angles larger than 360 degrees contradict the definition of angle

[Archimedes Plutonium]

Newsgroups: sci.math
Date: Sun, 12 Feb 2017 21:42:12 -0800 (PST)

Subject: 360 degrees is the last angle, and 370 is not an angle;; sine
function in purely polynomial form
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Mon, 13 Feb 2017 05:42:12 +0000


360 degrees is the last angle, and 370 is not an angle;; sine function in purely polynomial form

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

On Monday, February 13, 2017 at 1:23:09 AM UTC-6, Archimedes Plutonium wrote:

Now is there some sort of evidence that 360 degrees is the last and final degree to be?

Well there is the idea i mentioned that no geometry figure of two rays has more than 360 degrees.

Another argument would say- imagine a angle of 450 = 360 + 90 where 0 and 180 are the x-axis, then 90 and 270 the y-axis so then 450 and 630 would constitute the z axis and so 540 and 720 degrees would make 4th dimension and as we further go around we have more perpendiculars in higher dimensions. Which is not true by physics.

AP

On Monday, February 13, 2017 at 2:20:30 AM UTC-6, Archimedes Plutonium wrote:

Now maybe if this holds up as true, for i am not convinced myself that angles beyond 360 are as fiction as witches flying on brooms. To overturn something you have accepted for much of your life is not something to be done in one day with a few arguments.

But let us just say that Logic biulds the definition of angle and as that one ray of two rays meet in 360 degrees that 370 is just fiction.

And as someone counter argues that a marker on a wheel rolling marks out 360 degree as pi distance and 370 degrees as pi distance and a little more, still fails logic as angle defined by two rays and not by a wheel rolling for distance-- angle is not length, angle is the separation of two rays from a vertex.

Now, why am i pursuing this so avidly? It is because i want to construct the sine function as purely a polynomial of x and y without ever having to instruct someone-- get a circle and spin right triangles around the inside of this circle.

Now algebra has the formula of circle as Y = sqrt ( 1 - x^2)

Similarly, what i want to do is write a formula that is sine in terms of y and x, where you never have to say or use "sine"

Now what progress do i have on that account?

I have two functions Y = 1 and Y = -1 which gives me the periodic of sine (since angles no longer provide that for trig)

And i can split up the domain so i have a semicircle from 0 to 2 for Y = 1 then a semicircle from 2 to 4 for Y = -1. Here the domain of x gives sine its periodic characteristic. But do i need two functions?

Another idea that popps to mind is to have one function x^2 +y^2 = 1 and have two separated domains-- the usual x-axis and a second domain of the Naturals superimposed.

The definition of function only prohibits more than one y value but not banning two separated domains.

Now also, if true that 360 is the last and largest angle would be an ideal teaching tool for the massive crowd of math oafs currently in math who do not understand a borderline exists between finite and infinite numbers 1*10^604, because, if their is a borderline for angles at 360, only a stir crazy oaf would not admit to a borderline for numbers.

AP

On Monday, February 13, 2017 at 2:45:57 AM UTC-6, Archimedes Plutonium wrote:

am i close? ;; sine function in purely polynomial form

Alright i have two modes of posting-- desktop when serious with long detailed posts; iphone when casual and reflective sitting next to heater and snacking and thinking. Iphone posts are short and with grammar and spelling errors, but highly relaxing and convenient.

Perhaps a better remedy of sine as pure polynomial

We have formula of circle in particular is x^2 + y^2 = 1

We have a composite function of the circle with Y = 0, the x-axis.

When x is 1, 3, 5, .. those are the centers of the circle and then the semicircle of positive numbers is graphed at centers 1, 5, 9, .. For centers 3, 7, 11, ... negative numbers semicircle is graphed.

Is this the polynomial function of sine? I hope so

AP


On Monday, February 13, 2017 at 5:04:02 AM UTC-6, Archimedes Plutonium wrote:

am i close? ;; sine function in purely polynomial form

Now let us look at another argument in favor of the existence of angles greater than 360. The argument that the hexagon interior angles are 6 times 120 degrees to make 720 degrees.

720 degrees is two full rotations about a circle, does it feel as though if you walked the sides of a hexagon that you went around twice when in truth you went just once as 360 degrees, and worse yet let us say you walked around the hexagon exterior to it where its 6 vertices have exterior angles of 240 times 6 is 1440 degrees.

So, here is an example of where illogical mathematicians make a definition of angle as two rays from a vertex angle the degrees is the distance subtended by the rays in a unit circle. That is the definition of angle and degrees. So what went wrong with the hexagon?

Simple, the interior angle at a specific vertex is 120 and exterior is surely 240 but to speak of a 720 degrees asks what are the two rays involved and where is the vertex of this 720 degree angle of two rays.

There is none. Boneheads of math looked at the hexagon and simply disobeyed their definition of both angle and degrees.

True there are 6 angles of 120 degrees apiece, but there is totally nothing in a hexagon of 720 degrees.

In math, every angle larger than 360 degrees is a fictional angle.

AP

On Monday, February 13, 2017 at 5:41:17 AM UTC-6, Archimedes Plutonium wrote:

Proof that the largest angle to exist is 360 degrees; any larger are fakes

Sorry i cannot sleep when discovering something big and important. Here is a proof that the definition of angles in math will not allow the existence of angles larger than 360. Just as witches, ghosts and fire breathing dragons are fictional so are angles greater than 360

Proof: we have the definition of angle as two rays with vertex and the degrees subtended by the rays. We have the default case of 1 ray of 0 degrees. That is the definition. Now we draw a circle and apply the definition with two radii. We go through all the angles from 0 to 360. However we note that the two rays always has an interior and exterior subtended angle so for example 10 degrees interior and 350 exterior. Now what happens when someone claims a angle of 370 exists, what is its exterior angle?

If you have angles greater than 360, you lose the concept of interior and exterior angle.

So what is this prattle of a hexagon having 720 degrees? Hexagons have 6 angles which are 120 degrees each, but 720 is a meaningless number regarding angles. Every angle beyond 360 is a meaningless number.

QED

Is there some analogy to this? Why a simple analogy is to say add 5 horses with 5 grasshoppers and end up with 10 horses.

AP

[Jan]

On Tuesday, February 14, 2017 at 2:01:21 PM UTC-8, Archimedes Plutonium wrote:
> Newsgroups: sci.math
> Date: Sun, 12 Feb 2017 21:42:12 -0800 (PST)
>
> Subject: 360 degrees is the last angle, and 370 is not an angle;;

It is.

Next problem?

--
Jan

[Don Redmond]

> So what is this prattle of a hexagon having 720 degrees? Hexagons have 6 angles which are 120 degrees each, but 720 is a meaningless number regarding angles. Every angle beyond 360 is a meaningless number.
>
> QED
>

> AP

So what is the angle sum in a hexagon? O?

Don

[abu.ku...@gmail.com]

exterior angles are 360 degrees

[Archimedes Plutonium]

If I had 6 cherries and added 4 cherries I get 10 cherries. If I had 6 cherries and added 4 bananas I do not get 10 cherries. You cannot add the two unlike items unless you say a nondescript 10 items or say 6 cherries plus 4 bananas.

You can add 120 degrees with 120 degrees and get 240 degrees. You can add three of them and get 360 degrees.

What is say 370 degrees? Is it one full revolution and 10 degrees more? Well, it is a meaningless number just as 10 cherries when it really 6 cherries with 4 bananas.

The definition of Angle involves two rays with vertex and the subtended space. This is Plane Geometry only for the definition in elliptic and hyperbolic of angle is different.

In Plane Geometry every angle has its complimentary angle so for 10 degree it is 350 degree. What is the compliment of 370 degree? Would you say it is 350 or is it 710 degrees or something else.

When you define angle as per rays and vertex, that permits you only 360 maximum and nothing beyond 360.

If you were to stumble upon a angle of 10 degrees in a field, you would see the 10 and its two rays and vertex, and you would be able to measure the 10 and the 350. But, as you stumble on that angle in the field of life, would you say, oh, I landed on an angle of 370. You see how corny that is.

The simple fact is, you have six angles of 120 degrees in a hexagon and if you add them you get 720 as a number but not 720 degrees because there is no two rays with vertex that subtends 720.

Now, I am trying to use this as another proof of the Infinity Borderline, that where 360 degrees is the end of Angles as we know of angles, and so the infinity borderline at 1*10^604 is the end of finite numbers as we know of numbers.

One promising lead on this adventure of a Angle borderline is the fact that as you increase the edges of a regular polygon, you end up where the angle converges to being 180 degrees, in other words a straight line no longer a coming back around. I once saw a 257-gon or thereabouts be touted as 178 degrees. So I suspect a 1000-gon maybe having angles of 179 degrees or thereabouts. So, at what number do we get a n-gon of 179.9 degrees? When does that appear? At a 10,000-gon?

Do you sense the absurdity of thinking that adding up these angles in a hexagon of 720 means degrees?

AP

[abu.ku...@gmail.com]

I don't think they are differrent in measure,
just how they are measured; always,
the diameter subtends the whole sphere
by three right dihedral angles

[Archimedes Plutonium]

Alright i may have found another proof the infinity borderline is 1*10^604 by applying the practical idea of interior regular polygon angles such as 120• for hexagon.

It is obvious that as you increase the number of sides the angle at vertex approaches 180• but can never be 180• for thence there would be no vertex and the polygon would fail to go around.

Coinciding with these facts is that a regular polygon inscribed inside a unit circle has a arclength value of the digits of pi 3.14159...

If we had a regular polygon of 1*10^604 sides then with three 0 digits in a row preceding the -604 exponent place-value we have the vertex point disappear and the 10^604 regular polygon a straight line and not a closed figure polygon. The three 0 digits in a row cause the angle to slip from 179.99999.. to be 180. At least i suspect such.

AP

[Archimedes Plutonium]

So why not two zeroes in a row in the digits of pi in the regular polygon proof?

Well, because the vertex of two sides has to be a 0 and the vertex itself a 0 as this shows


B
A C

as being

0
0 0

When pi digits have just two 0s in a row, the three vertices ABC are not made flat, but once all three are 0. It irons the vertices onto one straight line segment.

AP

[konyberg]

360-gon gives 179 degrees.

3600-gon gives 179.9 degrees.

Formula: (n - 2) * 180 / n = [interior angle]

KON

[Archimedes Plutonium]

Alright so let us graph the sequence-function

Y= 180 - (360/n) on the domain of Grid systems starting with 3.

In the College Calculus portion of the textbook we often graph functions such as sequence functions connecting present point to future point by a straightline segment forming a straightlinecurve then comparing that graph to a more "continuos function". Like recently, graphing the fibonacci sequence function starting at (2,1) then (3,2) then (4,3) and comparing to 10Ln

x 10Ln(x)
2 6.9
3 10.9
4 13.8
5 16
6 17.9
7 19.4
8 20.7
9 21.9

Fibonacci sequence function
x y
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34

If one flips over the 10Ln(x) function and tries a "curve fitting exercise" we see the two are closely matched.

In the College Calculus we move functions around alot and we try curve fitting alot, as if a function is a French Curve in artwork. Keeping in mind that a major goal of college calculus is to graph any function in the 4 quadrants of Cartesian coordinate system and then move the entire function up into the 1st Quadrant only.

AP

[Archimedes Plutonium]

So now this formula Y = 180 - (360/n) tells us that in a Grid System that infinity border is taken care of by three decimal place values. What i mean is in 10 Grid we can only have one 9s as in .9 before 1. In 100 Grid we have .99 in 1000 we have .999. The number 180 and 360 belong in the 1000 Grid.

The importance of this, is the fact that the digits of pi have three 0 digits in a row before the exponent 604 place value.

That means the distance traveled between 3 vertex points is a 0 distance because the arc in the circle is no longer a arc but instead is a flat straightline, meaning the regular polygon interior angle has turned from being 179.999.. Into being 180 degrees.

AP

[abu.ku...@gmail.com]

perfecto ... a.p just doesn't gAf

[konyberg]

You have compacted the formula I gave you. Good!

y(angle) = 180 - (360/n) and n > 2 (integers).

Now a lesson for you: Why does this work?

Area of the circle with radius r is A = pi*r^2 = ((2*pi*r)*r)/2.

Isn't this the formula used on a triangle?

A = g*h/2, where g = 2*pi *r (circumference) and h = r (radius)?

Could it be that a circle is actually a triangle? That is exiting!

Or since when n goes to infinity your y (and mine) goes to 180 degrees; a circle is a straight line?

KON

[lon...@wcps.k12.md.us]

If I rotate my body 370 degrees, I get dizzy. If I rotate 10 degrees I do not get dizzy. Therefore, they are different angles of rotation.