Alright I touched on all of this in my textbook series TEACHING TRUE MATHEMATICS, where I in fact teach calculus in High School.

But the pathetic history of mathematics education is that almost every math professor is kookish about teaching math-- for they seem to not want to make math simple and easy, but just the opposite, make math incomprehensible, so that they "look smart" and everyone else looks dumb because they cannot understand that garbage hieroglyphics on the chalk board.

Part of the problem is how math professors are advanced-- by publishing in journals, leaving their classrooms a disaster of teaching.

What AP has proposed and written about is that Functions of math are not this dumpster full of all kinds of functions. No, the only valid function in mathematics ae Polynomials. These are the easiest functions in all of math to do the calculus upon.

So some idiot math professor comes running in and wanting to put sine and cosine on the blackboard. No, no, no, no, no. You foolish idiot math professor in calculus class, convert you kook trig to a polynomial over an interval, then proceed to put that on the blackboard, and the students all happy because all those students can just simply take the Power Rules and have a derivative and integral faster than the math professor can eat a donut and slurp coffee in the math lounge.

This book is a calling demand to overhaul math education from 5 years old to 26 years old graduate school.

No longer should any student in any math class be tortured and driven to nightmares and insanity, all because math education never seems to ever want to make math easy and fun. There is one exception -- Harold Jacobs and his Mathematics: A Human Endeavor.

AP

AP's 245th book of science-- Overhaul and Revitalization of Calculus, making it breathtakingly simple that High School students master Calculus and more advanced than todays 3rd year college students in calculus

Now I am fascinated by how recent prior books of mine seem to propell me forward on upcoming books. For in my 240th book of science-- New True Geometry starting with cycloid correction and Geometry-of-Motion // math research
by Archimedes Plutonium, where I end the book with a proof that 3 arbitrary non-collinear points of the plane determines a unique circle but also a unique ellipse. That in that proof I stumble across a technique of where I have 1 unit square is a 45-45-90 set of right triangles, then add another and it is a 2 by 1 rectangle and what is the set of right triangles? Then what is the set of 3 by 1 rectangle etc etc.

So this question then can lead to the start of Trigonometry.

In my TEACHING TRUE MATHEMATICS I start trigonometry by a semicircle centered on (0,0) for cosine as it descends from (0,1) to (1,0) and I start sine with semicircle centered on (1,0) and as it ascends from (0,0) to reach (1,0).

So I am thinking that I can start trigonometry with this adding on more unit squares, 2 by 1, then 3 by 1, then 4 by 1, and asking in each new term what the angles of that set of right triangles are for that rectangle.

So writing one book facilitates writing the next book.

AP