One of the easiest fames in physics when Oersted noticed the compass needle deflect when placed near a electric current. Instant fame and recognition for a simple experiment.
Anything like that in math history? I think not. However, there easily could have been from assigning angles greater than 360 degrees as having completed a full revolution and now you repeat the older angles such as 10 is now 370 degrees, 20 is now 380 degrees. No fame for that, but what if someone said, alright, sine function has gone from (0,0) to (4,0) in 360 degrees and is now repeating that pattern because degrees after 360 resembles the same pattern.
In other words, what makes the trig functions periodic, is merely the notion that after 360 degrees, you just increase the angle size but which is really the same angles from 0 to 360.
Few people realize this, even those in mathematics, realize that what makes trig functions periodic is not something ingrained in trig functions, but is only due to the fact that you increase the size of angle, repeats the trig function involved.
Now, let us have a moment of philosophy-- is an angle of 370 degrees really existing and if so, is it really just another way of saying 10 degrees? Now most would say it exists for it is a full revolution plus 10 more degrees. But then someone versed in Logic may say the definition of angle from 0 to 360 involves two rays for which geometry cannot have angles larger than 360.
In other words, if there had been someone to notice, like Oersted, that angles larger than 360 claimed to be valid angles just as 370 is valid as is 10 degrees, and that the existence of trig functions as periodic functions, depends merely on the notion that there exists angles larger than 360 degrees.
The periodicity of trig functions is all because, we believe angles larger than 360 degrees exist.
But do they, in truth exist?
I say they do not, that angles give out when you reach 360 degrees. That 360 means going around completely. if there is a angle of 370, then there has to be a figure in geometry that has a angle of 370. Squares have 360, but never 370. Circles have 360 but never 370.
So, if ever there was a Oersted who claimed one of the greatest prizes in physics for doing almost nothing, then there should be a Oersted of math, who founded the idea that because you go beyond 360 in angles, even though they are nonexistent angles, and thus founding of trigonometry, because the trig functions are not periodic, save for the silly notion that angles greater than 360 are genuine angles when they are not. Now, do not get me wrong, Oersted found truth in physics with his demonstration and deserves fame.
And whoever was the mathematician that is ascribed as founding angles greater than 360 is probably not a famous mathematician for that work, for, in my opinion, angles do not go larger than 360 degrees. To me, angles have a borderline, just as numbers have a borderline of finite and which numbers larger are different numbers. The borderline of angles is 360 degrees, and beyond such as 370 is not 10 degrees.
So, the idea of the trig functions being periodic, was only a illusion, based upon the crippled idea that angles beyond 360 exist. If you want to talk about angle 370 degrees, it is not an angle but something else.
Alright, previously I wrote:
On Saturday, February 11, 2017 at 1:54:36 AM UTC-6, Archimedes Plutonium wrote:
Alright, ever notice how odd sine is? Ask for a function and usually what you get is something like this y= 2x^2 + 3. You get algebra in 99.9% of the time.
But if someone gave you sine as function how odd is that for it is asking you not to use operators on numbers but rather asking you to place a circle on graph paper and spinning around right-triangles inside the circle.
So, what New Function Theory aims to do is dliver the sine function in a form using Y = some x's, where we no longer have the word "sine" telling us to do some task on circle and right-triangles.
First question-- is this possible and the likely answer is that since a circle has the equation x^2 + y^2 = 1 which is rendered into a function by cutting in half, and further means nothing preventing it from replacing sine.
Now, Old Math people have a somewhat silly excuse as to why sine and cosine are periodic. Their excuse is that as you reach 360 degrees the angles are different and larger 450 =90 degrees with same triangle values repeating.
In New Function theory we open a floodgate of new periodic functions, all of them written in polynomial type of function.
Let me start that with a step function, and see if i get into any trouble.
The function Y=1 and function Y= -1, two parallel lines, the upper and lower bounds of sine and cosine.
Now, if you have not noticed, all straight lines are periodic functions, but i have two of them to form into sine. So what i need to do is manipulate the domain and range so that Y = 1 is good for x=0 to 1.9, then from x=2 to 3.9 in 10 Grid, Y= -1 and alternating back and forth.
So how do i accomplish that without violating my rule that a single formula forms the entire function? For i seem to have two functions.
Well here is where i manipulate the domain with range. For what i seek looks like this
___ ___ ___
___ ___
Now i do not have to worry about vertical lines nor discontinous for in New Math Grids we must always connect up present points with successor points and so no discontinuity nor vertical
___
\____
And so far i built a box shaped sine functiion from straightline functions. Once i replace them with semicircles or semiellipse i will have achieved a polynomial trigonometry.
AP
Newsgroups: sci.math
Date: Sun, 12 Feb 2017 00:43:56 -0800 (PST)
Subject: Re: How do you get the sine function without using circles or right triangles
From: Archimedes Plutonium <
plutonium....@gmail.com>
Injection-Date: Sun, 12 Feb 2017 08:43:57 +0000
So here is a bit dicey, here.
I want to get a periodic Function of repeating semicircles or repeating semiellipses, or even repeating sawtooths or repeating semi trapezoids.
I want to get them all with one formula.
I have at the moment, I have two parallel lines Y = 1 and Y= -1
And if I play around with the domain, by saying Y =1 for all x from 0 to 1.9 then Y= -1 for all x from 2 to 3.9.
Seems like I violated my one formula only.
Or have I ?
If I have, maybe I need to say that a Function can have at most two formula.
You see, the final aim of this pursuit, is we no longer write sin(x) or tan(x), but rather write something like this
x^2 + y^2
We make it where all of Calculus has only x, y, constants as terms. We make it where the Power rules reach into every function, giving them a derivative and integral.
We no longer say a Function where you have to do some sort of geometrical acrobatics of spinning right triangles inside a circle, or rolling a wheel on the x-axis marking off points traversed. No longer do we have alien symbols of sine, cosine, tangent, Ln, asking you to do something out of the ordinary. We have just x to powers of x and y to powers of y. We have just x and y.
AP