All we know that PI = 22/7. But how and why it is 22/7 rather other fractions?
- 20 Contributors
- forum114 Replies
- 280 Views
- 9 Years Discussion Span
- comment Latest Post by Sriman_Laxmi
Narue 5,707
>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.
Edited
by Narue: n/a
vegaseat 1,735
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 812
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.
mrnutty 761
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 990
Circumference = Diameter x 3.1416
GrimJack 1,410
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 812
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 1,410
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.
Edited
by GrimJack: n/a
vegaseat 1,735
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 969
You can also calculate pi with this simple mathematical formula:
4*.atan(1) :)
cwarn23 387
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.
mvmalderen
commented:
Your statement is obviously wrong! +0
GrimJack 1,410
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 178
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 387
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 178
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 387
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 178
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 387
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 178
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
Edited
by Paul Thompson: n/a
mrnutty 761
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.
Sorry man, but this I find stupid. First This statement is wrong :
<quote> If pi were infinite in length then the circle would have have an infinite circumference.</EOQ>
Just because the sequence is infinite length does not mean that
its value is infinity, and therefore the circumference of the circle is
not infinite.
And you can't use any software to draw a circle and prove that pi
is not 3.14159... because the circles are actually pixels, which are
rectangles. What you are trying to disprove is math. And if anything in this world,
I know that math is purely deductive.
Edited
by mrnutty: n/a
Paul Thompson 178
Thankyou! Thats what i have been trying to say.
GrimJack 1,410
I was hoping to let him off the hook by assuming it was a joke but he just would not let it go. I think he should read Flatland and see how polygons are made into circles.
What he does not understand is that there are no straight lines in a circle and in any paint/graphics program it is always a straight line between each pixel - ie if the circumference of a circle was made up of one million pixels, it would not be a circle, it would be a polygon of 1 million sides. You can use Pythagoras' theorem to calculate a reasonable facsimile of PI- just create an internal and an external polygon on the circle. Now imagine 3 ants walking - one walks on the perimeter of the internal polygon, one walks on the perimeter of the external polygon and one walking on the perimeter of the circle and the problem is to get the 3 ants to travel the same distance. Using the Pythagorean Theorem to calculate length of each side of the inner polygon and the outer polygon, add them up and divide by the 2*radius/diagonal and average the answer and you get a pretty good approximation of PI - only if you do it by hand. When You do it by binary computer errors begin to creep in around 32768 sides - the approximation is good to about 9 decimal places (3.141592653).
Any errors of thought are mine - Pi has been known and approximated for more than 4,000 years. The Babylonians approximated it one way, the Egyptians a different way. I think it was Archimedes who first used the Pythagorean Theorem to approximate PI.
cwarn23 387
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
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.
Paul Thompson 178
This is maths, you dont talk about atoms, thats in science. You are trying to mix the two where they should not be mixed. No matter how darn small a circle is it never made up by a countable number of points. Ever. This is maths... If you actually read my last link you would have learnt something.
And just for a point, no circle that you ever draw, or make in real life will actually work with pi. Thats because they are not perfectly accurate. But models are not perfect maths.
cwarn23 387
This is maths, you dont talk about atoms, thats in science. You are trying to mix the two where they should not be mixed. No matter how darn small a circle is it never made up by a countable number of points. Ever. This is maths... If you actually read my last link you would have learnt something.
Maybe you should take up a physics degree... One of the basics is there is a thing called a periodic table and you have just denied that be denying the science of atoms. Another thing. To understand maths we need to understand science. Maths and science are directly related and when combined can be called Physics. Obviously you and many others don't understand the science behind making a circle so that is why we are stuck with pi. I wonder how many people in this world agree with me about that previous sentence because I'm guessing there isn't that many.
William Hemsworth 1,339
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.
Why stop at the atomic level? maths works with the infinitely small. What if you consider an electron to be spherical?
Paul Thompson 178
Thanks will..
Maths, never, ever, ever, ever, ever, ever, ever, ever, ever, deals with atoms when dealing with pi, or circles. Maths goes smaller than atom, as small as anything you ever want.
And before spouting your theory read the wikipedia article on pi, it shows exactly why it cannot be rational. Do your research before preaching to us.
jonsca
commented:
I don't know what to say, I'm speechless +0
cwarn23 387
Well electrons are charges of electricity aren't they? So wouldn't there be another substance which would make up everything around us. 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. Although I have limited knowledge in this area I do know a few basic things. And an atom was an example. I could have just as easily said a particle. But you get the general idea.
Paul Thompson 178
stop talking about atoms, it has nothing to do with the maths you are talking about.