Pi solved

[connector]

Pi, solved..

 

The reason pi is infinite is because people forgot what pi is actually describing - a lie.

from 2d to circles to 3d spheres, nothing has a perfectly smooth or round surface.

 

Just like in computer model space, a true circle or sphere cannot possibly be created, it's simply more and more sides to a polygon that only appears to be a circle or sphere.

imagine if you were on a computer, drew a circle, then zoomed into that circle so much that you could see the single pixels, it would always be a collection of straight lines.

 

If you take a measurement of something such as a round lid in the real world, no matter what measurement device you used such as a high precision laser, the laser moved in tiny straight lines around the circular object making a polygon path, then you try and do an equation that has to do with a perfectly round surface (which doesn't exist), and of course you're going to get a nonsensical answer.

 

Pi has always been and always will be a rough estimate tool to make the complex real world appear more simple and more usable for practical purposes such as engineering, not something representing reality.

 

A bit more in depth, since gravity is the fabric of the universe so to speak, nothing is in the simple nice shapes we use to make practical things anyway, it's much more convoluted than the nice equations mathematicians love - same case with cause and effect, people will talk about the uncertainty principle as proof of free will instead of the obvious factor of unaccounted for variables, such as dynamic air flow, gravity changes, charges in space, etc, making the path of least resistance or most attraction for electrons appear random but actually just being beyond the measurement and comprehension of our current technology. *rolls eyes*

 

So, in summary, simply take a reference point such as the atoms that make up a seemingly circular object, such as a lid. imagine you can zoom in and then draw a lines connecting all the atoms on the outside edge of the lid (using nucleus in the connect-the-dots game for simplicity), what are you left with? a polygon, not a circle, even if you zoom out and it looks like a circle because your eyes cannot see the full detail, does not mean that it's a circle. Outside of our imagination, a circle doesn't exist. Therefore, there cannot be a finite number to describe an infinitely impossible concept - the circle, nor a finite number to describe an abstract of this impossible concept, such as the circumference of a measureless concept - a circle, divided by the diameter of an again, measureless, nonreal, shape. Pi is infinite, without any true pattern ever emerging. You're welcome.

Edited February 24, 2012 by connector

[the tree]

The reason pi is infinite is because people forgot what pi is actually describing

The period of e^ix? A consequence of the axioms of euclidean geometry?

a lie.

Hmm?

from 2d to circles to 3d spheres, nothing has a perfectly smooth or round surface.

So?

If you take a measurement of something such as a round lid....

Then you wouldn't be doing mathematics would you?

You're welcome.

Prey tell, for what?

 

Seriously. Most real numbers have an infinite decimal expansion. It's not a big deal and you don't need to make up ridiculous explanations for it.

[connector]

The tree, by realizing that using a formula for a shape with infinite polygonal sides you will get an infinite 'estimate', we can learn valuable things such as:

Pi will go on forever

Pi will never have a pattern

True circles are an impossibility, why would we expect them to work out on paper?

 

that is what is useful

the original post:

 

"When we try to write Pi in decimal notation, we get an endless stream of digits. 3.141592653589723.....and so on forever.This seems counter-intuitive. You'd think that a simple thing, like the ratio between the radius and circumference of a circle, ought to be a simple, precise number. After all, isn't the Universe made almost entirely of circular and round things."

 

my post answers this perfectly, sorry if it was 'ridiculous' and 'self evident' to you at the sane time, as most truths are when no one has mentioned them until someone else does and it was exactly what the original poster was missing. *rolls eyes*

Edited February 24, 2012 by connector

[the tree]

The tree, by realizing that using a formula for a shape with infinite polygonal sides you will get an infinite 'estimate', we can learn valuable things such as:

Pi will go on forever

Pi will never have a pattern

How do these follow?

For that matter it'd be trivial to contrive a smooth curve with an integer length, even though it's length actually would be regarded as the sum of infinite straight lines.

True circles are an impossibility, why would we expect them to work out on paper?

We don't expect them to: they do.

[connector]

How do these follow?

For that matter it'd be trivial to contrive a smooth curve with an integer length, even though it's length actually would be regarded as the sum of infinite straight lines.

We don't expect them to: they do.

 

Now we have reached the point where it's I say they don't, you say they do, and it's up for everyone else to make up their minds on this matter too. There is apparent proof that you can't have an infinite polygon shape, so there is no such thing as a circle, therefore you can't work out a circle on paper - it doesn't exist. If you try and measure the circumference of what you call a circle, you aren't, you're measuring a bunch of tiny straight lines making up a polygon - not a circle. It would be a circle if it was perfectly round, but it's not, it's got straight lines making up the shape.

 

Since you are in denial of this fact, it will have to be left up to everyone else rather to take the definition of a circle to mean a polygon which it isn't or not. Really what you are doing is lying to yourself, trying to take a more sophisticated straight-lined polygon and call it a round shape, and do some math with it. Unfortunately you assumed that such a shape is possible when it isn't, therefore your math is just an estimate and inaccurate. Incredibly useful math because it's a shortcut, but still an impossible shape which explains why pi goes on for infinity and why making a circle is impossible unless you make-believe that many-sided polygons are circles. Have fun in your own imaginary world.

 

Keep in mind that a hexagon will appear as a circle to someone with very blured vision/bad eyes, or a giant human 30x bigger than us. does that make a hexagon a circle just because their eyes see it that way? no. and neither is the case for us.

Edited February 24, 2012 by connector

[the tree]

• Okay we all know that you can't draw a perfect circle in the physical realm, no-one is contending that.
  
• But we're talking about pi as a mathematical object, not a physical one.
  
• A mathematical object that has plenty definitions that don't mention a single geometric concept, let alone circles.
  
• If you're trying calculate pi then you're doing a calculation which is different than a measurement in that it's not the same thing
  
• The proof that pi is irrational is actually a little bit complicated
  
• It's not just "rah rah smooth surfaces approximate unsmooth ones"
  
• That's not what a proof is
  
• Or an argument
  
• Or really anything that has any place in mathematics
  

 

As an aside, the square root of two is also irrational and can fairly easily be depicted with a finite amount of straight lines, how does that contend?

Edited February 24, 2012 by the tree

[connector]

• Okay we all know that you can't draw a perfect circle in the physical realm, no-one is contending that.
• But we're talking about pi as a mathematical object, not a physical one.

When you talk about a circle as a mathematical object, you're talking about a continually generating sides type polygon which is getting more and more sides to appear more and more round the more you try to analyze it, but it NEVER reaches true perfect roundness, which is why even a mathematical circle is impossible. The best you can do is get an 'even bigger number of sides for a seemingly round polygon' than the last guy. This is still not a circle, you can't draw a circle in the nonphysical realm either, you can only pretend to for the sake of simplicity.

 

If you try and base a system of numbers on something that doesn't yet exist, the numbers will go on forever trying to find an end point in vain - they will create more and more straight lined sides on the polygon in the eternal search for complete perfect roundness but never achieve it, which is why it's absolutely not possible to talk about a circular mathematical object until it attains circularity, which it doesn't, ever. It doesn't exist as a mathematical object, it exists because you and other people using math pretend it does, for the sake of simplicity.

 

If you're trying calculate pi then you're doing a calculation which is different than a measurement in that it's not the same thing

 

In order to do a calculation, something has to have measurements and dimensions. If you have a measureless, dimensionless object, you can't do any calculations on it. That's why when you calculate many sided polygons you pretend it has the shape of a circle and pretend you know the exact circumference or diameter or the ratio thereof when you don't, you made an approximation based on a polygon and not a true circle because true circles don't exist.

 

• The proof that pi is irrational is actually a little bit complicated
• It's not just "rah rah smooth surfaces approximate unsmooth ones"

 

And I just made it simple for everyone, which is far more elegant by using universal principles rather than a complicated system of equations. The only problem here seems to be your inability to comprehend it. It's obvious to me that you don't have the open mindedness to accept anything except your orthodox views and behavior towards reality and mathematics, so what is the point in talking to someone who can't learn? You seem to believe everything you read instead of putting it to the test like you should (as in the case of sqrt of 2 below).

 

For example, what do you mean the square root of 2? I've never ever found a number that can multiply by itself to equal 2, have you? Please share. As far as I know there is no square root of 2, only something really really close. Really close is an approximation just like pi.

 

Many people get confused about things like sqrt of 2 and pi because they believe they are based on real measurements, when really they are approximations to help people understand complex objects, nothing more.

Using logic, we can discern valuable things from this realization for like the 3rd time now:

Computations based on imaginary measurements or shapes will never give non-imaginary computations which end, they go on forever.

This helps everyone learning about mathematics which has trouble understanding the origin of why pi and sqrt of 2 go on forever, by explaining why this happens.

It also gives broad understanding of these functions by realizing they are tools of approximation by simplicity, and not based on reality.

It helps people to understand that circles in math are trying to be generators of more and more complex round shape polygons, but in reality are polygons as true circles are impossible.

It helps physicists understand that our universe is connected in a linear fashion as forces are strongest in the shortest possible distance - always making straight lines at the fundamental level.

 

There are two things that advance our understanding as a species, one is the discovery of new scientific principles and the other is the abolishment of incorrect ones.

We all learned that electrons orbit the nucleus in a circular fashion or elliptical fashion or that Earth does the same, but really these are not round or smooth paths, but very very close to round/smooth paths with many straight lined movements, revealing a fabric to the universe which is likened to computer model space (if you've ever worked with computer graphics), even though it's far too detailed for our primitive eyes or even technology to see.

Edited February 25, 2012 by connector

[the tree]

For example, what do you mean the square root of 2? I've never ever found a number that can multiply by itself to equal 2, have you? Please share. As far as I know there is no square root of 2, only something really really close. Really close is an approximation just like pi.

Are you seriously suggesting that just because a number doesn't have a finite decimal expansion, that means it doesn't exist?

[connector]

Are you seriously suggesting that just because a number doesn't have a finite decimal expansion, that means it doesn't exist?

 

I'm saying the square root of 2 doesn't exist, yes, only something really close to the square root of 2 exists. Can you prove that it does exist, rather than just parroting whatever you've read or learned? I mean, seriously, if it's so appalling to you that something doesn't exist just because you've thought it does for most of your life or have had everyone assume that it does right beside you, then there is something really wrong with your capacity to discern truth.

 

If you grew up in a world of snake worshippers does that mean that a snake created the universe? Are you just going to take their word for it that the square root of 2 exists or are you going to tell me the number that equals 2 when multiplied by itself instead of 1.9999999999999 and so on?

 

It's nice for primitive humans to use sqrt of 2 in figuring things out rather than 1.999999999, but that doesn't mean that its based on reality, just like pi, its an approximation, and when trying to figure out why it doesn't work out to a nice finite number, we can gain understanding by realizing its just an approximation and very close to being true, but isn't actually true. That's what the original poster had trouble understanding (why some things like pi go on forever), and that is what I explained, how much simpler can I say it.

Edited February 25, 2012 by connector

[the tree]

Nah that's fine I'll take it.

 

I guess we can throw out the numbers 5, 17, 130.2 and 9, while we're at it.

[connector]

Nah that's fine I'll take it.

 

I guess we can throw out the numbers 5, 17, 130.2 and 9, while we're at it.

 

I'm new here but from what I can see you have absolutely no sense.

If we draw a polygon such as a octogon in computer space and calculate the area not using pi, but by breaking it up into triangles, we can get a finite and accurate answer without having to estimate using pi. This is actually what all circles are - polygons, and therefore they could all theoretically be figured out by this method instead of estimating using pi. Pi is fictional, the triangle method is not.

http://www.math-prof.com/Geom/Geom_Ch_27.asp

 

therefore there is no reason in the future to work with imaginary circles or pi, it will be outdated when we can compute better with computers as it's an estimate and inaccurate.

 

Please tell me you can comprehend this. There is absolutely no correlation to throwing out 5, 17, etc with throwing out primitive approximation tools like pi.

[MathIsCool]

connector, please don't even try to deny that [math]\sqrt{2}[/math] is a real number. Do you know how the reals are constructed/defined?

 

By the way, if it makes you happy:

 

[math]\pi=\int_{0}^{1} {\frac{4}{x^2 +1} dx}[/math]. Take that as a "definition" and explain where your problem is.

[the tree]

I'd sort of given up the non geometric view of pi, since connector seemed so obsessed with the idea that circles were a requirement in some way.

 

Also he's saying that sqrt(2) doesn't exist.

 

What the hell.

[MathIsCool]

I'm wondering whether he actually knows what [math]\mathbb{R}[/math] is... no offence by any means.

[John Cuthber]

I'm saying the square root of 2 doesn't exist, yes, only something really close to the square root of 2 exists. Can you prove that it does exist, rather than just parroting whatever you've read or learned?

 

Yes.

It's the length of the diagonal of a square with unit sides. It clearly exists, even if we can't draw with perfect accuracy.

[connector]

It clearly doesn't exist. The length of the diagonal of a square with unit sides is the number closest to the theoretical sqrt of 2, but the sqrt of 2 doesn't exist. Mathematicians pretend it does because it's useful to do so and is close enough for all real world applications.

 

The bottom line here is that often people have trouble understanding why there are these irrational numbers involved in math because it doesn't make sense to the newbie, and there is an intuitive explanation for all of it as I just explained, pi, sqrt of 2, and other irrational number aspects of math are approximation tools because we can't measure or compute exact reality (yet), and therefore all of these numbers and formulas involving them have a slight margin of error, not because the universe necessarily is mathematically erroneous, but because we started our calculations with a small margin of error in the first place (because it's the best we can currently do, as John Cuthber implied).

[MathIsCool]

It clearly doesn't exist. The length of the diagonal of a square with unit sides is the number closest to the theoretical sqrt of 2, but the sqrt of 2 doesn't exist. Mathematicians pretend it does because it's useful to do so and is close enough for all real world applications.

It does exist, and it's exactly the length of the diagonal in the unit interval. By the way, in [math]\mathbb{R}[/math], there is never such a thing as a "closest number". You obviously don't know what you're talking about.

 

The bottom line here is that often people have trouble understanding why there are these irrational numbers involved in math because it doesn't make sense to the newbie, and there is an intuitive explanation for all of it as I just explained, pi, sqrt of 2, and other irrational number aspects of math are approximation tools because we can't measure or compute exact reality (yet), and therefore all of these numbers and formulas involving them have a slight margin of error, not because the universe necessarily is mathematically erroneous, but because we started our calculations with a small margin of error in the first place (because it's the best we can currently do, as John Cuthber implied).

 

Often people have trouble understanding that they are wrong. The "intuitive" explanation you give is wrong, as has been pointed out.

 

Also, irrational numbers exist, they aren't approximation tools. Please study the definition of [math]\mathbb{R}[/math]. You have yet to reply to my question above, what's wrong with [math]\pi := \int_{0}^{1} \frac{4}{x^2+1} dx[/math]?

 

Now please don't reply with yet another pointless post but try to address the points I made.

[connector]

You're not going to succeed in distracting anyone from the original error you made by asking me to do this and that

Once you tell me what number multiplied by itself gives 2, then it will exist, but you can't do this.

You can only get really close.

I'll address all of your nonsense as soon as you fix the error you made.

Saying that sqrt of 2 is the length of something is false, because that length multiplied by itself doesn't give 2, does it?

 

Please stop being retarded.

 

Just for everyone elses understanding, mathematicians accept that sqrt of 2 exists by broadening their definitions to include that one exception to a rule, but mathematicians broadening their own personal definitions even if they all agree with eachothers doesn't change the definition and substance of something in hard fact.

Edited February 27, 2012 by connector

[MathIsCool]

You're not going to succeed in distracting anyone from the original error you made by asking me to do this and that

Like I made an error.

 

Once you tell me what number multiplied by itself gives 2, then it will exist, but you can't do this.

You can only get really close.

 

This is so funny. The number you're seeking is [math]a=\sqrt{2}[/math]. I'm not going to bother explaining this to you because this place is for mathematics, not

for people who don't know 7th grade stuff and babble about pseudomathematical nonsense. My advice would be to find out how [math]\mathbb{R}[/math] is defined.

 

 

I'll address all of your nonsense as soon as you fix the error you made.

Saying that sqrt of 2 is the length of something is false, because that length multiplied by itself doesn't give 2, does it?

 

Please stop being retarded.

 

Funny taking insults from people who don't know what they're talking about. Do you know Pythagoras' theorem? If you have a square with lengths 1, it follows

for the length a of the diagonal that [math]a^2=1^2+1^2=2[/math].

 

Just for everyone elses understanding, mathematicians accept that sqrt of 2 exists by broadening their definitions to include that one exception to a rule, but mathematicians broadening their own personal definitions even if they all agree with eachothers doesn't change the definition and substance of something in hard fact.

 

The only hard fact is that you're completely wrong. I don't know why I'm actually debating with you because it's a hard fact that [math]\sqrt{2}[/math] exists.

Like you could argue about a fact.

 

What's your mathematical background?

[khaled]

Connector,

 

[latex]\mathbb{R}[/latex] is the set of real numbers,

 

[latex]\mathbb{R}[/latex] is closed on Multiplication,

 

we have [math]a \times a = b[/math] where [math]a, b \in \mathbb{R}[/math],

 

[math]a \times a = b \;\rightarrow\; a^2 = b \;\rightarrow\; a = \sqrt{b}[/math]

 

Let's substitute b = 2, we get [math]a \times a = 2 \;\rightarrow\; a^2 = 2 \;\rightarrow\; a = \sqrt{2}[/math]

 

where [math]a \in \mathbb{R}[/math]

[connector]

there is no number that satisfies a x a = 2

only a number extremely close to it.

I'm not saying that sqrt of 2 shouldn't be used or is somehow bad, I'm saying it's an estimate, because it is, and splitting these hairs solely for the understanding of the newbie mathematician who wants to know the origin of why sqrt of 2 goes on forever instead of being a nice finite number. This is to help the newbie understand sqrt of 2, in order to do this he has to realize that it doesn't fit the definition of an exact number, it's an estimate, it gets really close to being sqrt of 2, but no such number has been proven to exist.

 

Unfortunately mathiscool has absolutely nothing to argue with except trying to attack my character and distract everyone rather than (ironically) overcoming his ignorant bliss and admitting his error in claiming sqrt of 2 exists anywhere but his and other mathematicians imagination.

 

he seems to somehow forget that the Pythagorean theorem only works when you round, or estimate, c. Instead this nutcase believes that because it works out on his calculators or estimates where he rounds it up that somehow sqrt of 2 actually exists and satisfies the equation exactly - it doesn't, it never has.

[DrRocket]

It clearly doesn't exist. The length of the diagonal of a square with unit sides is the number closest to the theoretical sqrt of 2, but the sqrt of 2 doesn't exist. Mathematicians pretend it does because it's useful to do so and is close enough for all real world applications.

 

The number closest to the sqrt of 2 IS the sqrt of 2.

 

There is no rational number closest to the sqrt of 2. Between any two real numbers there is a rational number (in fact there are infinitely many of them).

 

 

 

 

 

The bottom line here is that often people have trouble understanding why there are these irrational numbers involved in math because it doesn't make sense to the newbie, and there is an intuitive explanation for all of it as I just explained, pi, sqrt of 2, and other irrational number aspects of math are approximation tools because we can't measure or compute exact reality (yet), and therefore all of these numbers and formulas involving them have a slight margin of error, not because the universe necessarily is mathematically erroneous, but because we started our calculations with a small margin of error in the first place (because it's the best we can currently do, as John Cuthber implied).

 

The bottom line is that this is nonsense.

Edited February 27, 2012 by DrRocket

[connector]

you can't define a number simply by saying it exists, for example, the definition:

 

 

"The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2."

 

There is no number that produces 2 when multiplied by itself, therefore there is no square root of 2.

The problem is that you keep saying there is, when there isn't. Show me the number, not a formula relying on the rounding up of a number to get 2, but an actual number multiplied by itself that equals two without any rounding or estimating. Then you will have an exact square root of 2, as all square roots must be exact.

It seems like everyone is brainwashed with orthodox education here, instead of figuring things out for themselves to be true or untrue.

Edited February 27, 2012 by connector

[DrRocket]

you can't define a number simply by saying it exists, for example, the definition:

 

 

"The square root of 2, often known as root 2, is the positive algebraic number that, when multiplied by itself, gives the number 2."

 

There is no number that produces 2 when multiplied by itself, therefore there is no square root of 2.

The problem is that you keep saying there is, when there isn't. Show me the number, not a formula relying on the rounding up of a number to get 2, but an actual number multiplied by itself that equals two without any rounding or estimating. Then you will have an exact square root of 2, as all square roots must be exact.

It seems like everyone is brainwashed with orthodox education here, instead of figuring things out for themselves to be true or untrue.

 

I can CONSTRUCT the real numbers, including sqrt of 2 and pi using nothing except the natural numbers and simple set theory. Yep, I figured it out for myself to be true, along with rather a lot more mathematics.

 

You can see this done in print in Landau's Foundations of Analysis or Rudin's Principles of Mathematical Analysis.

 

There is no brainwashing involved. All that is required is to have a brain in the first place and to use it to understand real mathematics.

[connector]

Funny, I ask the guy to give me the number which multiplied by itself to equal 2 without rounding, and his response is that 'he can construct it'

 

 

Where is the number?.....cricket...cricket.

 

Oh wait, not quite cricket. More character attacks to try and distract everybody from the fact that after 15 posts or more they still haven't found a number to satisfy the definition of a square root of 2, instead they can only say things implying that they are smarter than me or that I'm ridiculous. Newsflash, your arguments have no substance. Prove what you preach instead of attacking my character or suggesting I go digging through books. The burden of proof is on you to prove something. Hundreds or thousands of people all saying something is true is not proof (Unless Allah, Christian Trifecto, and Zeus are all real instantaneously plus a lot of other contradictions because a bunch of people say so). Spouting formulas which require rounding in order to prove an exact number exists is not proof. You are fools.

Edited February 28, 2012 by connector