MATHOPEDIA-- List of 75 fakes and mistakes of Old Math. AP's 174th book. Soon to be published as a Kindle book. Details of all of these are found in already published Kindle books, such as the geometry proof of Fundamental Theorem of Calculus.
Last revision was 21Sep2021. I added the correction of the Natural Logarithm Ln(x) to base 2.71... for its definition using Y= 1/x of an integral over an interval from 1 to x in 1/t dt is very much flawed and incorrect. The true definition of Ln(x) has to be from a geometry that allows for the equiangular logarithmic spiral. A Ln(x) based upon 1/x does not give a equiangular log spiral. What does give a equiangular log spiral are the Decimal Grid Number System where you have equal spacing of discrete numbers. So for example in Old Math their Ln(1.02) was 0.0198... while in New Math where we have a corrected and true Ln(x) that Ln(1.02) = 0.02 exactly.
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 19May2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.
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. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. 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?
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.
Length: 137 pages
Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1307 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 137 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
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#20 in Calculus (Kindle Store)
Preface: I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds question of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).
Some of these can be found in AP's TEACHING TRUE MATHEMATICS series, but the entries keep changing and added on new, means I need to have a separate book for these fakes, mistakes and errors of Old Math.
TEACHING TRUE MATHEMATICS: Volume 3 for ages 18-19 Freshperson College, math textbook series, book 3
Teaching True Mathematics, by Archimedes Plutonium 2019
Listing the Errors of Old Math, list of 1 to 50.
Alright, well, mathematics is a closed subject. What I mean by that is due to the textbook series of Archimedes Plutonium TEACHING TRUE MATHEMATICS, that once you learn the polynomial transform and learn the two Power Rules of Calculus, you reached the peak, the pinnacle of all of mathematics, and anything further in math is just details of what you learn in that textbook series. Math is a completed science because it has this "peak of calculus", unlike the other 5 hard sciences of physics, chemistry, biology, geology, astronomy. Those other five will continue to find new ideas, new things, while math remains static and complete to its peak of calculus understanding. Mathematics is finished complete as far as a science goes because the peak of math is going nowhere. And even though Physics will find new science such as how the proton toruses inside of atoms are configured in geometry, the geometry and calculus used in that configuration, that new science does not change nor does it create or require a new math peak/summit to handle the new physics.
Now I do need to discuss the Errors of Math in General and the errors of math in geometry in particular. I have the feeling that Geometry is the more important of the two-- algebra - geometry. This list appears in most of AP's Teaching True Mathematics textbook series by Archimedes Plutonium, meant to be a guide and orientation, and a organizing of what must be covered before graduating from College, and what math to steer clear of.
Errors mostly, but not always, for some are included because too much time spent on them.
The listings in Mathopedia of errors, mistakes and fakes is based on the idea that Calculus is the supreme achievement of all of mathematics for it is the essential math of doing Physics electricity and magnetism. And in order to have a proof of the Fundamental Theorem of Calculus, we must clean up and clean out all the mistakes, fakes and errors of Old Math, erst, we have no Calculus. So calculus is the consistency maker for the rest of all of mathematics.
1) Calculus requires a geometry proof of Fundamental Theorem of Calculus, a proof that derivative and integral are inverses of one another, just as addition and subtraction are inverses, or, multiplication and division are inverses. The only way to obtain a geometry proof is to clean up and clean out all the fakes, mistakes and errors of Old Math, such as their fake numbers-- the Reals. Their fake definition of function allowing anything be a function. Their fakery of a continuum when even physics by 1900 with Planck onwards in Quantum Mechanics proving the Universe is discrete Space not a continuum, yet by 1900 onwards those in mathematics following the idiotic continuum in the Continuum Hypothesis with even more avid interest, when they should have thrown the continuum on a trashpile of shame.
2) The true numbers of mathematics are the Decimal Grid Numbers, because you have to need and apply one mechanism only to obtain the true numbers of mathematics-- Mathematical Induction. In Old Math they had just a tiny few intelligent mathematicians, Kronecker, who emerged from the gaggle crowd of kooks to notice that Naturals all come from one single mechanism-- Mathematical Induction. But Old Math never had a crowd of mathematicians with logical brains to say-- all our numbers need to come from the one mechanism of Mathematical Induction.
3) The true numbers of math have empty space between successor and predecessor numbers. For example the 10 Grid is 0, .1, .2, .3, . . . , 9.8, 9.9, 10.0. Where no numbers exist between .1 and .2, etc. Only discrete numbers allow us to give a proof of Fundamental Theorem of Calculus.
4) All functions of mathematics must be a polynomial, and if not a polynomial, convert the offering to a polynomial over a specific interval.
Where is that stupid thread in sci.math, poising as a puzzle problem when it had no functions only pretend functions?
A few days back, 11Aug2021 appeared a stupid puzzle problem here in sci.math. Of someone pretending he had 3, 4 even 5 or 6 functions and wanting to prove equality.
Then I stepped into the conversation saying he had no functions at all, until they are converted into polynomials over a specified interval, then you can do calculus on those true real functions.
So, the world wide math community has got to begin to learn, no function is a function, until, and unless they are polynomials. This is an axiom of math and is proven true by the geometry proof of Fundamental Theorem of Calculus. You cannot have a FTC, if you have functions that are not polynomials.
So there is a trade off-- does math want calculus or no calculus? If you want calculus, all your functions have to be polynomials. This has to do with the concept of discrete geometry, not a continuum, for polynomials are discrete.
5) Space is discrete and all lines in space are strings of attached straight lines.
6) No curves exist in Geometry, only finer and smaller straight line segments attached to one another.
We can still keep the name "curve" as long as we know it is a string of fine tiny straightline segments strung together in what looks like a smooth curve. If curves exist, then the Calculus in Fundamental Theorem of Calculus cannot be proven and thus Calculus does not exist. We all know that we have to have Calculus, and so we throw out onto the trash pile the curve of Old Math. And this is reasonable because starting in 1900 in physics there arose the Quantum Mechanics of Space being discrete. And a discrete space has no continuum, has no curve of Old Math.
7) Space has gaps in between one point and the next point. These gaps are empty space from one point to the next point, for example in 10 Grid there is no number between .1 and .2, and in 100 Grid there exists no number between .01 and .02.
8) Limit analysis was an insane fakery in Old Math, concocted because Old Math needed the excuse of some proof, so they invented the monster con-artist trick that a limit analysis would divert the fact it is no proof at all, but a Non Sequitur argument. Limit analysis is juju totem witchcraft dance around a desire to prove the Fundamental Theorem of Calculus. Just as idiotic as dancing around a sick person of a virus is going to cure the person.
9) Infinity has a borderline and there is a microinfinity compared to a macroinfinity. For example in 10 Grid, the microinfinity is .1 if we exclude 0 and so there is no number smaller than .1 and no number larger than 10 in 10 Grid, where 10 is macroinfinity.
10) The 1st Quadrant Only in Coordinate System Geometry. Sad that the first coordinate system of Descartes was correct but soon became corrupted with 4 quadrants. See Mathematical Thought, Volume 1, Kline, 1972, page 303. Where Fermat then Descartes starts the Cartesian Coordinate System as 1 axis only and from 0 rightwards, meaning in our modern day math, 1st Quadrant Only. Why did math screw up on coordinate systems? I suppose some clowns thought negative numbers were true and they wanted ease of drawing a circle with center at 0. When they could have just as easily drawn the circle in 1st Quadrant Only.
11) Calculus needed a Geometry proof of the Fundamental Theorem of Calculus, but Old Math never provided such, instead they provided some stupid Limit argument. The reason for the creation of the Limit disaster was that the French mathematician Cauchy got sick and tired of hearing his smartest students complain that the width of rectangles in the integral are 0 width, and those smart students could not, for the life of them understand how a rectangle with 0 width has any interior area. So instead of the math community denouncing the limit, instead they elevated the fakery.
12) Further in Calculus, they knew you could do a transform of coordinate points to turn any function into a polynomial function, a method of Lagrange. However, they in Old Math were too stupid to take this transform to its highest form-- all functions are polynomial functions and only polynomial functions. When you learn that-- the derivative and integral of any and every function of math is a snap breeze simple and easy.
13) With the error filled 4 quadrants, when it should be 1st Quadrant Only, we have Trigonometry's sine and cosine with the fakery of sinusoid wave when it never was that. The sine and cosine are semicircle waves, and no sinusoid wave exists.
14) There is only one Geometry-- Euclidean, and there is not three distinct geometries of elliptical Riemannian or hyperbolic Lobachevsky. Those two are just duals that make up Euclidean.
15) Torus, volume and surface area formulas in Old Math are all screwed up and in error because they imagined bending a cylinder to form a torus. This brings back memories, for I had to do a percentage formula, since I could not follow the fake way of bending a cylinder. Where 78.5% of Disc Torus (pi)R^2h - (pi)r^2h is the volume of Circle Torus, and 78.5% of Disc Torus 2(pi)Rh + 2(pi)rh + 2 ((pi)R^2 - (pi)r^2) is the surface area of Circle Torus.
16) Ellipse is never a single cone slant cut, always a cylinder slant cut. Although you do get an ellipse from double cones of this configuration <> which in Old Math was the hyperbola, but two hyperbolas joined together to form a ellipse.
17) All Parallelepipeds reduced to a Rectangular Box by making 2 cuts and pastes. Volume of the original Parallelepiped is simply a*b*c of the Rectangular Box length*width*depth formed. Old Math never understood that a precise definition of Parallelepiped has two kinds, the parallelepiped that has 90 degree angles and the parallelepiped that has no 90 degree angle.
18) All of Old Logic such as the textbooks by Copi and Boole and Jevons with their messed up operators -- their logic connectors of AND, OR, If->Then, Equal+Not, Boole went insane with logic for he never lived a logical life as he even thought cold bathes and a wet bed would cure him of pneumonia, so insane was Boole he taught class shivering in rain soaked clothes and so when it came time to decide for Boole what AND should be, he thought its table was TFFF, not realizing that if just one statement among many statements is true, then the entire collection is true and thus the true truth table of AND must be TTTF and now in modern day computer making times of 1990s onward we see clearer the Boole error of logic for the computers are expressing the thoroughly wrong and muddle headed Boole logic of 2 OR 1 = 3 with AND as subtraction of 2 AND 1 = either 1 or 2 as in subtraction of the other. And the Boole mistake of AND and OR is easily fixed as we correct AND to be TTTF and we accept only a OR truth table of FTTF.
19) Set theory is thrown out completely from math and belongs in Logic and Pragmatism philosophy, although we can use the word "set" to mean a sequence or function of math. All of Cantor set theory is phony baloney, not worth reading. There never was anything to set theory and was seen as the "part of math inhabited by those crippled in mind to doing regular math" as they played around with Venn diagrams when they should be learning true math of calculus. Set theory is geometrical logic of Pragmatism.
20) Rationals and Negative Numbers thrown out completely because the only true numbers are Decimal Grid Numbers. Some would complain, why AP throws out Rationals? And the answer is simple, that numbers must be free of operations, for Rationals are unresolved divisions. Numbers are free and clear of any operator. Numbers have to be formed purely from mathematical-induction and having no unfinished operator. The Smallest set of Grid numbers is the 10 Grid System with its infinitesimal being .1, and the entire collection of 10 Grid is 0, .1, .2, .3, . . , 9.9, 10.0 where .1 is microinfinity and 10 is macroinfinity. In 100 Grid the infinitesimal is .01, in 1000 Grid the infinitesimal is .001, etc etc. In such a true system of numbers, all the numbers are built by mathematical-induction. Not just one group of numbers-- counting, but all numbers from mathematical-induction.
21) Irrationals thrown out completely (ditto to Rationals and Negative numbers).
22) Reals thrown out completely (ditto).
23) Imaginary numbers and Complex numbers are b.s. and thrown out completely.
24) Trigonometry pared down so much-- 90% thrown out, and no trigonometry ever enters Calculus. Only real use of trigonometry is when you have an angle and side, you can figure out the rest of the right triangle. But no, when you give true math to a gaggle of kooks, it is not long before they stretch true math way way out of its "zone of truth". And even fill up by 50% of calculus, when trig should never be in calculus.
25) Continuum and continuity thrown out as horrible fakery (in fact the Quantum Mechanic Physics of early 1900s had a better handle on the truth and reality of math with discrete space).
26) Topology is junk and a waste of time for many reasons such as continuum does not exist, and the fact that the idea of "bending" is not really ever a mathematical concept.
27) Prime numbers are fakery for the Naturals never had division in the first place. The real true numbers of mathematics are the Decimal Grid Numbers and they do not have a concept of "prime". The key evidence that primes were silly stupid error, was the fact that there never existed a "pattern for primes". And all of mathematics is a science of "pattern". If any part of mathematics has no pattern, is indication that such was a phony fake concept to start with. Below begins a write-up of Math topics all have pattern, if not, then not math. Now some may worry about the idea that no primes ever existed for they worry about the Unique Prime Factorization Theorem of Old Math. But here again, there is no worry. For "Factors exist" just not prime factors.
28) Limit in Old Math was a horrible fakery, built by lowly idiots of math who wanted to get away from the smart students asking them-- stupid professor, come back here,-- how does a zero width rectangle even have interior area.
29) Lobachevsky, Riemann geometries and all NonEuclidean geometries are fakery and a waste of time. Many math professors want to spice up their boring math, so they ventured way way off into the twilight-zone of math with NonEuclidean geometry, like eating the hottest peppers in the world for breakfast.
30) Boole logic a horrid gaggle of monumental mistakes; one colossal error was their insane 10 OR 4 = 14. Boole was a monumental idiot of logic that he went to college to teach in a rainstorm without umbrella and when he got there, shivering, and no commonsense to switch into dry clothes, taught in rain soaked clothes with his students laughing at the fool he was for catching pneumonia. Boole was so logically insane that he ordered his wife to give him cold bathes and wet his bed in order to fight pneumonia, and western culture, now, elevates this insane logical fool, and puts such a logical misfit as the Father- of- logic. And modern day schools of 2020 are as insanely crazy as was Boole for they continue to teach that 4 OR 1 = 5, when even a village idiot society knows better with 4 AND 1 = 5.
31) Galois Algebra of Group, Ring, Field a fakery and waste of time.
32) Dimension stops at 3rd, and 3rd is the last and highest dimension possible, for there is no 4th or higher dimensions.
33) High School in Old Math spends too much time on quadratic equations with their negative numbers and imaginary-complex numbers when such never existed in the first place and where they violate a principle of algebra-- that an equation of algebra-- the right-side of the equation must always have a greater than zero number. So we throw out all quadratic equations of Old Math as fake math.
34) High School in Old Math spends too much time on teaching in geometry the congruence of SSS, ASA etc etc and we should pare that back somewhat, as excess teaching of a tiny minor concept.
35) Ordinary and Partial Differential Equations are now seen as superfluous when all functions are polynomials and need only the Power Rule. In Old Math we throw out all the insane ridiculous myriad of fake rules-- the Chain Rule, Simpson's Rule, Trapezoidal Rule, all because math has only one type of function-- polynomials and that makes for only one rule-- Power Rule.
36) Parametric Equations thrown out-- for what need is there of a sack of dung when all functions are polynomials. Interchanging equation with function.
37) Graph theory-- 90% worthless for it is based on the fakery of continuum.
38) Probability and Statistics theory now becomes a part of Sigma Error in New Math, the Old Math Probability and Statistics theory were wastrel and thrown out for it is based on a continuum and they had no proper definition of "probability" that fits with statistics. We keep Probability and Statistics in new math but revise and overhaul it completely.
39) We definitely throw out all Old Math Calculus textbooks as mostly propaganda, based on the silly Limit and the Continuum.
40) We throw out the Euclidean Axioms of Geometry and start anew, with axioms based on Physics as geometry truth.
41) Fractal theory totally junk and a waste-- uses ill-defined infinity.
42) Multivariable Calculus, Line Integrals, div, curl, Vector Calculus, Chaos theory, Complex Analysis, utter junk and waste of time since polynomial theory covers all functions.
43) Differential geometry, Measure theory fakery since they never had the correct numbers of math, and they had the fakery continuum.
44) We throw out all the Apollonius conic sections because he misidentified the ellipse. The ellipse is a cylinder section, never a conic section and the oval is the slant cut of the cone, never the ellipse. We replace the entire conic sections by the AP theory of axes of symmetry using Decimal Grid Numbers for algebra and strip-wavelength-geometry axioms.
45) Most of Algebra, starting with Linear Algebra is esoteric minutiae, or, just cute tools for specialized math, just as the Binomial Theorem and the Pascal triangle, all cute esoteric minutiae. Certainly none of which is appropriate in school math education. These topics are for those interested in sideline math, but does not belong in mainstream math. Algebra reaches its pinnacle of importance with the Polynomial Function transform. Anything else in Algebra is sideline esoteric minutiae. These are not wrong or false math, just not important enough math to be mainstream worthy of math education.
46) Gaussian Curvature is esoteric exotica, perhaps even fakery. It is a fallacy of "idealism". There has never been any physics application for now 200 years. But most damaging is the fact that Euclidean is the only geometry, and that elliptic and hyperbolic are just dualities for which if you compound them together is Euclidean geometry.
47) Manifolds in Old Math were fakery, since topology is fake with its "bending" and math cannot define "bending" which belongs to physics and chemistry. Bending is a physics phenomenon, not something that ever belonged in mathematics. Topology with its continuum and ill-defined infinity is fakery, then also is its manifold. In New Math, all 2-Dimensional figures are handled by polynomial transforms, so also all 3-Dimensional figures. How so much easier is it, that doing a Polynomial Transform, rather than the silly fakery and obfuscation of manifolds.
48) Fourier, Laplace and other transforms, all of them thrown out the window because the only valid transforms are polynomial transforms. Polynomials are the only valid functions, hence, polynomials are the only valid transforms. And here in mathematics we begin to see that Polynomial transform is the mirror image of physics wanting a unification of the 4 forces of Old Physics, where the EM unification of physics, is like the Polynomial transform of mathematics that unifies all so-called-functions.
49) The correction of the Natural Logarithm Ln(x) to base 2.71... for its definition using Y= 1/x of an integral over an interval from 1 to x in 1/t dt is very much flawed and incorrect. The true definition of Ln(x) has to be from a geometry that allows for the equiangular logarithmic spiral. A Ln(x) based upon 1/x does not give a equiangular log spiral. What does give a equiangular log spiral are the Decimal Grid Number System where you have equal spacing of discrete numbers. So for example in Old Math their Ln(1.02) was 0.0198... while in New Math where we have a corrected and true Ln(x) that Ln(1.02) = 0.02 exactly.
50) Principle of Logic, that Physics is king of sciences, and that means math is but a tiny subset. But in 20th and 21st century, we still have goons and kooks of math that think math is bigger than physics. These goons and kooks think that the Universe is a mathematical equation. They belong in an asylum, not the sciences.
51) There are many Principles of Logic which were unknown or ignored in Old Math. One of those principles caused the horrendous failure of sine and cosine trigonometry. The failure that a graph of a function in 2D or 3D, where the axes, all have to be the same numbers. You cannot have the x-axis as angles and the other axis as numbers. You abandon mathematics when you enact such a policy. You may as well have bar graphs and pie-charts and call them foundation mathematics, when you do sine and cosine with different representations of axes.
52) Principle of Logic-- follow your definitions exactly. When you do not follow your definitions you end up with the craziness of thinking sine is a sinusoidal wave when in truth it is a semicircle wave. You defined sine as opposite/hypotenuse of right triangles in a circle. That means, it is impossible from the definition for sine and cosine to be anything other than a semicircle wave.
53) Principle of Reality in a Equation-- You formed equations in mathematics where one side is the same as the other side. This is the algebra axiom of where the rightside can only be a positive nonzero decimal Grid Number. Equations must have "reality" on the rightside of the equation, in order for the equation to even exist. We cannot put negative numbers, or zero, or imaginary numbers on the right side of an equation and expect there to even be an "equation of mathematics". Math like physics deals with "reality". And that means a equation of mathematics must have a true substantive reality on the rightside of the equation all by itself. You can clutter up the leftside of the equation and solve for unknowns, but the rightside of the equation has all by itself a positive, nonzero Decimal Grid Number. Anything else is not mathematics.
54) The Reductio Ad Absurdum, RAA, or some call it proof by contradiction is not a valid proof argument in mathematics. RAA at best is a strong hypothetical, but not a guarantee of truth or proof. The trouble with RAA is the trouble with the IF-->Then connector of Logic which has a truth table of True, False, Unknown, Unknown. Old Logic had this connector of If-->Then as TFTT. It is the unknowns in F--> T and F--> F that neither has a true conclusion but an unknown conclusion that renders RAA as non workable in math.
55) The primal axiom of Physics-- All is Atom and atoms are nothing but electricity and magnetism reigns not only over physics but mathematics as well. Most of the Teaching True Mathematics textbook series books have physics experiments involving electricity and magnetism.
56) Geometry is discrete with not only discrete numbers but empty space in between numbers as coordinate points of a graph and with a discrete angle. No continuum exists in either algebra or geometry.
57) True geometry cannot have all volumes by stacking 2D figures, for example the torus, where the circles near the donut hole would be spaced too close together versus the circles near the rim of the circumference have wide empty space gaps. Stacking to achieve volume is not a universal method.
58) Mathematics has a peak, a pinnacle, a climax of understanding with Calculus, the motion of physics and the energy of physics. This is expressed in the 2D and 3D calculus. It closes the subject of mathematics. And once we learn how to transform polynomials, and apply the power rule in High School, all the rest of mathematics we learn in life is just mere details of our teachings that took place in High School. Math is a closed subject beyond Calculus.
59) Mathematics is a closed subject, meaning it has a summit, a peak and that peak mirrors the Physics of motion. It is called calculus. Once you learn calculus, and it is very easy for it is just the Power Rule upon Polynomials. Once you learn this in High School, all the rest of mathematics is just details concerning motion. Mathematics is a tiny tiny subset of Physics. Everything of mathematics comes from physics. The reason the world has numbers is because physics has atoms and atoms are numerous. The reason the world has geometry is because atoms come in various shapes and sizes.
60) Math is a closed subject, a tiny subset of physics, and ever since 2019, the writing of this Calculus Guide, all the important topics of mathematics can be taught in junior and senior year High School. Any mathematics beyond High School is mere details of that junior and senior year teaching-- namely polynomial transform and Power Rules for derivative and integral of calculus.
61) The AP-EM equations of physics and mathematics. They replace the error ridden Maxwell Equations.
If you desire, you can replace E, electric field with L, angular momentum. Where V is voltage, i or A is current, B is magnetic field, E is electric field, kg is kilogram mass, m is meters, s is seconds, C=quantity of current A*s.
a) Magnetic primal unit law Magnetic Field B = kg /A*s^2
b) V = C*B*E New Ohm's law, law of electricity
c) V' = (C*B*E)' Capacitor Law of Physics
d) (V/C*E)' = B' Ampere-Maxwell law
e) (V/(B*E))' = C' Faraday law
f) (V/(C*B))' = E' the new law of Coulomb force with EM gravity force
PHYSICS LAWS
a) Facts of chemistry and physics
b) Voltage V = kg*m^2/(A*s^3)
c) Amount of current C = A*s = magnetic monopoles
d) Magnetic primal unit law Magnetic Field B = kg /(A*s^2)
e) Electric Field E = kg m^2/(A*s)
f) V = C*B*E New Ohm's law, law of electricity
g) V' = (C*B*E)' Capacitor Law of Physics
h) (V/C*E)' = B' Ampere-Maxwell law
i) (V/(B*E))' = C' Faraday law
j) (V/(C*B))' = E' the new law of Coulomb force with EM gravity force
62) Research into what I call "pencil ellipses" that are ellipses of enormous semimajor axis and tiny tiny semiminor axis, whose importance to physics is ultra important.
63) Light waves are not straightline arrows, open ended arrows but rather instead are pencil ellipses always connected as a closed loop circuit with the source of that light.
64) Old Math in its fakery and stupidity never had a 3rd Dimension Calculus, for theirs was only 2nd dimension. Their colossal mistake of never a geometry proof of Calculus for the idiots believed in "limit analysis of 0 width rectangles for integral", that those Old Math idiots could never understand there exists 3rd dimension calculus.
65) Apollonius geometry corrected, especially the two cones put base to base <> and not the error filled apex to apex >< and the ellipse = 2 hyperbolas and the oval = 2 parabolas.
66) A well defined oval as being two parabolas joined at their widest width circle.
67) Their minor error of listing pi as 3.14... when using radius in formulas when they should list pi as 6.28... whenever using radius, because area of circle is really 1/2 pi*r^2 to match the prefix factor of 1/2 mv^2 as kinetic energy. Old Math never had a full brain of logic when they did Old Math, but always puttering around with a 1/10 tank of logic.
68) The single biggest fake and error of Old Math is their Calculus, with no geometry proof of Fundamental Theorem of Calculus. It is the biggest mistake because providing a geometry proof alerts the mathematician that they are mistaken about a "limit" mistaken about what are the true numbers of math (Decimal Grid Numbers, not the Reals), they are mistaken about infinity without a borderline. So fixing their calculus forces them to fix so many other ills of Old Math.
69) AP is reinventing Multivariable Calculus because the AP-EM Equations of physics demand it. See AP's TEACHING TRUE PHYSICS 1st year College for details. And this revision ends up throwing out Old Math's Gradient theorem, Green's theorem, Stokes theorem, Divergence theorem, manifolds, ugly and difficult and incomprehensible Old Math. Apparently in Old Math, they rather have kook math that no-one ever understood than no math at all. In AP's reinvention of Multivariable Calculus we throw out all of the above and able to teach Multivariable Calculus to bright seniors of High School. So that AP throws on the trash pile the Green's theorem, Gradient theorem, Stokes theorem, Divergence theorem, manifolds, throws them all out and replaces all of Multivariable Calculus with a technique of volume of box versus surface area of ellipsoid. All of which was invented or discovered to deal with Electromagnetism starting with the Maxwell Equations of 1860s.
70) When all functions and equations of physics are polynomial then the calculus is another polynomial function as the solution to the original polynomial. Thus, no multivariable calculus is needed.
71) Since the polynomial dispenses the Multivariable Calculus, it also dispenses the vector of mathematics. What replaces the vector is the "unit concept". No need of vectors when units means the same thing. And the direction in Old Math vector is actually the derivative of calculus. So the concept of vector in Old Math was unit-derivative. The concept of vector is part of the unit concept and the derivative concept. So vector is duplicity.
72) The Serre, Taniyama-Shimura, Ribet, Wiles Programs of representing Counting Numbers as elliptic curves is all a pile of illogical and worthless garbage. When you have the true numbers of mathematics-- Decimal Grid Numbers, the proper Representation of Counting Numbers is the numbers from 0 to 0.5 between 0 and 1. None of these listed so called mathematicians even knew of the axiom of algebra of what a "valid equation" was.
73) The Langlands program of Old Math is a gigantic sack of worthless garbage, using fake numbers of Reals and stupid outdated Galois group theory. My gosh, Langlands was not even aware of the critically important axiom of algebra, that a valid equation is one in which a positive decimal grid number is all alone at all times on the rightside of the equation, and does anyone expect any math to come from Langlands? AP replaces the Langlands program with the AP program.
74) We set up a matrix of the terms in Voltage = Coulomb x magnetic Field B x electric field E = CBE and the all possible permutations of differential equations C', B', E', V'. We set this matrix up in order to help interpret what each term means.
V'BE/(BE)^2 - VB'E/(BE)^2 - VBE'/(BE)^2
current production - Lenz law - DC, AC direction
V'CE/(CE)^2 - VC'E/(CE)^2 - VCE')/(CE)^2
B production - Displacement current - parallel attract
V'CB/(CB)^2 - VC'B/(CB)^2 - VCB'/(CB)^2
(E production = inverse square of distance) - synchronicity - push versus pull
C'BE + CB'E + CBE'
V production + DC current of dipoles from monopoles + AC current dipoles from monopoles
75) Now the proof that 3rd dimension is the largest and last dimension possible comes best from physics, more so than mathematics. Although in math we can see that a perpendicular to 3rd dimension remains a part of 3rd dimension and nothing new is built from adding a perpendicular.
But in Physics the proof is far more compelling. For it trespasses unto Electromagnetic theory of the speed of light. Do we have the speed of light a maximum constant and thus Special Relativity is true and allowing the existence of electricity and magnetism. Or, do we accept 4th dimension and higher, and toss out EM theory onto the trash pile. So here we have the choice of EM theory, the daily electricity we all use, or the choice of accepting 4th and higher dimension.
Because the physics proof that 4th and higher dimensions can not exist is that the speed of light is a constant, meaning, that it has no acceleration. Speed is meter/second. The derivative of calculus of speed is acceleration. So acceleration is meter/second^2. Acceleration is found in Force F = ma. Force is a subset of Energy where E =mv^2 or E = mc^2. Acceleration, force, energy are all 2nd dimensional inside of a 3rd dimensional Space-time. If a 4th dimension exists, then the units of Energy would have to be mccc not mcc. The speed of light would have to have acceleration in order to have a Force = mass x derivative of acceleration. The speed of light would have to be a variable for 4th dimension to exist of meter/second^2. For 4th dimension to exist, the light speed is no longer a maximum constant.
In Old Physics, they played a fool's game by saying time was the 4th dimension to 3 spatial dimensions. This is wrong for the derivative of speed is a time derivative and is exactly why 4th dimension cannot exist for it makes light speed a variable. And in Old Physics they played another game of calling higher dimensions curled up as the reason we cannot see them. This again is a fool's game.
Experiment to prove no 4th dimension.
We can actually devise a physics experiment to prove no 4th dimension or higher. We notice that a light beam or a star, or our Sun, radiates energy in light waves. We can theoretically determine how much light our Sun is supposed to radiate. If a 4th dimension exists, that dimension would decrease the amount of light than if we had just 3 dimensions. Because each higher dimension absorbs light radiation. Think of light as water as a analogy. So one dimension would be a sluice box of water. And second dimension would be a field. Third dimension would be all of Earth. So as the dimensions increase, you need more water to fill the more dimensions. Same thing with light, we can calculate what a radioactive decay beta emitter produces (beta is magnetic monopoles, not atom electrons). We know beta emissions and how much light they give. If the Universe is 3rd dimension and no more, then we observe how much light from beta emitters. If the Universe has a 4th dimension, much of the beta emission in radioactivity will go to filling 4th dimension and we would see less light than if the Universe was just 3rd dimension.
Truth in all sciences, is you know the truth, if you can teach it in High School. In Old Math, you could never even teach calculus in high school because of their mindless "limit concept-- which is fakery". Let alone teach Multivariable Calculus. Most of the history of mathematics for the 20th century was where "kooks of math" got a hold of math, and had their suppression and hold on math. Looks like the 21st century is where Math is made free from kooks stranglehold, and math able once again to be taught, all of it, in High School.
True mathematics is a subject that is always easy, clear, and comprehensible. Old Math never had a program of "let us make the subject easy and clear and accessible to all". Old Math was about fame and fortune for a grubby few arrogant and ignorant fame seekers to those seeking fame and fortune by adding fake math, incomprehensible, hard, worthless, at the expense of torturing young students who all they wanted was a foundation understanding of true mathematics.
Old Math cared more about having a few kooks run out and about, getting fame and fortune by piling incomprehensible trash onto mathematics, than it ever cared about going into a classroom and teaching math that everyone can understand. Of the four hard sciences, physics, chemistry, biology, mathematics, there is no reason in the entire world, that math is the easiest of those 4 sciences. The only reason today, that math is not the easiest of those four sciences, is because after Descartes for 5 centuries now, mathematics was given over to kooks of math who sought for fame and fortune at the expense of keeping math simple and easy. Kooks of math filling up math so that math is now in 2020 a gaggle of kook ridden incomprehensible garbage. Ask your local kook math professor why he/she holds onto Boole logic with his 10 OR 4 = 14 when you know well that 10 AND 4 = 14. Ask your local kook math professor why he keeps teaching ellipse is a conic when you can show him on the spot with a paper cone and a lid that the slant cut is a oval, never a ellipse. And ask your local kook math professor why he/she never is able to give you a geometry proof of Fundamental Theorem of Calculus. And the answer is always-- they are kooks of math, not mathematicians.
This list is ongoing, and is a bulletin-board of errors of Old Math and useful for Teaching True Mathematics. I insert this list as a guide. To show students what math to avoid, to steer away from, as a total fake and waste of time.
AP
King of Science
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More people reading and viewing AP's newsgroup than viewing sci.math, sci.physics. So AP has decided to put all NEW WORK, to his newsgroup. And there is little wonder because in AP's newsgroups, there is only solid pure science going on, not a gang of hate spewing misfits blighting the skies.
In sci.math, sci.physics there is only stalking hate spew along with Police Drag Net Spam of no value and other than hate spew there is Police drag net spam day and night.
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of stalkers and spammers, Police Drag Net Spam that floods each and every day, book and solution manual spammers, off-topic-misfits, front-page-hogs, churning imbeciles, stalking mockers, suppression-bullies, and demonizers. And the taxpayer funded hate spew stalkers who ad hominem you day and night on every one of your posts.
There is no discussion of science in sci.math or sci.physics, just one long line of hate spewing stalkers followed up with Police Drag Net Spam (easy to spot-- very offtopic-- with hate charged content). And countries using sci.physics & sci.math as propaganda platforms, such as tampering in elections with their mind-rot.
Read my recent posts in peace and quiet.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium