Archimedes Plutonium
2018-08-16 06:10:49 UTC
1b,Let us thank AP for removing 95% of Trigonometry and making the 5% left--clear and easy
Now, please do not get me wrong, I am not throwing out 100% of trigonometry but 95% of trigonometry. We save that part that is true and useful. Since math has no continuum, then 95% of trigonometry is fakery. Since math has no continuum the only true part of trigonometry is that you have one side of a right triangle, not the hypotenuse, and you have one angle other than the 90° angle, and from that side and angle you can determine via trigonometry another side and then using Pythagorean theorem determine the hypotenuse. That is the sum total use of trigonometry. So, why are our Calculus textbooks and other math books filled with this garbage trigonometry? Only because nattering nutters keep hyping trigonometry. Trig is a article of Old Math, that was never evaluated as for validity and whether there was a better way-- Chart of Angles by AP. Trigonometry by 2018 is like teaching the 4 humors as medicine-- yellow bile, black bile, blood, phlegm.
By 1930 when Physics proved the Universe is discrete-- quantum mechanics, by 1930, trigonometry of Old Math should have started to shrivel up and blow away, for the discrete universe means trigonometry is 95% fakery.
134- Let us thank AP for removing 95% of Trigonometry and making the 5% left--clear and easy
Tell me, how many times in life did you actually use secant, cotangent, sinh, cosh, arctangent, and that basketcase of hieroglyphics chicken scratching trig functions, after having been forced to learn that b.s.? Is it because math teachers have no time to teach actual true math but a lot of time to teach fake math. Here we throw out 95% of Old Math fake trigonometry, and save you, the student of that barbwired nightmare.
Subject: Let us thank AP for making Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the trash pile of math
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Wed, 11 Jul 2018 21:50:33 +0000
Let us thank AP for making Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the trash pile of math
This thread is going to be a commentary on the fabulous feat of AP, to unclutter and make Trigonometry accessible to all people. To lift trigonometry out of the hands of Old Math kooks of mathematics.
The first sign to AP, that trigonometry was a sham fakery, a kookfest but not science or mathematics, is when AP noticed many years ago (have to look the exact date up), noticed that the sinusoid wave was purely fiction, as a result of stretching the x-axis by 3.14...- 2 = 1.14.... stretching that x axis when math never allows stretching of axes, just to suit the whims of knuckleheads in mathematics.
Old Math defined trig as sine being opposite divided by hypotenuse. Nothing wrong with that. And so, when you have a Unit Circle radius 1, the sine is going to be opposite/1. Still no problem. The unit circle forces 90 degrees to be 1. Then, because 90 degrees is 1 for unit circle, means you are forced to assign 180 degrees as being 2, never being 3.14...
You see, in the history of mathematics, some knucklehead who had no logical mind in doing trigonometry, assigned 90 degrees as 1, but then arbitrary assigned 180 degrees to suit his illogical taste as being 3.14... One can only guess, he had no logical mind to see that 90 degrees = 1 forces 180 degrees to be 2. Thus, he created a fictional wave called the sinusoid. The sinusoid exists only because you stretch one axis abnormally, which is not-mathematics at all, in fact it is anti-math. Mathematics stops if you arbitrarily stretch an axis.
Many years ago I discovered this.
But recently I discovered the decay and disease in trigonometry is an immense decay, so much so, that we throw out all of Old Math Trigonometry,,,,
More later,,,,
--- old post of 2016 ---
Newsgroups: sci.math
Date: Wed, 21 Sep 2016 19:31:18 -0700 (PDT)
Subject: Huge Error of Old Math, sine and cosine are semicircle curves not
sinusoidal Re: sine, cosine as OOOOO Re: Precalculus pages TALK textbook
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 22 Sep 2016 02:31:18 +0000
Huge Error of Old Math, sine and cosine are semicircle curves not sinusoidal Re: sine, cosine as OOOOO Re: Precalculus pages TALK textbook
Now, you can make a Sinusoidal curve in Old Math by altering amplitude or frequency or period. So you can turn a Semicircle Wave into a sinusoidal wave.
But the original wave of Y=sin(x) or cos(x) are semicircle waves, not sinusoidal waves.
And, one thing that should have caught our attention early in math training is the absence of a Semicircle curve. And now we realize why that absence. It was there all along as sine and cosine only we mislead ourselves to be corrupted in mind by letting the x-axis not equal to y-axis.
Look at Wikipedia's page on sine function, for they have rectangles in which their y distance of 1 is made to appear equal to pi/4. They thus exaggerate the curve, when the curve is just truly a semicircles strung together.
AP
Newsgroups: sci.math
Date: Wed, 11 Jul 2018 17:25:26 -0700 (PDT)
Subject: telling it straight about trig Re: Let us thank AP for making
Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the
kook pile of math
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 12 Jul 2018 00:25:27 +0000
telling it straight about trig Re: Let us thank AP for making Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the trash pile of math
So, by 2016, September, AP found a huge flaw in Old Math trigonometry, that no sinusoid wave actually exists but is rather a semicircle wave. Sure you can manipulate the sine wave with various alterations of frequency or period or wavelength etc in order to make the sine wave look like a sinusoid, but in reality sine itself is semicircle wave. So, that was an error noted by me in September of 2016.
Now comes July of 2018, and recently working on the Altitude of Right Triangles, and in that process of finding a general method of solving for the Altitude, I was able to place Trigonometry-- the whole of the science of trigonometry into its fitting, true, logical position in math. Where Trigonometry of the past-- has been so inflated, so badly, poorly inflated beyond all its worth and value, that it is an entire subject that is corrupt mathematics.
Here is a recent passage I wrote -- evaluating the whole of trigonometry as taught in schools today--
Essentially, all of trig is about the idea that if given an angle of a right triangle, and given a dy or a dx side of the right triangle, you can find the other side (not the hypotenuse). That is all that trig is about, given angle and one side-- find the other side.
So if that is all that is trigonometry, why is math of today filling books with that trig crap? Why?
Newsgroups: sci.math
Date: Tue, 10 Jul 2018 23:19:48 -0700 (PDT)
Subject: Searching for the general-method, apparently division by 2 is not in
the cards Re: Give me any right-triangle in the plane-- I need be able to
compute its altitude via a dy-dx
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Wed, 11 Jul 2018 06:19:49 +0000
Searching for the general-method, apparently division by 2 is not in the cards Re: Give me any right-triangle in the plane-- I need be able to compute its altitude via a dy-dx
I had better do some slanted line functions like Y = 1/2x or Y = 3x or Y = 1/3x + 1 to get some smaller angles, but then every right triangle that has a large angle, has a small angle.
And I should get this altitude problems into some routine method, before too long.
Trig in a sentence is really nothing more than given an angle and a side of a right-triangle- then find the other side. That is all there is to trig. But you would never know that picking up any trig or calculus book today. In the AP program of Calculus, we turn all functions into a Polynomial, so that the words sine, cosine, tangent cosecant secant sinh, you name it, you will never see in that Calculus textbook, because they are not functions and even if they were functions, they would be translated into a polynomial like -1.44x^2 + .44x + 1 = Y
Our jobs as teachers, is not to make money for schooling or book publishers, our job is to teach trigonometry the easiest way and how easy trig is.
Newsgroups: sci.math
Date: Wed, 11 Jul 2018 18:05:27 -0700 (PDT)
Subject: math and trig of the future-- why students will love math once again
Re: telling it straight about trig Re: Let us thank AP for making
Trigonometry clear and easy
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 12 Jul 2018 01:05:29 +0000
math and trig of the future-- why students will love math once again Re: telling it straight about trig Re: Let us thank AP for making Trigonometry clear and easy
What will trigonometry look like in the near future as the AP corrections take affect?
Well, you will never again see the words sine, cosine, tangent, arctangent, secant, cosecant, sinh, cosh and a score of other silly stupid terms. You will never see those again in any future math book, but in place, you will see dy or dx. And would that not be so heavenly to all students of science-- to never be bothered or see the silly sine and cosine.
You will no longer see any Trig table, neither on a hand calculator or on the Internet, except for historical purposes-- to see how dumb they were in the past. And what will replace Trig tables?
What replaces trig tables is the 1by1 Square of Angles where 10 blocks long and 5 blocks high is an angle of 27 degrees or its complement 63 degrees.
No more trig tables because a chart of Angles is all the trig values you need.
And since All of Calculus Functions, all of them-- are polynomials such as Y = x^3 + 2x^2 + x + 3 as an example, no student will ever be bothered with the crazy Old Math with their horrible incomprehensible crap like this
(Strang, page 33, sec(t) + csc(t)/ tan(t) + cot(t) = sin(t) + cos(t))
Like wallowing in a cesspool of mire. No, longer will students be insulted and despised and given incomprehensible crap.
In fact, if we throw out all trig crap from the textbooks of Calculus,-- how much or many pages would we be left with? With Strang- his 615 pages abomination would be pared down to probably 85 pages.
With Apostol's barbwired nightmarish text would be pared down by 1/2, and with Ellis & Gulick only 50% remains.
MATH OF THE FUTURE:
trigonometry is a meagre chapter of calculus, just as percentage concept is a meagre chapter of arithmetic
You will no longer see functions as flaky and creepy words-- sine, cosine, tangent, Log, Ln, sqrt, etc but rather, every function is just a polynomial.
Students will love trigonometry and New Math, because there is nothing difficult in it-- once the corrupt creeps of Old Math are removed.
AP
On Thursday, July 12, 2018 at 12:49:36 AM UTC-5, Archimedes Plutonium wrote:
Make no mistake about it— AP is advocating that all trigonometry be removed out of math except on those rare occasions where you find the missing side of a right triangle.
Percentage concept is a tool in math yet it does not flood math. And trig is just a tool, no better than percentage, yet it floods and muddies much of math.
Angles do not make functions.
Angles are just ratios of dy to dx
All of math has to standardize what a function is— all functions are polynomials— for in that way you can compare all functions— compare one to another. But as long as math allows anyone with a prescription for a function, math is a cesspool.
If a function cannot be written as a polynomial— it is not a function
Surprizingly cosine can be written as Y = -1.44x^2 +.44x + 1 in interval 0 to1 with only a sigma error of 5%.
The point is — all legitimate functions must be able to be a polynomial so that any two of them can be compared. You can compare x^2 with 2x-1 with 3x^3 but you cannot compare sin(x), sqrt(x), log(x).
AP
Newsgroups: sci.math
Date: Thu, 12 Jul 2018 11:08:01 -0700 (PDT)
Subject: converting functions 1/x and tractrix into polynomials Re: All trig
functions if functions are converted to polynomials
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 12 Jul 2018 18:08:01 +0000
converting functions 1/x and tractrix into polynomials Re: All trig functions if functions are converted to polynomials
Y = -1.44x^2 + .44x + 1 return to old post on quarter circle as polynomial
Let me return to some old posts of Curve Fitting, maybe I be better off
On Monday, February 20, 2017 at 2:18:16 AM UTC-6, Archimedes Plutonium wrote:
quartercircle of sine is -1.44x^2 + 2.44x + 0 = Y
So, I employed the tool:
The Polynomial Generator is this tool::
For 2 coordinate points, (x0, y0) (x1, y1), we produce the 1st degree polynomial, a straightline or line segment
P(x) = y0(x-x1) / (x0-x1)
+ y1(x-x0) / (x1-x0)
For 3 coordinate points, (x0, y0) (x1, y1) (x2, y2), we produce the 2nd degree polynomial, a compilation-curve
P(x) = y0(x-x1)(x-x2) / (x0-x1)(x0-x2)
+y1(x-x0)(x-x2) / (x1-x0)(x1-x2)
+y2(x-x0)(x-x1) / (x2-x0)(x2-x1)
For 4 coordinate points, (x0, y0) (x1, y1) (x2, y2) (x3, y3), we produce the 3rd degree polynomial, a compilation curve
P(x) = y0(x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
+y1(x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
+y2(x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
+y3(x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)
Obviously I need the tool for 3 coordinate points:
quartercircle sine (0,0) (.5,.86) (1,1)
And what I end up with is this polynomial
-1.44x^2 + 2.44x + 0 = Y
Now, was that so much easier than playing around-- I think so. For that equation gives me exactly sine at those sought for 3 points. And, the bonus is that it is still quadratic.
And it looks as though the cosine, which I have not yet worked out, but is also quadratic since the last term of y2 is 0 and thus ending as a power of 2 quadratic.
So, let me work that one out, ....
Quartercircle for cosine is Y = -1.44x^2 + .44x + 1
Very crude dot picture of 5f6, 94TH
ELECTRON=muon DOT CLOUD of 231Pu
::\ ::|:: /::
::\::|::/::
_ _
(:Y:)
- -
::/::|::\::
::/ ::|:: \::
One of those dots is the Milky Way galaxy. And each dot represents another galaxy.
. \ . . | . /.
. . \. . .|. . /. .
..\....|.../...
::\:::|::/::
--------------- -------------
--------------- (Y) -------------
--------------- --------------
::/:::|::\::
../....|...\...
. . /. . .|. . \. .
. / . . | . \ .
http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
Read my recent posts in peace and quiet.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium
Now, please do not get me wrong, I am not throwing out 100% of trigonometry but 95% of trigonometry. We save that part that is true and useful. Since math has no continuum, then 95% of trigonometry is fakery. Since math has no continuum the only true part of trigonometry is that you have one side of a right triangle, not the hypotenuse, and you have one angle other than the 90° angle, and from that side and angle you can determine via trigonometry another side and then using Pythagorean theorem determine the hypotenuse. That is the sum total use of trigonometry. So, why are our Calculus textbooks and other math books filled with this garbage trigonometry? Only because nattering nutters keep hyping trigonometry. Trig is a article of Old Math, that was never evaluated as for validity and whether there was a better way-- Chart of Angles by AP. Trigonometry by 2018 is like teaching the 4 humors as medicine-- yellow bile, black bile, blood, phlegm.
By 1930 when Physics proved the Universe is discrete-- quantum mechanics, by 1930, trigonometry of Old Math should have started to shrivel up and blow away, for the discrete universe means trigonometry is 95% fakery.
134- Let us thank AP for removing 95% of Trigonometry and making the 5% left--clear and easy
Tell me, how many times in life did you actually use secant, cotangent, sinh, cosh, arctangent, and that basketcase of hieroglyphics chicken scratching trig functions, after having been forced to learn that b.s.? Is it because math teachers have no time to teach actual true math but a lot of time to teach fake math. Here we throw out 95% of Old Math fake trigonometry, and save you, the student of that barbwired nightmare.
Subject: Let us thank AP for making Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the trash pile of math
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Wed, 11 Jul 2018 21:50:33 +0000
Let us thank AP for making Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the trash pile of math
This thread is going to be a commentary on the fabulous feat of AP, to unclutter and make Trigonometry accessible to all people. To lift trigonometry out of the hands of Old Math kooks of mathematics.
The first sign to AP, that trigonometry was a sham fakery, a kookfest but not science or mathematics, is when AP noticed many years ago (have to look the exact date up), noticed that the sinusoid wave was purely fiction, as a result of stretching the x-axis by 3.14...- 2 = 1.14.... stretching that x axis when math never allows stretching of axes, just to suit the whims of knuckleheads in mathematics.
Old Math defined trig as sine being opposite divided by hypotenuse. Nothing wrong with that. And so, when you have a Unit Circle radius 1, the sine is going to be opposite/1. Still no problem. The unit circle forces 90 degrees to be 1. Then, because 90 degrees is 1 for unit circle, means you are forced to assign 180 degrees as being 2, never being 3.14...
You see, in the history of mathematics, some knucklehead who had no logical mind in doing trigonometry, assigned 90 degrees as 1, but then arbitrary assigned 180 degrees to suit his illogical taste as being 3.14... One can only guess, he had no logical mind to see that 90 degrees = 1 forces 180 degrees to be 2. Thus, he created a fictional wave called the sinusoid. The sinusoid exists only because you stretch one axis abnormally, which is not-mathematics at all, in fact it is anti-math. Mathematics stops if you arbitrarily stretch an axis.
Many years ago I discovered this.
But recently I discovered the decay and disease in trigonometry is an immense decay, so much so, that we throw out all of Old Math Trigonometry,,,,
More later,,,,
--- old post of 2016 ---
Newsgroups: sci.math
Date: Wed, 21 Sep 2016 19:31:18 -0700 (PDT)
Subject: Huge Error of Old Math, sine and cosine are semicircle curves not
sinusoidal Re: sine, cosine as OOOOO Re: Precalculus pages TALK textbook
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 22 Sep 2016 02:31:18 +0000
Huge Error of Old Math, sine and cosine are semicircle curves not sinusoidal Re: sine, cosine as OOOOO Re: Precalculus pages TALK textbook
So, is anyone in math today able to explain how the sine function becomes sinusoid and not strung together semicircles?? Is this the hugest blunder in the history of math education?????
Apparently, what happened is that there exists no sinusoidal curve, no sine curve, because it is a half circle curve. So how did this become a huge error in math? Probably because when graphing Y = sin(x) they let the y axis be normal but they used pi multiplies for the x-axis as does Wikipedia on sine function. So they distort the graph of Sine function with y and x axis as unequal.Now, you can make a Sinusoidal curve in Old Math by altering amplitude or frequency or period. So you can turn a Semicircle Wave into a sinusoidal wave.
But the original wave of Y=sin(x) or cos(x) are semicircle waves, not sinusoidal waves.
And, one thing that should have caught our attention early in math training is the absence of a Semicircle curve. And now we realize why that absence. It was there all along as sine and cosine only we mislead ourselves to be corrupted in mind by letting the x-axis not equal to y-axis.
Look at Wikipedia's page on sine function, for they have rectangles in which their y distance of 1 is made to appear equal to pi/4. They thus exaggerate the curve, when the curve is just truly a semicircles strung together.
AP
Newsgroups: sci.math
Date: Wed, 11 Jul 2018 17:25:26 -0700 (PDT)
Subject: telling it straight about trig Re: Let us thank AP for making
Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the
kook pile of math
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 12 Jul 2018 00:25:27 +0000
telling it straight about trig Re: Let us thank AP for making Trigonometry clear and easy-- and throwing Old Math's trigonometry onto the trash pile of math
So, by 2016, September, AP found a huge flaw in Old Math trigonometry, that no sinusoid wave actually exists but is rather a semicircle wave. Sure you can manipulate the sine wave with various alterations of frequency or period or wavelength etc in order to make the sine wave look like a sinusoid, but in reality sine itself is semicircle wave. So, that was an error noted by me in September of 2016.
Now comes July of 2018, and recently working on the Altitude of Right Triangles, and in that process of finding a general method of solving for the Altitude, I was able to place Trigonometry-- the whole of the science of trigonometry into its fitting, true, logical position in math. Where Trigonometry of the past-- has been so inflated, so badly, poorly inflated beyond all its worth and value, that it is an entire subject that is corrupt mathematics.
Here is a recent passage I wrote -- evaluating the whole of trigonometry as taught in schools today--
Essentially, all of trig is about the idea that if given an angle of a right triangle, and given a dy or a dx side of the right triangle, you can find the other side (not the hypotenuse). That is all that trig is about, given angle and one side-- find the other side.
So if that is all that is trigonometry, why is math of today filling books with that trig crap? Why?
Newsgroups: sci.math
Date: Tue, 10 Jul 2018 23:19:48 -0700 (PDT)
Subject: Searching for the general-method, apparently division by 2 is not in
the cards Re: Give me any right-triangle in the plane-- I need be able to
compute its altitude via a dy-dx
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Wed, 11 Jul 2018 06:19:49 +0000
Searching for the general-method, apparently division by 2 is not in the cards Re: Give me any right-triangle in the plane-- I need be able to compute its altitude via a dy-dx
Now let me get to Altitude again, for there were some glitches in that, which I need to iron out.
And I will do Altitude for these six functions, Y=x, Y=x^2, Y=x^3, Y=x^4, and the quarter circles Y = -1.44x^2 + .44x + 1 , Y= -1.44x^2 + 2.44x
And I will do Altitude for these six functions, Y=x, Y=x^2, Y=x^3, Y=x^4, and the quarter circles Y = -1.44x^2 + .44x + 1 , Y= -1.44x^2 + 2.44x
And I should get this altitude problems into some routine method, before too long.
Alright, well for function Y = x^2, I need a right triangle so will do the plotting of points 2 and 3
x y
2 4
3 9
On my graph paper, plot points (2,4) to (3,9) forming a right triangle with ((3,4) and measuring the angles with protractor I get a 79-11-90 right triangle
Now, look up the 1by1 Square Angle chart, the chart that replaces the phony baloney Trig tables of Old Math
1by10 2by10
10 5 3.3 2.5 2 1.6 1.4 1.2 1.1 1 dy/dx, slope, derivative
90 84 79 73 68 63 59 55 51 48 45 these are angles made from (0,0)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
90 84 79 73 68 63 59 55 51 48 45, slope 1, rt-triangle 10by10
42, slope .9, rt-triangle 10by9
39, slope .8, rt-triangle 10by8
35, slope .7, rt-triangle 10by7
31, slope .6, rt-triangle 10by6
27, slope .5, rt-triangle 10by5
22, slope .4, rt-triangle 10by4
17, slope .3, rt.triangle 10by3
11, slope .2, rt-triangle 10by2
6, slope .1, rt-triangle 10by1
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
And we clearly see that a 79 degree angle is complementary to a 11 degree angle and both have a 2by10 or 10by2 rectangle of linear blocks, either 2 blocks high and 10 blocks wide or 2 blocks wide and 10 blocks high.
So instead of the Old Math going to some silly trig tables what we do is just look where the angle fits into the above. It need not fit exactly such as 79degrees, but could be an angle in between two in the square above.
So, in New Math we just want to know the angle, and then the chart tells us we are dealing with a ratio of 2 to 10, or, with 10 to 2. That is what Old Math would have done with their silly sine and cosine table-- tell you .2 is cosine 79 degrees or thereabouts. But why have a table when we can easily construct the chart that will go with you the rest of your life for trigonometry.
So I said in prior posts, that Trig is more like Percentage algebra than anything else, and now, let us see how that is true.
So I have a right triangle of (2,4) (3,9) (3,4) with angles 79-11-90, and say I only knew two numbers, I knew 79 degrees and I knew the length of 1 base from (2,4) to (3,4), and what I want to know is the distance of the other side (3,4) (3,9). Pretend as if we do not know this distance at all. So, this is what trig is really all about in the first place, you know an angle and one of the sides, you do not know the other side and trig was discovered to help you find this other side, given two numbers-- angle and one side.
This is a shame, huge huge shame, that trigonometry is so easy a subject and on par in ease with that of Percentage concept. So that math should have never made trigonometry a subject course itself, for percentage is not a full year study course, but rather a topic. And in this light, we should have taught trigonometry as a topic and perhaps every math year, reinforce the topic, but certainly do not make it a full year course. And, why was it made into a full year course and such incomprehensible ideas as those far flung trig functions, that csc, sinh, arctangent, etc etc. Why? I think the answer is money. Many can make money, books-- papers, lectures, teaching, on trigonometry, if there is a "demand for it". So instead of making trigonometry as simple and easy as percentage, math professors kept trigonometry as a mess pile of unlearnable and unteachable crap. Money is usually behind corruption, and Old Math Trigonometry was very corrupt.x y
2 4
3 9
On my graph paper, plot points (2,4) to (3,9) forming a right triangle with ((3,4) and measuring the angles with protractor I get a 79-11-90 right triangle
Now, look up the 1by1 Square Angle chart, the chart that replaces the phony baloney Trig tables of Old Math
1by10 2by10
10 5 3.3 2.5 2 1.6 1.4 1.2 1.1 1 dy/dx, slope, derivative
90 84 79 73 68 63 59 55 51 48 45 these are angles made from (0,0)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
90 84 79 73 68 63 59 55 51 48 45, slope 1, rt-triangle 10by10
42, slope .9, rt-triangle 10by9
39, slope .8, rt-triangle 10by8
35, slope .7, rt-triangle 10by7
31, slope .6, rt-triangle 10by6
27, slope .5, rt-triangle 10by5
22, slope .4, rt-triangle 10by4
17, slope .3, rt.triangle 10by3
11, slope .2, rt-triangle 10by2
6, slope .1, rt-triangle 10by1
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
And we clearly see that a 79 degree angle is complementary to a 11 degree angle and both have a 2by10 or 10by2 rectangle of linear blocks, either 2 blocks high and 10 blocks wide or 2 blocks wide and 10 blocks high.
So instead of the Old Math going to some silly trig tables what we do is just look where the angle fits into the above. It need not fit exactly such as 79degrees, but could be an angle in between two in the square above.
So, in New Math we just want to know the angle, and then the chart tells us we are dealing with a ratio of 2 to 10, or, with 10 to 2. That is what Old Math would have done with their silly sine and cosine table-- tell you .2 is cosine 79 degrees or thereabouts. But why have a table when we can easily construct the chart that will go with you the rest of your life for trigonometry.
So I said in prior posts, that Trig is more like Percentage algebra than anything else, and now, let us see how that is true.
So I have a right triangle of (2,4) (3,9) (3,4) with angles 79-11-90, and say I only knew two numbers, I knew 79 degrees and I knew the length of 1 base from (2,4) to (3,4), and what I want to know is the distance of the other side (3,4) (3,9). Pretend as if we do not know this distance at all. So, this is what trig is really all about in the first place, you know an angle and one of the sides, you do not know the other side and trig was discovered to help you find this other side, given two numbers-- angle and one side.
Trig in a sentence is really nothing more than given an angle and a side of a right-triangle- then find the other side. That is all there is to trig. But you would never know that picking up any trig or calculus book today. In the AP program of Calculus, we turn all functions into a Polynomial, so that the words sine, cosine, tangent cosecant secant sinh, you name it, you will never see in that Calculus textbook, because they are not functions and even if they were functions, they would be translated into a polynomial like -1.44x^2 + .44x + 1 = Y
Our jobs as teachers, is not to make money for schooling or book publishers, our job is to teach trigonometry the easiest way and how easy trig is.
Newsgroups: sci.math
Date: Wed, 11 Jul 2018 18:05:27 -0700 (PDT)
Subject: math and trig of the future-- why students will love math once again
Re: telling it straight about trig Re: Let us thank AP for making
Trigonometry clear and easy
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 12 Jul 2018 01:05:29 +0000
math and trig of the future-- why students will love math once again Re: telling it straight about trig Re: Let us thank AP for making Trigonometry clear and easy
What will trigonometry look like in the near future as the AP corrections take affect?
Well, you will never again see the words sine, cosine, tangent, arctangent, secant, cosecant, sinh, cosh and a score of other silly stupid terms. You will never see those again in any future math book, but in place, you will see dy or dx. And would that not be so heavenly to all students of science-- to never be bothered or see the silly sine and cosine.
You will no longer see any Trig table, neither on a hand calculator or on the Internet, except for historical purposes-- to see how dumb they were in the past. And what will replace Trig tables?
What replaces trig tables is the 1by1 Square of Angles where 10 blocks long and 5 blocks high is an angle of 27 degrees or its complement 63 degrees.
No more trig tables because a chart of Angles is all the trig values you need.
And since All of Calculus Functions, all of them-- are polynomials such as Y = x^3 + 2x^2 + x + 3 as an example, no student will ever be bothered with the crazy Old Math with their horrible incomprehensible crap like this
(Strang, page 33, sec(t) + csc(t)/ tan(t) + cot(t) = sin(t) + cos(t))
Like wallowing in a cesspool of mire. No, longer will students be insulted and despised and given incomprehensible crap.
In fact, if we throw out all trig crap from the textbooks of Calculus,-- how much or many pages would we be left with? With Strang- his 615 pages abomination would be pared down to probably 85 pages.
With Apostol's barbwired nightmarish text would be pared down by 1/2, and with Ellis & Gulick only 50% remains.
MATH OF THE FUTURE:
trigonometry is a meagre chapter of calculus, just as percentage concept is a meagre chapter of arithmetic
You will no longer see functions as flaky and creepy words-- sine, cosine, tangent, Log, Ln, sqrt, etc but rather, every function is just a polynomial.
Students will love trigonometry and New Math, because there is nothing difficult in it-- once the corrupt creeps of Old Math are removed.
AP
On Thursday, July 12, 2018 at 12:49:36 AM UTC-5, Archimedes Plutonium wrote:
Make no mistake about it— AP is advocating that all trigonometry be removed out of math except on those rare occasions where you find the missing side of a right triangle.
Percentage concept is a tool in math yet it does not flood math. And trig is just a tool, no better than percentage, yet it floods and muddies much of math.
Angles do not make functions.
Angles are just ratios of dy to dx
All of math has to standardize what a function is— all functions are polynomials— for in that way you can compare all functions— compare one to another. But as long as math allows anyone with a prescription for a function, math is a cesspool.
If a function cannot be written as a polynomial— it is not a function
Surprizingly cosine can be written as Y = -1.44x^2 +.44x + 1 in interval 0 to1 with only a sigma error of 5%.
The point is — all legitimate functions must be able to be a polynomial so that any two of them can be compared. You can compare x^2 with 2x-1 with 3x^3 but you cannot compare sin(x), sqrt(x), log(x).
AP
Newsgroups: sci.math
Date: Thu, 12 Jul 2018 11:08:01 -0700 (PDT)
Subject: converting functions 1/x and tractrix into polynomials Re: All trig
functions if functions are converted to polynomials
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Thu, 12 Jul 2018 18:08:01 +0000
converting functions 1/x and tractrix into polynomials Re: All trig functions if functions are converted to polynomials
Two functions not trig are especially interesting Y= 1/x and the tractrix. I suspect those two to be related.
What I have in mind here, is to do to all functions not already polynomials, is to plot graph several points in an interval and use the Polynomial Generator to find the function formula. Much the same as the Generator found the quarter circles in 0 to 1.Y = -1.44x^2 + .44x + 1 return to old post on quarter circle as polynomial
Let me return to some old posts of Curve Fitting, maybe I be better off
On Monday, February 20, 2017 at 2:18:16 AM UTC-6, Archimedes Plutonium wrote:
quartercircle of sine is -1.44x^2 + 2.44x + 0 = Y
So, I employed the tool:
The Polynomial Generator is this tool::
For 2 coordinate points, (x0, y0) (x1, y1), we produce the 1st degree polynomial, a straightline or line segment
P(x) = y0(x-x1) / (x0-x1)
+ y1(x-x0) / (x1-x0)
For 3 coordinate points, (x0, y0) (x1, y1) (x2, y2), we produce the 2nd degree polynomial, a compilation-curve
P(x) = y0(x-x1)(x-x2) / (x0-x1)(x0-x2)
+y1(x-x0)(x-x2) / (x1-x0)(x1-x2)
+y2(x-x0)(x-x1) / (x2-x0)(x2-x1)
For 4 coordinate points, (x0, y0) (x1, y1) (x2, y2) (x3, y3), we produce the 3rd degree polynomial, a compilation curve
P(x) = y0(x-x1)(x-x2)(x-x3) / (x0-x1)(x0-x2)(x0-x3)
+y1(x-x0)(x-x2)(x-x3) / (x1-x0)(x1-x2)(x1-x3)
+y2(x-x0)(x-x1)(x-x3) / (x2-x0)(x2-x1)(x2-x3)
+y3(x-x0)(x-x1)(x-x2) / (x3-x0)(x3-x1)(x3-x2)
Obviously I need the tool for 3 coordinate points:
quartercircle sine (0,0) (.5,.86) (1,1)
And what I end up with is this polynomial
-1.44x^2 + 2.44x + 0 = Y
Now, was that so much easier than playing around-- I think so. For that equation gives me exactly sine at those sought for 3 points. And, the bonus is that it is still quadratic.
And it looks as though the cosine, which I have not yet worked out, but is also quadratic since the last term of y2 is 0 and thus ending as a power of 2 quadratic.
So, let me work that one out, ....
Quartercircle for cosine is Y = -1.44x^2 + .44x + 1
Very crude dot picture of 5f6, 94TH
ELECTRON=muon DOT CLOUD of 231Pu
::\ ::|:: /::
::\::|::/::
_ _
(:Y:)
- -
::/::|::\::
::/ ::|:: \::
One of those dots is the Milky Way galaxy. And each dot represents another galaxy.
. \ . . | . /.
. . \. . .|. . /. .
..\....|.../...
::\:::|::/::
--------------- -------------
--------------- (Y) -------------
--------------- --------------
::/:::|::\::
../....|...\...
. . /. . .|. . \. .
. / . . | . \ .
http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
Read my recent posts in peace and quiet.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium