How do we know the value of PI ?

[babug]

All we know that PI = 22/7. But how and why it is 22/7 rather other fractions?

[Narue]

>All we know that PI = 22/7.
Apparently not, because those of us who are correct know that PI < 22/7. Further, because PI is an irrational number there's no combination of x and y where x/y = PI.

>But how and why it is 22/7 rather other fractions?
PI is the ratio of a circle's circumference to its diameter. 22/7 is a reasonable approximation of that ratio.

[vegaseat]

Actually 22/7 is pretty crude. The Chinese Approximation of pi is much better. Simply use 355/113. You can remember this by looking at the first three odd integers written this way 113355.

[MosaicFuneral]

You know there's whole sites dedicated to the history of PI. You're just one Google search away. Wikipedia has a nice easy to read summary.

[firstPerson]

Well,

The circumference of a circle is 2*pi*r, but 2*r is the diameter so its :

C = D*pi, where D is the diameter of the circle.

Now if we divide the circumference by the Diameter then we are
just left with pi :

D*pi / D = pi.

In experiments, if you calculate the perfect circumference of a circle,
meaning how long the circle is if we un-wound it, and divide that number
by its diameter, then we would get PI.

Additionally, there are a series representation of pi. And a interesting
fact is that people have used super computer to calculate more than 1 trillion digits of pi.

[crunchie]

Circumference = Diameter x 3.1416

[GrimJack]

Isaac Asimov posited that if there was a god - the place to put the evidence was in PI.

Consider best way to get a 'true' random number is to use a pseudo-random number to point to digit in PI and use that number to find a digit in PI. So if PI is completely random then what better place for proof to show up.

[MosaicFuneral]

Isaac Asimov posited that if there was a god - the place to put the evidence was in PI.

Which made for a great movie , too.

[GrimJack]

Which made for a great movie , too.

Thanks! I had forgotten that movie - why this thread didn't bring it up to the fore I will never understand. That scene with the power drill is ..... scary.

[vegaseat]

Since the only thing that 22/7 has in common with PI is 3.14, you can also remember that using Albert Einstein's birthday of March 14th.

[sneekula]

You can also calculate pi with this simple mathematical formula:
4*.atan(1) :)

[cwarn23]

I also have a theory and am still working on a formula to prove that pi is not infinite in length. If pi were infinite in length then the circle would have have an infinite circumference. And using MS Paint I have found that pi is not always 3.1415. It can vary depending on the size of the circle. For example, a circle about 6 atoms in diameter will produce pi of 3 instead of 3.1415... This can be proven with 2d cg models so try to draw a perfect circle in MS Paint. Then count how many dots in the circumference and divide it by the number of dots in the diameter and you will rarely get pi to more than 1 digit for a small circle.

[GrimJack]

I also have a theory and am still working on a formula to prove that pi is not infinite in length. If pi were infinite in length then the circle would have have an infinite circumference. And using MS Paint I have found that pi is not always 3.1415. It can vary depending on the size of the circle. For example, a circle about 6 atoms in diameter will produce pi of 3 instead of 3.1415... This can be proven with 2d cg models so try to draw a perfect circle in MS Paint. Then count how many dots in the circumference and divide it by the number of dots in the diameter and you will rarely get pi to more than 1 digit for a small circle.

You are trying to disprove PI using a Microsoft product as proof? I love your sense of humor.

[Paul Thompson]

I don't even know if i would trust Ms Paint to measure something to the nearest cm let alone to decimal places. :S

[cwarn23]

I don't even know if i would trust Ms Paint to measure something to the nearest cm let alone to decimal places. :S

In MS Paint your not using cm's as the measurement but instead pixels. And pixels can be substituted for atoms. So 1 pixel = 1 atom. And with this info you can count exactly how many atoms are in the diameter and circumference then when you divide the two you will rarely get pi to two or three digits unless the diameter is huge (probably a few trillion pixels/atoms). And you can use any other 2d artwork program for the same, example: Paint Shop Pro or Paint.Net

[Paul Thompson]

Uh, sorry to burst your bubble. But a circumference is not the measure of atoms in the circle. Its the measure of distance, so therefore you have to measure the difference between 2 pixels, a diagonal it would be. But that isnt a proper circle. So then you would bisect the diagonal and make it into two diagonals between two pixels. But that still isnt a perfect circle so then you would do that again and again, never finding a perfect circle and thats why you can tell there is no end to pi. Because you can never get a measurable amount of 'atoms' that make up a circle without the circle not being a perfect circle.

kapish?

[cwarn23]

Uh, sorry to burst your bubble. But a circumference is not the measure of atoms in the circle. Its the measure of distance, so therefore you have to measure the difference between 2 pixels, a diagonal it would be. But that isnt a proper circle. So then you would bisect the diagonal and make it into two diagonals between two pixels. But that still isnt a perfect circle so then you would do that again and again, never finding a perfect circle and thats why you can tell there is no end to pi. Because you can never get a measurable amount of 'atoms' that make up a circle without the circle not being a perfect circle.

kapish?

Well I would hate to spoil the surprise but everything we see in the real world is basically digital. Made of atoms and energy. Then when measuring objects we use measurements that only measure a group of atoms the the number of atoms in that group always varies. 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. However if you make the circle much smaller (lets say 10 atoms wide) then that means that there hasn't yet been enough loops to get the first couple of digits. It is kinda like Vieta's pi formula where it calculates every circle starting from a circle that is 1 atom wide. But I haven't confirmed that is what Vieta's formula does but suspect it does calculate every possible circle that you could possibly assemble on an atomic level. So I believe something along the lines of Vieta's pi formula shows how to calculate pi you need to calculate every circle or at least every circle which is selected when counting up from ^2.

[Paul Thompson]

But maths isnt digital.. Thats the magic of it, its not bound by the laws of nature.

And if you call something of 10 atoms of diameter a circle, you would have mathematicians up in arms because it could probably be classified as a polygon. This shape may not live up to the expectations of pi

But mathematically, a shape of 10 units (no matter how small) wide that was a perfect circle would obey the rule of pi and make 3.14... as the value of pi.

So its up to you if you interpret in a mathematical way or in a graphical/environmental way.

And also think, if pi could be disproved. Wouldn't one of the millions of brilliant mathematicians done it already?

[cwarn23]

But maths isnt digital.. Thats the magic of it, its not bound by the laws of nature.

And if you call something of 10 atoms of diameter a circle, you would have mathematicians up in arms because it could probably be classified as a polygon. This shape may not live up to the expectations of pi

But mathematically, a shape of 10 units (no matter how small) wide that was a perfect circle would obey the rule of pi and make 3.14... as the value of pi.

So its up to you if you interpret in a mathematical way or in a graphical/environmental way.

And also think, if pi could be disproved. Wouldn't one of the millions of brilliant mathematicians done it already?

If you believe it would still be 3.1415 then draw a circle on a grid of 10 by 10 in paint then divide number of pixels in the circumference by the number of pixels in the diameter and see if that equals pi. That test revels pi is false. And yes that is an accurate circle even though it looks very pixulated. I am writing a formula that will calculate the true circumference based on the number of pixels/atoms on the horizontal diameter and the diagonal diameter as they are two different numbers for half the circles.

[Paul Thompson]

And yes that is an accurate circle even though it looks very pixulated.

No it isnt, not at all. To calculate pi precisely using an actual model you would need an amazingly accurate circle.

Its obvious your not understanding what i am talking about so its rather futile. What i am trying to say is that maths and diagrams are not perfect representations of each other. Just because your MS Paint doesn't work for pi doesn't mean much. pi is made for circles, and i would count any circle made my MS Paint that is only 10 pixels wide to not be an actual circle and rather a many sided shape (polygon)

someone back me up here? :S

EDIT: Read this http://mathforum.org/library/drmath/view/58308.html it explains everything