Naked Science Forum

On the Lighter Side => New Theories => Topic started by: aetzbar on 11/09/2017 20:58:53

Title: The second mistake of the mathematicians, after pi
Post by: aetzbar on 11/09/2017 20:58:53
https://proofwiki.org/wiki/Limit_of_Sine_of_X_over_X
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 12/09/2017 06:24:40
The second mistake of Math

Sin X is always represented with a straight line segment
X is always represented with a section of a round line
Wiki asks about the ratio  X\sinX  when the length of the round segment  X  is close to zero

This question has two possible answers, 1 and 1.007

If X is a tiny segment of a huge circle the answer is 1
If X is a tiny segment of a very tiny circle, the answer is 1.007

Wiki does not offer the answer of 1.007, for lack of knowledge of the changing pi
Pi of a very tiny circle = 3.164, and pi  of a huge circle 3.1416

3.164 \ 3.1416 = 1.007
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 12/09/2017 06:36:09
If you are not convinced that there are two answers, look at the next picture
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 12/09/2017 06:55:50
The three errors of mathematics
The three errors appear in the geometric field.

1: Mathematics thinks that the basic geometric concept is the point.
So she made up the wrong account, which creates a line from infinity points.

2: Mathematics thinks that pi is a fixed number, which will appear in all circles, tiny and huge.

3: Mathematics offers only a single answer to the ratio x\sinx

The answer of 1.007 does not exist in mathematics
Title: Re: The second mistake of the mathematicians, after pi
Post by: evan_au on 12/09/2017 13:30:59
Quote from: aetzbar
The second mistake of Math...
Sin X is always represented with a straight line segment
No, it isn't. Have a look at the page you quoted (https://proofwiki.org/wiki/Limit_of_Sine_of_X_over_X#Proof_1).

If you expand this equation for sin(x), with x in radians, you get:
sin(x) = x - x3/1.2.3 + x5/1.2.3.4.5 - x7/1.2.3.4.5.6.7 + x9/1.2.3.4.5.6.7.8.9 - ...

If mathematicians always did a straight-line approximation to sin(x), they would have said: "sin(x) = x", which is dramatically different (and much shorter) than what they do say.

So let's see what happens if we calculate sin(x)/x as x gets closer to 0:
x          sin(x)                   sin(x)/x
1          0.8415...                0.8415...
0.1        0.09983...               0.9983...
0.01       0.0099998...             0.99998...
0.001      0.0009999998...          0.9999998...
0.0001     0.0000999999998...       0.999999998...


What we find is that as x gets closer and closer to 0, sin(x)/x gets closer and closer to 1.00000.

When you enter sin(0.0000000001)/0.0000000001, you calculator suffers severe rounding errors, and could indeed report the value to be 1.007.
- You could use something like EXCEL, which internally calculates to about 15 digits
- Or (even better), use an arbitrary precision calculator, like: https://apfloat.appspot.com/

When you enter 0/0, your calculator says ERROR.
- In reality, this question needs more information to give an exact, unique answer.
- L'Hopital's rule gives you the additional information you need to calculate this answer exactly.
- You differentiate x (→1)
- You differentiate sin(x) → cos(x), which has the value 1 when x=0
- So the exact answer for sin(x)/x when x=0 is given by cos(x)/1 = 1/1 = 1

It is definitely not 1.007.

PS: If you make the mistake of using a calculator in "Degrees" mode instead of "Radians", you will end up with sin(x)/x = 0.0174... for x→0, but that is just because mathematicians use the more "natural" units of Radians for angles, rather than the Babylonian concept of 360 degrees in a circle.
Title: Re: The second mistake of the mathematicians, after pi
Post by: phyti on 12/09/2017 16:25:57
The second mistake of Math

Sin X is always represented with a straight line segment
X is always represented with a section of a round line
Wiki asks about the ratio  X\sinX  when the length of the round segment  X  is close to zero

This question has two possible answers, 1 and 1.007

If X is a tiny segment of a huge circle the answer is 1
If X is a tiny segment of a very tiny circle, the answer is 1.007

Wiki does not offer the answer of 1.007, for lack of knowledge of the changing pi
Pi of a very tiny circle = 3.164, and pi  of a huge circle 3.1416

3.164 \ 3.1416 = 1.007

If you scale a circle up or down, (zoom in or out), the ratios of  components does not change. These are topologically invariant attributes.
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 12/09/2017 20:12:16
'll try to explain the idea.
We are dealing with a tiny arc of a circle, and in a string of arc.
If the circle is huge, the arc / string ratio will approach 1 (the line of the arc is almost straight)
If the circle is tiny, the arc / string ratio will be close to 1.007 (the line of the arc is very crooked)
There is no mathematical calculation for the problem of the arc and the string.
This problem is resolved after the discovery of pi variation between 3.1416 and 3.164
  Mathematics can not handle circles, nor is it capable of the problem of the arc and string.
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 12/09/2017 20:48:08
'll try to explain the idea.
We are dealing with a tiny arc of a circle, and in a string of arc.
If the circle is huge, the arc / string ratio will approach 1 (the line of the arc is almost straight)
If the circle is tiny, the arc / string ratio will be close to 1.007 (the line of the arc is very crooked)
There is no mathematical calculation for the problem of the arc and the string.
This problem is resolved after the discovery of pi variation between 3.1416 and 3.164
  Mathematics can not handle circles, nor is it capable of the problem of the arc and string.
You keep saying this.
But you offer no evidence.
Get back to us when you have some reasons why we should believe you.
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 12/09/2017 23:30:35
We discuss the simplest issue of lines
There are straight open lines, and there are closed round lines.

A 32 mm straight line is similar to a straight line of 800 mm
A 32 mm round closed line, is not similar to a closed 800 mm round line

Closed round line 32 mm long, is bent a lot
Closed round line 800 mm long, is slightly bent.

The mathematical expression  - of the level of bending  - is a ratio number

The ratio number  of 32 mm is, for example, 3.1416001
The ratio number of 800 mm is for example 3.1416194

That's the whole story
Title: Re: The second mistake of the mathematicians, after pi
Post by: evan_au on 13/09/2017 04:05:40
Quote
2: Mathematics thinks that pi is a fixed number, which will appear in all circles, tiny and huge.
As mentioned above, mathematicians use radians to measure angles.

Radians have the nice property that, in Euclidean geometry, s = rθ
where:
- θ (Greek theta) is an angle, measured at the center of a circle
- s is the length of the circle's segment,subtended by angle θ
- r is the radius of the circle

There are 2π radians in a complete circle, so in this case, circumference s = 2πr
So it doesn't matter if the radius r is 1 mm or 1 light-year, the circumference is always 2π times larger than the radius
- and π times larger than the diameter, regardless of what the diameter is
See: https://en.wikipedia.org/wiki/Radian#Definition

Quote
3: Mathematics offers only a single answer to the ratio x\sinx
The function sin(x)/x is widely used in communications systems - at least as a simplified example.

But the value at x=0 is the same: 1.

Quote
Sin X is always represented with a straight line segment
A polynomial of degree 2 can have up to 2 zero-crossings, and 1 change in direction.
- A polynomial of degree n can have up to n zero-crossings*, and (n-1) changes in direction.
- sin(x) has an infinite number of zero crossings (and an infinite number of changes in direction), so it is a polynomial of infinite degree
- So mathematicians will not confuse sin(x) with a polynomial of degree 1 (a straight line)
 
*Actually, a polynomial of degree n does have n zero-crossings (roots), but sometimes they are hidden in non-obvious locations, like "multiple roots", "imaginary roots" and "roots at infinity".

Quote
every revolutionary idea sounds strange at first
Euclid had 5 postulates on which his geometry was based.
The 5th postulate was that you can only draw 1 line through a point so it is parallel to another line (assuming that the other line doesn't already go through the point).

For over 2,000 years, mathematicians tried to justify this postulate. They found that it impacted other assumptions like:
- The sum of the angles inside a triangle is always 180 degrees (or π radians, if you are a mathematician)
- π = 3.14159....

Around the 1900s, some mathematicians created alternative geometries that had multiple different lines passing through the point, but never intersecting the given line (or indeed, mind-bending geometries where there are no such lines possible).
- These geometries have different values of π - and even values for π which change with the size of the circle.

This did revolutionise mathematics and physics, but it took a few decades. Today, we call these "non-Euclidean geometries". Unfortunately, they are not usually taught in high school.
See: https://en.wikipedia.org/wiki/Parallel_postulate
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 13/09/2017 05:19:11
You quote acceptable knowledge, and I present unacceptable knowledge.
The main message: Mathematics can not calculate the length of a round line.
Look and see: Mathematics always replaces a round line, in many tiny segments of a straight line.
The result: the mathematics could not detect the marvelous geometry of the round lines.
The conclusion: There is a geometry of straight line segments, and Pythagorean theorem belongs to it, and there is a geometry of round lines that science can not yet handle.
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 13/09/2017 17:47:25
We discuss the simplest issue of lines
There are straight open lines, and there are closed round lines.

A 32 mm straight line is similar to a straight line of 800 mm
A 32 mm round closed line, is not similar to a closed 800 mm round line

Closed round line 32 mm long, is bent a lot
Closed round line 800 mm long, is slightly bent.

The mathematical expression  - of the level of bending  - is a ratio number

The ratio number  of 32 mm is, for example, 3.1416001
The ratio number of 800 mm is for example 3.1416194

That's the whole story

You keep saying this.
you keep failing to provide evidence

Why don't you provide some actual evidence, or accept that you are wrong.?
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 13/09/2017 20:13:03
I expect a scientific institution to decide to test my idea and conduct the experiment described here.
This is the only way to change the misconception of 2000 years.
Until then ... there is no point in talking much.
The last word in science, provides the actual experiment.
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 13/09/2017 20:31:32
I expect a scientific institution to decide to test my idea and conduct the experiment described here.
This is the only way to change the misconception of 2000 years.
Until then ... there is no point in talking much.
The last word in science, provides the actual experiment.

Why would anyone investigate your hallucination?
It would cost money and we have no reason to think  it would tell them anything they didn't know.
Also, once again, you are ignoring the fact that the experiment has been done.
It showed that pi was constant.
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 13/09/2017 21:54:05
A fixed number for a pi is boring.
Variable number to pi, it is dramatic and intriguing.
Therefore, I have no doubt that a scientific institution will conduct the experiment, and will merit fame.
I suggest you wait patiently, the historical experiment will come.
I have a lot of patience.
Title: Re: The second mistake of the mathematicians, after pi
Post by: phyti on 14/09/2017 18:22:13
We are dealing with a tiny arc of a circle, and in a string of arc.
If the circle is huge, the arc / string ratio will approach 1 (the line of the arc is almost straight)

as the degrees decrease! 
It never equals 1, that's the property of limits in this case.
You missed the point.
Making geometric forms larger or smaller does not change the ratio of its' components.

An arc has curvature and no straightness. The radius has straightness and no curvature. They are incommensurate.

Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 14/09/2017 18:55:00
A small square is perfectly similar to a large square.
Lines of squares will overlap perfectly with each other
A small circle is not exactly like a large circle.
Lines of circles will never overlap.
Hence the idea of changing pi
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 14/09/2017 21:02:56
Variable number to pi, it is dramatic and intriguing.
And wrong.
I suggest you wait patiently, the historical experiment will come.
The experiment has been done (no matter how often you ignore it)
Pi was still pi.
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 14/09/2017 21:13:27
A small square is perfectly similar to a large square.
That's a good start.
Now draw a a circle in the square so that it just touches all 4 sides.
The circle has a diameter that is the same as the length of the side of the square
Then start to fill the gaps between the circle and the square with smaller squares.
Using smaller and smaller squares you can fill the whole of the gap as closely as you like.
Here's a very rough sketch. [ Invalid Attachment ]


Then do the same, but starting with a bigger square.

You can find the circumference of the circle by adding up the sides of the squares next to it.
The two sets of squares and circles are the same.
So pi is the same.

Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 14/09/2017 21:33:36
do you know that there is no mathematical formula for lines?
Mathematics can not describe a line.
So how would she manage to calculate its length?
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 14/09/2017 21:48:36
do you know that there is no mathematical formula for lines?
Did you know you are talking nonsense?
y=mx+c
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 14/09/2017 22:45:08
The formula you describe describes the position of points in the plane.
Can you view a formula that describes a line?
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 16/09/2017 00:49:23
The formula you describe describes the position of points in the plane.
Can you view a formula that describes a line?
Not that it's important to the OP;
What's the difference?
Title: Re: The second mistake of the mathematicians, after pi
Post by: phyti on 16/09/2017 17:56:52

If pi was incorrect, engineers who develop jet engines for example, would have discovered it decades ago with catastrophic engine failures.
Title: Re: The second mistake of the mathematicians, after pi
Post by: aetzbar on 16/09/2017 18:30:38
The idea of pi changes, has no effect on technology practice.
The effect is on the mathematicians' perception of reality.
They determined and even proved a wrong idea, which they teach for hundreds of years.
Mathematicians delayed the development of geometry.
This geometry produces a new fixed number (1.007) that will also appear in the physical field
Title: Re: The second mistake of the mathematicians, after pi
Post by: Bored chemist on 16/09/2017 22:02:46
The idea of pi changes, has no effect on technology practice.
The effect is on the mathematicians' perception of reality.
They determined and even proved a wrong idea, which they teach for hundreds of years.
Mathematicians delayed the development of geometry.
This geometry produces a new fixed number (1.007) that will also appear in the physical field

That's plainly nonsense.
Why do you keep saying it?