How do we know the value of PI ? - Page 2

[mrnutty]

If you believe Paint or any other circle drawing program isn't accurate then let me demonstrate in a 3d model using 3d blender. I have drawn a perfect circle using 12 cyphers and if you connect them it will make your circle. However, in real life they are bunched together like in the MS Paint model. This is because each atom is so tiny that each atom does not have enough sides to form the perfect circle. Basically in the 3d model because there are 32 sides for the cylinder that means it can attach on whatever angle. However if they can only attach on the sides or direct diagonal that is where the MS Paint model is by far more accurate. This is really going into atomic physics now. You will find that atoms cannot attach on any angle that we can write down (example 98.35869049696 degrees). However they can attach on a certain number of degrees. It is due to this limitation that pi will never be true. Why? Take a look at my diagram, all the circles are at different angles to each other. what if you had 4,000,000,000,000,000,000 points in that circle. In reality that is only a few cm's. Then you would have to have some atoms beside each other and above each other to be able to make the perfect circle. And remember that atoms need to all be attached. That forces another limitation. If they need to all be attached and they have very few sides then that will also force the atoms to go above and beside each other. Just keep that in mind.

Again : You cannot ever draw a perfect circle using a software
because they are all made up by pixels, and Pixels are rectangles.

Also realize that there might never be a perfect circle.

[William Hemsworth]

By the way, when did we introduce physics into this thread?
Even in physics, you can keep getting smaller and smaller.

It is because we are measuring so many atoms that pi appears to be so long. I have calculated that for about 1cm there would be just a little over 1,000,000,000,000,000 digits to pi.

How can I explain this, if you're calculating PI based from an atom count, how would you measure PI from a circle that's smaller than an atom? Circles have nothing to do with atoms.

[cwarn23]

Again : You cannot ever draw a perfect circle using a software
because they are all made up by pixels, and Pixels are rectangles.

Also realize that there might never be a perfect circle.

But if you print it out with a huge dpi (dots per inch) then it is a perfect circle. This is because the ink is 3d.

[GrimJack]

Well electrons are charges of electricity aren't they?

no electrons are not charges of electricity.

So wouldn't there be another substance which would make up everything around us.

ftw?

Now that I think about it, it would be electrons that make up 70% of the universe but not the other 30% we are talking about

How do you come up with this stuff? 70% by volume? by mass?

Although I have limited knowledge in this area I do know a few basic things.

we can see that you have a limited knowledge and do not even understand the basics

And an atom was an example. I could have just as easily said a particle. But you get the general idea.

An atom/particle/electron is an example of what?

Electrons are not charges of electricity; electrons can be viewed as a particle with a negative electrical charge and a spin of 1/2 the value of the Planck Constant ( h-bar, see forumla) which points right back to PI because PI in its irrational infinity is required to determine the Planck Constant.

[cwarn23]

How do you come up with this stuff? 70% by volume? by mass?

I remember seeing on a documentary about the race to see what makes up the missing proportion of the universe and turned out the missing 70% of our universe was energy. That makes the other 30% other elements such as solids, liquids etc. Although it goes into greater detail that is the basic concept and how it relates to this - well we were talking about that 30% of our universe and not the other 70% which is made of energy.

An atom/particle/electron is an example of what?

The one element that makes up the 30% of the universe. There is one element for all and what it is I don't know but I am guessing electrons.

[mrnutty]

But if you print it out with a huge dpi (dots per inch) then it is a perfect circle. This is because the ink is 3d.

No false, no matter how precise you get, its never a perfect circle.

[GrimJack]

I remember seeing on a documentary about the race to see what makes up the missing proportion of the universe and turned out the missing 70% of our universe was energy. That makes the other 30% other elements such as solids, liquids etc. Although it goes into greater detail that is the basic concept and how it relates to this - well we were talking about that 30% of our universe and not the other 70% which is made of energy.

The one element that makes up the 30% of the universe. There is one element for all and what it is I don't know but I am guessing electrons.

If 70% of the universe is energy then 70% of the universe cannot be a particle and 30% of the universe cannot be a particular particle. Even though matter and energy dance around the speed of light, it is not allowed to count particles as energy or energy as particles. Looking at those numbers, I am reminded of the search for 'dark matter' - we can account for 70% of the mass in the universe but 30% is 'missing' and called 'dark matter' for want of a better term.

Theories about dark matter abound - from "if you assume an infinitely small amount of mass to a neutrino, you could account for the missing mass" to "the missing matter is in a different dimension".

Current thought is that dark matter is composed of WIMPs (weakly interacting particles) - theoretical particles 100 times heavier than Protons. There are rumors about 2 different scientific teams having found a WIMP here on Earth but Nature denies that it has any paper in the works on WIMPs which means that there is no peer-reviewed finding and if it has not been peer-reviewed, it does not count.

[ddanbe]

But if you print it out with a huge dpi (dots per inch) then it is a perfect circle. This is because the ink is 3d.

Why are you always referring to a circle using matter or particles?
A circle is a mathematical object, like a line or hyperbola, whatever.
All the real numbers that follow the equation Y^2 + X^2 = R^2 (R being the radius) are belonging to the set we call a circle. There are an infinite number of those reals, just as there are an infinite number of reals on a straight line. You can never construct a circle with lego-blocks, atoms, pixels, printerink , grains of sand.....

[mrnutty]

There is no through getting to him. Just let him be.

[cwarn23]

Why are you always referring to a circle using matter or particles?
A circle is a mathematical object, like a line or hyperbola, whatever.
All the real numbers that follow the equation Y^2 + X^2 = R^2 (R being the radius) are belonging to the set we call a circle. There are an infinite number of those reals, just as there are an infinite number of reals on a straight line. You can never construct a circle with lego-blocks, atoms, pixels, printerink , grains of sand.....

I get what your saying but theoretically if we had the technology (which we don't) then we could construct a circle which would almost immediately be blown out of shape by gravity. That is theoretical. Also if electrons make an atom, what substance makes the electrons and what shape are they? Just curious...

Also as for why pi may not exist in my theory is that if the substance which makes all elements around us is a cube then that would mean the MS Paint model is very accurate. If however that substance is a cypher and it's self force pull comes from at least 18 directions then pi exists. But for now I shall assume that ultimately everything is made of cubes.

[lllllIllIlllI]

yep im with firstPerson, its a lost cause.

[ddanbe]

yep im with firstperson and with Paul Thompson, its a lost cause. :'(

[GrimJack]

I get what your saying but theoretically if we had the technology (which we don't) then we could construct a circle which would almost immediately be blown out of shape by gravity. That is theoretical. Also if electrons make an atom, what substance makes the electrons and what shape are they? Just curious...

The substance that makes up electrons? This is a bizarre question as electrons are 'fundamental' leptons which are a fundamental particle/wave (remember you can not think of electrons as just particles; they are also a wave function - and their behavior is both particle and wave and how you 'perceive' them is a function of your method of perception). A proton is a neutron minus an electron in an old-fashioned physics sort of way; in quantum theory a proton is composed of Up+Up+Down quarks and a neutron is Up+Down+Down quarks. In string theory, an electron is a closed-loop that vibrates/oscillates on different axes but you do not want to go there.

Also as for why pi may not exist in my theory is that if the substance which makes all elements around us is a cube then that would mean the MS Paint model is very accurate. If however that substance is a cypher and it's self force pull comes from at least 18 directions then pi exists. But for now I shall assume that ultimately everything is made of cubes.

Not sure how you are using 'cypher' here; not sure what you are referencing with the term 'self force' are you using it as a 'Lorenz gauge relaxation' or as a radiation reaction force.

You can not assume everything is made up of cubes. Nothing is made up of cubes - even the nucleus of He (2 protons + 2 neutrons) is not a cube. The way the weak forces work is they bring everything equidistant from the center. There are no sharp edges in the world of particles no matter if you consider them waves, strings, quarks or billiard balls - the universe is smooth and round.

Nothing in the universe supports the concept that MS Paint is the accurate model of anything. It does not even handle color very well.

[cwarn23]

You can not assume everything is made up of cubes. Nothing is made up of cubes - even the nucleus of He (2 protons + 2 neutrons) is not a cube. The way the weak forces work is they bring everything equidistant from the center. There are no sharp edges in the world of particles no matter if you consider them waves, strings, quarks or billiard balls - the universe is smooth and round.

If everything is not made of cubes then why are we in the 3rd dimension and not in something like the 256th dimension. Because theoretically all objects are limited to move along their axis. If however that is not how reality works then there is something terribly wrong with the theory of there being 3 dimensions. But other than that I am starting to get the science of how pi exists. Might write another pi calculator.

[lllllIllIlllI]

Sheesh, you dont quite get a major point. To PROVE something in mathematics, which has been done in the case of pi being irational, required rigor.

It requires that you prove it beyond any doubt at ALL. Look! There is even a wikipedia page on it http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational

Soo, perhaps read it (because you obviously havent read any of my other links) and understand it.

As well, every point in a sphere can be referenced with an X, Y and Z co-ordinate. Thats why we need 3 dimensions... Duh

[cwarn23]

As well, every point in a sphere can be referenced with an X, Y and Z co-ordinate. Thats why we need 3 dimensions... Duh

But for the object to move diagonally that would require moving along multiple axis making things ultimately move like cubes. This would also mean gravity and other forces would have a cube effect in their direction. So it would be impossible to just use 3 axis as 3 axis only allows the positioning of objects and not the diagonal movement of objects.

Also I read your link and is basically a bunch of formulas.

[lllllIllIlllI]

Also I read your link and is basically a bunch of formulas.

Thats what maths is.....

[mrnutty]

But for the object to move diagonally that would require moving along multiple axis making things ultimately move like cubes. This would also mean gravity and other forces would have a cube effect in their direction. So it would be impossible to just use 3 axis as 3 axis only allows the positioning of objects and not the diagonal movement of objects.

Also I read your link and is basically a bunch of formulas.

Wow. I tried so hard not to post.

Ok now listen to my argument :

Imagine you lye on a Cartesian grid, at the origin. OK ?

Now you say that to get at point, (1,1), we need to first move
1 unit in the x axis, then 1 in the Y axis. Correct ?
Thus the "cube effect" ? And that was your reasoning, correct?

Ok, now let me give you my rebuttal. So imagine you are again
located at point (0,0), in a Cartesian coordinate. And your
target is to get to point (1,1).

Now here is the question : Would, you first move right one, and then up one unit thus ending up at point, (1,1)
or would you simply take a diagonal step towards the point(1,1) ? Obviously, a sane person, would move diagonally. And the reason why one would take the diagonal step, is simple; because we can.

Now here is the more important part, Notice that you did not have to move one step right, and one step up, you simply just took a diagonal step to reach your target. Right ?

So realize that, Cartesian coordinate, polar coordinate, cylindrical coordinate, or any other coordinate one uses, is only a model. Its just a way to represents something. Its NOT REAL. So thus, your argument fails. Since you rely on something that is inductive.

[cwarn23]

Ok, now let me give you my rebuttal. So imagine you are again
located at point (0,0), in a Cartesian coordinate. And your
target is to get to point (1,1). Now here is the question :
Would, you first move right one, and then up one unit, or would you
simply take a diagonal step towards the point(1,1) ? Obviously, a sane person, would move diagonally. Now here is the more
important part, Notice that you did not have to move one step right,
and one step up, you simply just took a diagonal step to reach your
target. Right ?

From my understanding of what I have been taught you cannot move diagonally on the grid so say you were on point 0,0,0 (x y z) and wanted to get to point 1,1,1 (x y z) then you would need to first move up then move across x then move across y as the corners of where the lines meet on the grid are like barriers. And that is where the cube effect comes in which makes me wonder if there are by far more than 3 dimensions.

[GrimJack]

Go to your nearest sidewalk, note that it is one unit wide and on unit long, now tell me you can't walk from one corner to another.

The 'grid' is an artifact of Cartesian math, it is not real. Have you ever plotted a line on a grid? Did your teacher make you stay on the lines? Did your teacher ever say anything about having to stay on the lines? How are the lines like barriers?

Are you familiar with Euclid and/or Euclidean space? Do you know non-Euclidean geometry?

Here is one of the good things that has come out of this discussion:
Wolfram Math World and an example of what may be a Hilbert Space and to stay on topic (so to speak), here are some fun PI demonstrations

[ddanbe]

@cwarn23
Consider yourself as 2-dimensional.(Forget your cube thing)
You live in a 2-dimensional world, together with other 2-dimensional people. So the only things you know are length and width. Now if you are all enclosed in a circle, nobody can escape. Remember you are 2-dimensional! Now there is some smart guy who knows 3 dimensions, he has the concept of height!!! So he can just dissapear before your eyes and even move outside the circle!
Now consider again. You are 3-dimensional and you are together with a smart guy inside a giant football. You cannot move outside the fooball, right? Well the smart guy knows what the fourth dimension is and just dissapears right before your eyes :-O
Through a hole in the football you can see him again walking outside of it. You cannot leave the ball, you only have 3 dimensions:'(

[mrnutty]

From my understanding of what I have been taught you cannot move diagonally on the grid so say you were on point 0,0,0 (x y z) and wanted to get to point 1,1,1 (x y z) then you would need to first move up then move across x then move across y as the corners of where the lines meet on the grid are like barriers. And that is where the cube effect comes in which makes me wonder if there are by far more than 3 dimensions.

You just disregarded my main point :
"So realize that, Cartesian coordinate, polar coordinate, cylindrical coordinate, or any other coordinate one uses, is only a model. Its just a way to represents something. Its NOT REAL "

[lllllIllIlllI]

Proof of ignorance

in user Cwarn23 we can see:
    he doesn't read links (given)
    he doesn't know proper higher maths (obvious)
    he ignores all valid points (drawn from answers)
Therefore Cwarn23 is obviously missing the point and not worth our time.

There we go, a pseudo mathematical proof with reasoning. And i think we can all listen to it. I certainly shall.

[cwarn23]

Proof of ignorance

in user Cwarn23 we can see:
    he doesn't read links (given)
    he doesn't know proper higher maths (obvious)
    he ignores all valid points (drawn from answers)
Therefore Cwarn23 is obviously missing the point and not worth our time.

There we go, a pseudo mathematical proof with reasoning. And i think we can all listen to it. I certainly shall.

I wouldn't say that I'm ignorant but instead open minded. Exploring concepts that haven't been explored before and seeing if they can be true. When I'm worth a million dollars that will be a 1 million dollar quote. And I believe I could easily invent to AI algorithms for robotics when their tools are easily accessible.

@cwarn23
Consider yourself as 2-dimensional.(Forget your cube thing)
You live in a 2-dimensional world, together with other 2-dimensional people. So the only things you know are length and width. Now if you are all enclosed in a circle, nobody can escape. Remember you are 2-dimensional! Now there is some smart guy who knows 3 dimensions, he has the concept of height!!! So he can just dissapear before your eyes and even move outside the circle!
Now consider again. You are 3-dimensional and you are together with a smart guy inside a giant football. You cannot move outside the fooball, right? Well the smart guy knows what the fourth dimension is and just dissapears right before your eyes :-O
Through a hole in the football you can see him again walking outside of it. You cannot leave the ball, you only have 3 dimensions:'(

I don't know how to reply to that...

You just disregarded my main point :
"So realize that, Cartesian coordinate, polar coordinate, cylindrical coordinate, or any other coordinate one uses, is only a model. Its just a way to represents something. Its NOT REAL "

Yes it is a hard to understand concept I have made but although coordinates are represented by xyz there would have to be a number of other dimensions for something like a magnet to have a rounded magnetic pull. Why do I believe there are infinite or lots of axis's in our current dimension? Because my belief is that everything is made of a tiny cyphers including the strings in the string theory combining in different ways to make different substances on the periodic table. Weather that is true is to be proven but with that theory pi still exists as this topic is about.

I don't mean to offend anybody by saying something like newton is wrong but it just makes more sense as to how the universe works.

[ddanbe]

I don't know how to reply to that...

If you can't you are not able to think in a mathematical way as Paul Thompson already proved...

[William Hemsworth]

I wouldn't say that I'm ignorant but instead open minded.

I would say the exact opposite, being open minded means you accept certain facts and build on them, ignoring facts and making quick conclusions is stubborn.

[cwarn23]

I would say the exact opposite, being open minded means you accept certain facts and build on them, ignoring facts and making quick conclusions is stubborn.

I think the main problem here is that there are theories that contradict. Some of your theories contradict my theories and as I see evidence I choose which is best. However the main theory which is making this thread a mess is that everything on the periodic table is made of one substance with different densities. That is what I have and probably always will believe in as it explains everything such as light, liquids, solids etc and their origin. Unless there is a better theory that is what I have chosen for now... So as you can see I will accept new facts as long as they make a good case.

[ddanbe]

everything on the periodic table is made of one substance with different densities

one substance? different density? Ho boy... Ho boy...
It is no theory, it is a scientific FACT that any kind of material,(metal, wood, oil etc.) exposes one and only one density. It is defined as such! The mass of an amount of substance divided by its volume.
Unless of course you think the result of this division is made up of cubes you have to draw in MSPaint...

[VernonDozier]

I think the main problem here is that there are theories that contradict. Some of your theories contradict my theories and as I see evidence I choose which is best. However the main theory which is making this thread a mess is that everything on the periodic table is made of one substance with different densities. That is what I have and probably always will believe in as it explains everything such as light, liquids, solids etc and their origin. Unless there is a better theory that is what I have chosen for now... So as you can see I will accept new facts as long as they make a good case.

These aren't "our" theories. These are the "theories" of every mathematician since I don't know when. The people who proved that pi is irrational are long dead. Every mathematician currently living has accepted their proofs, so it's really doubtful that any "new" facts will ever come up, so if you're not convinced by what's out there now, I can't imagine there will ever be anything new that will convince you.

I don't think there's really much debate. I don't think there's a math textbook out there that says that PI doesn't exist, is rational, or is finite. I've also never seen any of the arguments you've mentioned come up in any math textbook.

Basically I think that if six billion or so people believe one theory and only you believe your theory, unless your name is Albert Einstein, chances are that you're wrong, not everyone else.

[GrimJack]

cwarn - you do not have theories, you do not even have hypotheses, you only have random 'thingies' that you try to string together. You do not even seem to understand the meaning of the few facts you repeat to support your 'thingies'.

Theory

Mathematics. a body of principles, theorems, or the like, belonging to one subject: number theory.

Hypothesis

A hypothesis is a tentative statement that proposes a possible explanation to some phenomenon or event. A useful hypothesis is a testable statement which may include a prediction.