Same is true of 2/3 =0.666.... as it reaches infinity borderline. 

No wonder in college math classrooms on the blackboard is mostly abstract symbols and symbolism, all because math has a Sigma Error, that we cannot be precise 100%, so we see junk like sqrt2, or sqrt3 or 1/3 or 2/3 or the hypocrite notion that 0.9999... equals 1.

So I am going to write a whole new textbook on the boundaries of mathematics where it is 100% precise perfect and where it is horribly in Sigma Error territory.

No wonder no math professor in any college or university around the world, especially USA, Germany, UK cannot admit slant cut of cone is Oval, not ellipse, nor can any of them do a geometry proof of Fundamental Theorem of Calculus, for they have little to no logical marbles in their head, as University of Virginia Steve Huffman says of the math failures of Univ Virginia and UCLA.


Steve Huffman lists science lunatics:
Reddit (symbol) r/math, 3 years ago Genius meets Lunatic: 1994 discussion between Terry Tao and Ludwig Plutonium
I remember Archimedes Plutonium and sci.math. He calculated the chromatic number of the plane: and it is 1 (color everything
..Is this crank perchance John Gabriel?

AP writes:: no, Terence Tao and Steve Huffman along with University of Virginia and UCLA are math failures who cannot do what a High School student can do--- drop a Kerr lid into a paper cone and see for yourself the slant cut is a Oval, not ellipse.

Univ Virginia math dept: Peter Abramenko, Julie Bergner, Mikhail Ershov, Jeffrey Holt, John Imbrie, Thomas Koberda, Slava Krushkal, Thomas Mark, Jennifer Morse, Ken Ono, Andrei Rapinchuk, Christian Reidys, Jim Rolf, Charles Dunki, Ira Herbst, James Howland, Craig Huneke, Thomas Kriete, Nicholas Kuhn, Irena Lasiecka, Barbara MacCluer, Kevin McCrimmon, Karen Parshall, Loren Pitt, Donald Ramirez, James Rovnyak, Leonard Scott, Lawrence Thomas, Roberto Triggiani, Harold Ward

Steve Huffman on math lunatics Terence Tao,
Steve Huffman University of Virginia,
Reddit (symbol) An other Archimedes Plutonium rant about irrational numbers  Reddit · r/badmathematics 10+ comments · 6 years ago An other Archimedes Plutonium rant about irrational numbers ... In Grid Systems, you are exact only to the Grid, and forget about the beyond. "The ...



UCLA chancellor: Gene D. Block (biology)

UCLA Physics dept
Ernest Abers, Elihu Abrahams, Katsushi Arisaka, Michalis Bachtis
Eric Becklin, Zvi Bern, Rubin Braunstein, Stuart Brown, Robijn Bruinsma
Charles Buchanan, Wesley Campbell, Troy Carter, Sudip Chakravarty
W. Gilbert Clark, John Cornwall, Robert Cousins, Eric D'Hoker
Robert Finkelstein, Christian Fronsdal, Walter Gekelman, Graciela Gelmini
George Gruner, Michael Gutperle, Brad Hansen, Jay Hauser, Karoly Holczer
Huan Huang, Eric Hudson, George Igo, Per Kraus, Alexander Kusenko
Thomas Mason, George Morales, Warren Mori, Steven Moszkowski
Christoph Niemann, Kumar Patel, Roberto Peccei, Claudio Pellegrini
Seth Putterman, B. Regan, James Rosenzweig, Joseph Rudnick
David Saltzberg, William Slater, Reiner Stenzel, Terry Tomboulis, Jean Turner
Willard Libby (chem), Julian Schwinger (physics), Paul Boyer (chem), Andrea Ghez, James Fraser Stoddart (chem), Louis Ignarro (physio-medic)

UCLA math dept.

Donald Babbitt, Kirby Baker, Andrea Bertozzi, Mario Bonk, Lennart Carleson, Tony F-C Chan, Shiu-Yuen Cheng, Robert Edwards, Gregory Eskin, Hector Fattorini, Thomas Ferguson, Theodore Gamelin, John Garnett, David Gillman, Mark Green, Nathaniel Grossman, Alfred Hales, Robert Jennrich, Paul Johnson, Alan Laub, Thomas Liggett, Donald Martin, Sidney Port, James Ralston, Paul Roberts, Bruce Rothschild, Murray Schacher, Roberto Schonmann, Masamichi Takesaki, Terence Tao, Veeravalli Varadarajan, James White, Donald Ylvisaker



Archimedes Plutonium

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Jul 10, 2026, 7:48:18 PM (11 days ago) Jul 10
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Now there is a beautiful but somewhat bizarre theorem in Math Geometry. It goes somewhat like this. Pick any three noncollinear points in the plane and those three points are points on a Unique Circle.

So in New Math, no curves ever exist. What exists are ever finer and finer tiny straight line segments. And a circle is thus at minimum a 96-Regular Polygon in any given Grid System where we borrow from higher Grids to make the 96-Regular Polygon.

I need to review how Old Math came up with their flawed proof, because when no curves ever exist in math, we have to wonder on what axioms are used to make this fake theorem of 3 noncollinear points determine a Unique Circle. When that theorem should be that 3 NonCollinear points in plane determines a unique 96 or higher Regular Polygon.

You see, when I tie together a fake proof of Old Math with a true proof in New Math, we end up inspecting what stupid axiom was used in Old Math to come up with their flawed proof.

And if I had to guess, what fake axiom is used, it likely is an axiom that thinks a Continuum exists, when all of physics and math works on Discrete Space, with numbers being discrete and having holes and gaps in between one number and the next number.

AP, King of Science

Archimedes Plutonium

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Jul 11, 2026, 4:26:11 AM (11 days ago) Jul 11
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Old Math failed at the starting line of Geometry, with their fatally flawed Axiom or Postulate of that of "Point".

No wonder Old Math could never do a geometry proof of Fundamental Theorem of Calculus.

No wonder that Physics started the truth of geometry in year 1900 with Max Planck kicking off the century with Quantum Mechanics saying physics is discrete, yet the fools and cranks of math still in their cesspool of continuums.

I shall go through all the math history books here at home that talks about the First Axiom of geometry.

Old Math:: A point has no length, no width, no depth.

New Math:: A point must have at minimum a length of 1*10^-604 length and that same amount for width and depth. Note--- at minimum but in most circumstances it can have larger proportions.

ANALYSIS
----------------

We can analyze the fatal flaw of Old Math's axiom on what a point is by pure Logic.

A Point is something, otherwise it is nothing.
If a point has no length, no width, no depth, then it has 0 length, 0 width, 0 depth.
Hence a point is nothing for zero is nothing.
But a point is something and not nothing.
Therefore, A point must have some tiny finite length, finite width, finite depth. The minimum amount of metric for a point would be the Infinity Borderline and the induction element is 1*10^-604.

Common Sense Explanation
--------------------------------------------
Physics is the material world science. The smallest thing in physics would be a point of math. Atoms are too big to be points, for they have subatomic particles. The smallest subatomic particle is the magnetic monopole of the 0.5MeV particle. Hence, the Point in Physics is the dimension of the magnetic monopole. 

Note: Old Physics and Old Chemistry were confused for the 0.5MeV particle is not the electron of Atoms, but rather instead the muon the 105 MeV particle is the true electron of Atoms.

The failure of Old Math to have a valid definition or postulate or axiom of "Point" contributed to the gargantuan failure of Old Math to understand what the Calculus was, and the derivative as part of the function graph, where the true numbers of mathematics have to be discrete with empty space in between one point and the next point.

Now, with Point having a tiny tiny finite size, we can backtrack and thus make Exacting Precision in Geometry figures such as a Circle is at minimum a 96-Regular Polygon when mapped on a Decimal Grid system.

AP, King of Science

I need to use these ideas in my Logic textbooks.

Archimedes Plutonium

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Jul 12, 2026, 1:01:47 AM (10 days ago) Jul 12
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Now I am going to go through a list of books that present Euclid's axiom of "point". For it is a Flawed Axiom that is self-contradictory.

GEOMETRY, 2nd edition Harold Jacobs, 1987, page 50 starts to talk about "points". Jacobs is following a practice that I suspect is dubious and flawed in that he insists on not defining "point". 

Which reminds me of Edwin Moise "Elementary Geometry from an Advanced Standpoint" 3rd edition, 1990, pages, 43, 44, who does not define point and thinks that the axioms will specify what a "point" is. I am dubious of this claim.

Morris Kline, "Mathematical Thought From Ancient to Modern Times" volume 1, 1972, page 58, and where Kline writes the Euclid Elements definition of "point"  as "1. A point is that which has no part." "2. A line is breadthless length."

AP writes: this caught me be surprise for I had remembered the Euclid definition as a Point has no length, no width, no depth. Could it be that "no parts" is the same as "no length, no width, no depth" ?  No, I beg to differ that those two ideas are not the same. So I looked through other books to see if that was truly Euclid's definition of "point". So I go to Britannica-Great Books to see if "no parts" was Euclid's axiom.

Britannica "Great Books of the Western World" 1952, page 1, Book One Euclid Definitions 1. A point is that which has no part. 2. A line is breadthless length. 3. The extremities of a line are points. 4. A straight line is a line which lies evenly with the points on itself. 5. A surface is that which has length and breadth only. 6. The extremities of a surface are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself.

AP writes:: I see room for a-lot of mistakes there, especially the difference between straight-line and curved line. For AP, no continuum curves exist but rather instead, a large collection of tiny fine straight line segments all connected together to appear like a curve.

But let me get back to this idea of Point as having "no parts" and Point as having "no length, no width, no depth" to me those two are different definitions. And that the concept of Point from Euclid to 2026 AP was fatally flawed.

As I wrote earlier the true definition of Point must involve the infinity borderline which by tractrix computation is 1*10^-604. Hence, all points have at minimum 1*10^-604 length, and that amount of width and that amount of depth. When working in 10 Grid and borrowing up to 10000 Grid then the length, width and depth of a point can be 1*10^-4 long, wide, deep.

Modern day math with Quantum Mechanics Physics updates the definition of Point so that it is no longer a Self Contradictory definition.

A Point is Something. If it has no parts, or if it is metrically described as no length, no width, no depth means it is 0 long, 0 wide, 0 deep and 0 is Nothing. But a Point must be Something. Hence we have a self contradiction here. Proving that a Point must have some tiny finite metric. And this makes absolutely Common Sense for we know the length of a line distance is the summation of all its points. If points are 0, then all lines are 0 length.

AP, King of Science




Archimedes Plutonium

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Jul 14, 2026, 5:02:22 PM (7 days ago) Jul 14
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Memory Chip of this book when picked up in the future
----------------------------------------

Alright, I am moving on and will write this book in the near future. But in that lag time, I may forget the gist of the argument. So let this be the last post and a memory of what was accomplished.

I wanted to know what regular polygon allows the eyes to see a figure as "being a smooth circle". Since geometry has NO Curves. No curves exist in reality, but instead are fine tiny straight line segments.

This is required because Calculus, in order to exist at all, must have empty space between one point and the next successive point. So we draw a straight line segment between one point and the next point. All of Geometry is tiny fine straight line segments and absolutely NO CURVES exist in geometry or in physics. The smallest things-- atoms and subatomic particles are surrounded in empty space.

So then the question was--- what is the smallest Regular Polygon that is the circle to our eyes--- answer was a 96 Regular Polygon. 

So then I pursued how a 96 regular polygon is a circle and how to draw it on a graph paper.

I immediately ran into problems and could only solve those problems if I started in 10 Grid and borrowed from 100 and 1000 Grids because I can only use the vertices of the squares to make the 96 Regular Polygon.

I then found I had a 96 Irregular Polygon, some sides bigger, some smaller than others.

So, finally I came to the solution that solves it all.

I dove into the axioms of geometry of what is a Point? There, the axiom is flawed and in need of repair.

If you have an axiom-postulate that says a point has no length, no width, no depth, is tantamount to saying a point is nothing when a point needs to be something. A point cannot be empty space but have some metric.

So when the axiom of point was invented by the Ancient Greeks, they made a mistake on "Point". It must have the smallest metric possible. Of course the Ancient Greeks had not the "tractrix" to find where the Infinity borderline was in mathematics, and once we have that borderline, the inverse of 1*10^604 (where pi digits have 3 consecutive zeroes in a row), once we have that infinity borderline, the inverse as 1*10^-604 is the Smallest metric that every point must have.

But when working in Decimal 10 Grid, borrowing from 100 and 1000 Grid, I can safely say the Point -- smallest point in that application is 1*10^-3.

So a point starting with 10 Grid has a length of 10^-3, a width of 10^-3 and a depth of 10^-3.

In that manner, all problems are solved to where ---- using only vertex points of 10, 100, 1000 Grid, I can draw a perfect 96 Regular Polygon.

AP, King of Science
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