11th published book of AP//World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition by Archimedes Plutonium (Author).

Today I wrote the first page of AP's 171st book of Science, where I replace the Hilbert standard bearer of problems with the AP problems, and found that I am lacking discussion of all functions as polynomials in my 11th book. So I need to revise my 11th book, once again.

May 8, 2021, 1:29 PM
to sci.math, sci.physics, plutonium-atom-universe
171st book of AP: AP Problems of Mathematics replacing the Hilbert Problems of 1900s.

Alright David Hilbert set a standard bearer of math purpose in making a list of problems for other mathematicians to solve. Trouble was, David Hilbert never had much logical brains to conduct a full sweeping Standard Bearer job over mathematics as David was pretty much in the weeds of math and logic himself. But, David did lead the way into making a Standard Bearer Job.

11th published book

World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 4Apr2021. This is AP's 11th published book of science.
Preface:
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had (1) a ill-defined infinity; (2) they had the fakery of Limit concept; and (3) they had the fakery of a continuum; and (4) perhaps most important of all as long as Old Math had the wrong numbers that compose mathematics that no geometry proof of Fundamental Theorem of Calculus was ever possible. Sad that starting 1900, Planck showed that Space is discrete in physics, not continuous, leading to the rise of Quantum Mechanics. But the fools of mathematics went the opposite direction in wanting ever more a continuum in mathematics. They spent the entire 20th century riding high on Cohen's depraved continuum. You could almost say that starting 1900, the people in mathematics compared to those in physics would become more and more ignorant and further estranged, and that a widening schism rift separated math from physics, from the realities of the actual world as the future decades and centuries rolled by. And who knows where this rift would leave math as a science decreasing in vim and vigor. Will it end in math becoming a third or fourth tier science, ranking it above say economics but far below even psychology, because much of math proof is kook psychology acceptance divorced of reality. In this view, physics, chemistry, biology, astronomy, even geology ranked far higher in power and wisdom than math.

By the 19th and 20th and 21st centuries, the single number one important topic and subject in all of mathematics was Calculus, and the reason being, is that Physics is mostly calculus, the science of motion and change. And everyone in math knows that calculus is geometry. So, then, to not have a geometry proof of Fundamental Theorem of Calculus is a failure and failing of being a mathematician.

The Fundamental Theorem of Calculus basically says the integral is inverse to the derivative and the derivative is inverse to the integral. By inverse is meant that you can go to one given the other and vice versa, such as add is the inverse of subtract, so if we had 10 + 4 = 14 then the inverse is subtract 4 and we have 14-4 = 10 back to 10 where we started from. And the geometry proof involves a rectangle and a right triangle hinged atop a trapezoid. You hinge it one direction you have dy*dx for area of a rectangle for integral area. You hinge it the other direction you have the dy/dx for slope or derivative from the trapezoid formed.

Sad that Old Math was so full of ill-defined concepts and fake concepts that never was a geometry proof of FTC ever possible in Old Math.

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.

---------------------------
Table of Contents
---------------------------

1) Preliminary mathematics needed to do the Geometry Proof of Fundamental Theorem of Calculus.

2) How the dumb limit concept was borne, that is a con-artist job.

3) When you know the true numbers of mathematics, Decimal Grid Numbers, you need no limit concept.

4) Mathematics has two houses, one is numbers, one is geometry.

5) All numbers come from physics because the Universe is just one big atom of 231Pu.

6) History of my discovery of Decimal Grid Numbers.

7) The error of having a proper Coordinate System to do the Calculus as 1st Quadrant Only with all positive Decimal Grid Numbers.

8) Concept of Infinity versus Finite for Calculus.

9) Brief proofs of the Infinity borderline, especially Huygens tractrix.

10) World's first picture diagram proof of the Fundamental Theorem of Calculus by 2015.

11) Calculus the very most important math to date.

12) Everyone in mathematics knows that Calculus is geometry.

Length: 39 pages

Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1236 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 39 pages
Lending : Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)

How important is it for a Geometry Proof of the Fundamental Theorem of Calculus to contain the idea that the only true functions of mathematics are Polynomial Functions?

I made a search through my published book, 11th, for the word polynomial. In hopes that I had at least mentioned and discussed the idea that all functions of mathematics, to be legitimate, to be valid functions, had to be polynomial functions. And that for instance, say you walked up to the Valid Functions booth of mathematics and handed in some trigonometry functions. That the caretakers of mathematics would dismiss your trig function unless you converted it into a valid true function by transforming it (Lagrange transform) over an interval of the trig function and converting it to a polynomial.

So I searched my text of the 11th book and found no polynomial conversion or transform discussed. Found that I had not mentioned the fact that all functions that are valid are Polynomial functions and anything else was a fake function, fake until it is converted over to being a polynomial in a specified interval.

How critical, how crucial is that idea for a Geometry Proof of the Fundamental Theorem of Calculus.

Well, up until today, with my first page of the 171st book, I had not realized how centrally important was this key requirement of -- the only valid functions in math are polynomial functions.

And so now, I need to further revise my 11th book, thanks to my start of the 171st book.

But it makes common sense that if all functions are polynomial allows for all functions to be series of tiny straight line segments where no curves exist. And for the right triangle atop a trapezoid in the Geometry Proof involves nothing but polynomials and the most famous of all polynomials is Y=mx+b the straightline function.

The reason I wrote first page of 171st book is in recognition of the fact that the Most Important of all mathematics is the Calculus, and the most important theorem in all of mathematics is a geometry proof of Fundamental Theorem of Calculus.

And the only Geometry Proof of FTC that is ever, ever possible is when you correct the horrible ugly huge mistakes of Old Math such as discrete rather than a continuum, such as Decimal Grid Numbers instead of the insane crazy Reals and Complex. But I omitted one other great idea in that of all valid functions are only polynomials.

You can easily see why AP makes a Geometry Proof of FTC the top number 1 problem in all of mathematics. Because by doing a valid geometry proof, you can only do it by first cleaning up all the mess and filth and ugly liaring of Old Math. You can only do a Geometry Proof of Fundamental Theorem of Calculus, by first cleaning up the fakes and mistakes and errors of Old Math.

A geometry proof of FTC FORCES a total clean up of Old Math.

And so, well, I thought that a well-defined infinity versus finite was necessary and hugely important for a geometry proof. But it turns out that it is necessary, but not hugely important as is the only valid functions of math are polynomials. You see, in my 11th book I stressed infinity definition too much emphasis. To be sure, a geometry proof corrects infinity with a borderline, but is not as important of a clean-up of Old Math as that of a Geometry proof of FTC demands that all valid functions be polynomials. And this makes commonsense for we all know that the Calculus is a straddling back and forth between 3 entities.

derivative to the left, and function in the middle, and integral to the right

So in Calculus we have starting Function and take the derivative, or take the integral. And we move constantly back and forth between those three entities, mind you all three are polynomials and thus polynomial functions, and in that sense alone should have have known that the only Valid Function has to be a polynomial for only a polynomial can shuffle back and forth between three entities.

So, in light of this 171st book, I need to go back and revise my 11th book, for I had topsy turvy too much emphasis on well defined infinity, when I should have emphasized the valid function of math has to be one and only polynomial functions.

AP
King of Science, especially Physics

Alright, I am going to have to revise my 11th published book of science.

11th published book

World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 4Apr2021. This is AP's 11th published book of science.
Preface:
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had (1) a ill-defined infinity; (2) they had the fakery of Limit concept; and (3) they had the fakery of a continuum; and (4) perhaps most important of all as long as Old Math had the wrong numbers that compose mathematics that no geometry proof of Fundamental Theorem of Calculus was ever possible. Sad that starting 1900, Planck showed that Space is discrete in physics, not continuous, leading to the rise of Quantum Mechanics. But the fools of mathematics went the opposite direction in wanting ever more a continuum in mathematics. They spent the entire 20th century riding high on Cohen's depraved continuum. You could almost say that starting 1900, the people in mathematics compared to those in physics would become more and more ignorant and further estranged, and that a widening schism rift separated math from physics, from the realities of the actual world as the future decades and centuries rolled by. And who knows where this rift would leave math as a science decreasing in vim and vigor. Will it end in math becoming a third or fourth tier science, ranking it above say economics but far below even psychology, because much of math proof is kook psychology acceptance divorced of reality. In this view, physics, chemistry, biology, astronomy, even geology ranked far higher in power and wisdom than math.

By the 19th and 20th and 21st centuries, the single number one important topic and subject in all of mathematics was Calculus, and the reason being, is that Physics is mostly calculus, the science of motion and change. And everyone in math knows that calculus is geometry. So, then, to not have a geometry proof of Fundamental Theorem of Calculus is a failure and failing of being a mathematician.

The Fundamental Theorem of Calculus basically says the integral is inverse to the derivative and the derivative is inverse to the integral. By inverse is meant that you can go to one given the other and vice versa, such as add is the inverse of subtract, so if we had 10 + 4 = 14 then the inverse is subtract 4 and we have 14-4 = 10 back to 10 where we started from. And the geometry proof involves a rectangle and a right triangle hinged atop a trapezoid. You hinge it one direction you have dy*dx for area of a rectangle for integral area. You hinge it the other direction you have the dy/dx for slope or derivative from the trapezoid formed.

Sad that Old Math was so full of ill-defined concepts and fake concepts that never was a geometry proof of FTC ever possible in Old Math.

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.

---------------------------
Table of Contents
---------------------------

1) Preliminary mathematics needed to do the Geometry Proof of Fundamental Theorem of Calculus.

2) How the dumb limit concept was borne, that is a con-artist job.

3) When you know the true numbers of mathematics, Decimal Grid Numbers, you need no limit concept.

4) Mathematics has two houses, one is numbers, one is geometry.

5) All numbers come from physics because the Universe is just one big atom of 231Pu.

6) History of my discovery of Decimal Grid Numbers.

7) The error of having a proper Coordinate System to do the Calculus as 1st Quadrant Only with all positive Decimal Grid Numbers.

8) Concept of Infinity versus Finite for Calculus.

9) Brief proofs of the Infinity borderline, especially Huygens tractrix.

10) World's first picture diagram proof of the Fundamental Theorem of Calculus by 2015.

11) Calculus the very most important math to date.

12) Everyone in mathematics knows that Calculus is geometry.

Length: 39 pages

Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1236 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 39 pages
Lending : Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)

And I had just revised it the 4Apr2021 this year, just a month ago. But the fact of the matter is, FTC is the towering jewel of all of mathematics because Calculus is the magnificent crowning glory of all of mathematics. FTC is the pinnacle peak importance of modern mathematics. It is the mathematics that surrounds electricity and magnetism of physics.

Trouble was, though, there never was a proof of FTC in Old Math. There was only a yakkity yack subterfuge talk analysis. A wishy washy hornswaggle called the "limit analysis". Which is not a proof at all but just a con-artist show and tell propaganda.

Everyone, I mean everyone in math knows that Calculus is geometry. Yet, ever since Newton and Leibniz, no-one looked for a geometry proof of FTC. And then by 2015, as AP was writing a series of Calculus textbooks, just out of the blue and no real focus of what I was up to, out of the blue came a sketch of a right triangle carved from the two sides of a rectangle and when hinged at the midpoint of the upper side of the rectangle hinged that right triangle, that the vertex of the right triangle lands on the next point of the function graph, hence the derivative. And when hinged back down is the area inside the rectangle is the integral.

So while writing these calculus series of books, by 2015, AP discovers the Geometry proof of Calculus Fundamental Theorem. Quite by accident, but of course, I never polluted my mind with the limit concept nonsense, nor did I pollute my mind with the idea derivative is a tangent slope of the function graph. Instead, I went into writing that calculus textbooks with a open free and clear and a logical mind.

For instance, I went into those textbooks with the idea that the function graph itself was the derivative being plotted, so that the derivative itself was the function graph, and this makes total sense because the tangent of the function Y= x is x itself. So in 2015, already I had the supreme logical notion that curves in math never really exist at all. That all functions and all graphs are tiny straight line segments such as Y=x^2 is a long series of tiny straight line segments stuck together, and gives only the appearance of a curve, because the straightline segments are too tiny to distinguish.

But now, I see that I need to trace back and revise my 11th published book, trace back and explain in full detail, how a GEOMETRY PROOF IS POSSIBLE, and how that throws out so much trash and garbage of errors and mistakes of Old Math. Their continuum is garbage, their limit is garbage, their curved lines is garbage, their Reals are garbage, their three other quadrants are garbage, and many many garbages and phony constructs.

So now, I go back and revise my 11th book. It will be much longer, far longer than 39 pages. It may even reach to being 100 pages or more. But that is to be expected of the very most important of all math theorems and truths. For without Calculus, physics goes nowhere.

AP
King of Science, especially Physics

World's First Geometry Proof of Fundamental Theorem of Calculus // Math proof series, book 2
by Archimedes Plutonium

Last revision was May2021. This is AP's 11th published book of science.
Preface:
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?

Everyone in mathematics knows that Calculus is vital to physics and math. Thus, everyone knows the Fundamental Theorem of Calculus is vital to physics and math. I have even called FTC the pinnacle peak of math success, the highest form of mathematics rests in FTC. And, everyone knows that calculus is Geometry. Yet, everyone must have been a scatterbrain fool of mathematics after Newton and Leibniz onwards because no-one after them in mathematics was looking for a Geometry proof of Fundamental Theorem of Calculus. AP cannot blame a chemical pollutant of dumbnification of the entire academic world from 1600 to 2015 as the cause of no-one in mathematics seeing that Calculus is geometry, therefore, forced to find a geometry proof. The chemical pollution of the world environments starts in large part in the 1800s. So then, the answer of why no-one felt the need to do a geometry proof must be the fact that no-one since 1600 had a powerful logical mind to do so, and were just lazy, and scatterbrained with little to no logical mind.

Now here is a picture of AP's 2015 discovery of the geometry proof of FTC, only reversed starting with the rectangle integral and proceeding to the derivative-as part of the graphed function.

If the Calculus was done correctly, conceived correctly, then a
minimal diagram explains all of Calculus. Old Math never had such a
diagram, because Old Math was in total error of what Calculus is, and
what Calculus does. And they all hid behind a con-artistry trick called the limit analysis.

The fundamental picture of all of Calculus are these two of a
rectangle and trapezoid. In fact, call the picture, the

FUNDAMENTAL THEOREM OF CALCULUS, Picture

Trapezoid for derivative as the roof-top of
the trapezoid, which must be a straight-line segment. If it is curved,
you cannot fold it down to form a integral rectangle. And the
rectangle for integral as area.

We start in positive Decimal Grid System of 1st Quadrant Only. This diagram is of 10 Grid System and for the midpoints we borrow from the 100 Grid System.

Start with this rectangle as the area or integral of a function from E to D interval:

__A__C
|         |
|B       |
|         |
---------
E D
And the derivative at x= A where A is the midpoint of top side of the rectangle, above is merely the dy/dx involving points A and B. Thus, it can never be a curve in Calculus. And the AB is part of the function graph itself.. No curves exist in mathematics and no continuum exists in mathematics.

So the derivative is a hinge at point A and we lift up the right triangle with hypotenuse AB and set it upon the other line segment AC.

To this:
        B
        /|
      /  |
 A /----| C
  /      |
|        |
|____|
E D

The trapezoid roof has to be a straight-line segment (the derivative)
so that it can be hinged at A, and swiveled down to form rectangle for
integral. The point A is the midpoint of the rectangle top side same as side ED.
This is why we need empty space so that the midpoint of ED is three
consecutive or successor points. This allows the derivative function to be
one and the same as the graph function itself.

Now we started this picture in 10 Grid System and suppose our function was Y= x. And suppose our rectangle above was E= 1.0 and D= 1.1. The midpoint would be 1.05 but that number does not exist in 10 Grid and we have to borrow from the 100 Grid System. Remember in Decimal Grid Systems-- the true valid numbers of mathematics are not a continuum but have empty space in between the numbers. This empty space is crucial and critical for giving a Geometry Proof of the Fundamental Theorem of Calculus.