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Where the right-triangle is now swiveled at midpoint but rather where a right triangle is cut-away from the Integral that is a rectangle and that right triangle is then discarded.

Yes, now two of the most interesting and fascinating downward slope functions in 10 Grid of 1st Quadrant Only would be the quarter circle and the tractrix.


Let me run a scenario for you, please.

There are 7-8 billion people on Earth today.

In the past 50 years we can roughly say that 50 million people studied Calculus in school or at home.

50 million people tried and attempted to learn calculus math.

I certainly was one amoung that 50 million.

And was AP the only one in 50 million to recognize that if you take polynomials as being the Only Valid Function that the Calculus becomes the Easiest, Super Easy math, because the Power Rules apply and where the derivative is simply a subtract 1 from
exponent and the integral is add 1 to exponent.

I find it extremely sad and hard to believe that only AP saw how to make Calculus Super super super easy? Surely there must have been at least 25 million of those 50 million who found the derivative and integral of polynomials a joy and pleasure to do.
Surely AP was not the only person in 50 million to see the Polynomial Calculus was a pleasure, fun and even exciting, rush to class to do a derivative or integral of a polynomial-- teacher, please give me more polynomial exercises. They are better than
Star Trek on TV.

This is the whole point of a Revolution in Math Calculus.

When we make the only valid function in all of math be a Polynomial, we reduce calculus to adding 1 or subtracting 1.

We do not allow creeps, goons and kooks to clutter the table of math and calculus with their horrible awful smelly functions which are not polynomials. No, we disband these kooks and tell them go home and convert your worthless crap to be a polynomial
before you can stink up the halls of mathematics. Convert your kook nonsense to a polynomial then you can come and do mathematics with us.

AP, King of Science

As a case in point, a mere example.

We have at MIT a Dr. Gilbert Strang with his Calculus textbooks, and I bought the 1991 edition of Calculus. And my opinion of Strang's text is scatterbrained. For I often find that Gilbert in lecturing on a topic is too quick to bring in side show issues,
never focusing on just one topic.

But worst of this Strang text is he has no valid proof of Fundamental Theorem of Calculus FTC, no geometry proof and his Limit analysis of FTC is idiot of a proof-- ie-- no proof at all, for we all analyze things in the course of a day, and none of us
are so preposterous as to think we have proven something above and beyond analyzing that something.

And so, I, AP reflects back to the time of 1968, when my name was Ludwig Hansen, sitting in a geology classroom of University of Cincinnati. Learning geology from a textbook that never discusses Continental Drift and this is 1968, mind you and Wegener
had given massive evidence of Continental Drift way back to 1915, some 53 years later, AP and the classroom suffering from Truth of Science by having to buy a book about static-Earth, being tested graded lectured upon fake geology.

Not much difference from students sitting in classrooms at MIT or elsewhere buying Strang's CALCULUS with no valid proof of Fundamental Theorem of Calculus, and where any fool function is allowed to enter, thousands and thousands of fool functions, when
Mathematics has only one Valid Function-- the Polynomial function. For you can only arrive at a True Valid Proof of Fundamental Theorem of Calculus by using polynomials as functions.

So how many students every year are punished by having to learn calculus with fool functions, with no valid proof of FTC. Where the calculus classroom puts students not through a Pleasure learning session but a gauntlet torture chamber, whipping the
students into nervous breakdowns and vomiting during exams.

All for what??? How much money does Dr. Strang make from his awful book Calculus?? Let me guess estimate.

The book probably costs $100 in our inflation environment. And typically a author gets 1/2 of that in royalties.

Say MIT teaches a class of 100 students in calculus per year would be 50 x 100 = $5,000. And say a estimate that around the world there are 100 schools teaching from this book of 100 students in their classroom would make Gilbert $500,000 per year in
book sales of his Calculus.

Same can be said of AP back in 1968 having to learn fake geology with no Continental Drift plate tectonics, so that some so called scientists reaps a reward of 1/2 a million dollars in book sales. And that thousands of students taught lectured and tested
upon fake geology.

This is one of the grand benefits of a Usenet and a Internet, that we speed up the process of throwing out Fake -Math, fake-geology and all other fake sciences. Freedom of Speech of Internet of Usenet allows for science to be Showered, Cleaned UP, bathed
from its wretched stink of Old fake science. Clean Up their science.

The only valid functions in mathematics are Polynomial Functions, which in turn, makes Calculus be super super super easy. No more vomiting by students in a calculus exam. No more nervous breakdowns by students taking calculus.

AP

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