X *r *pi = 360 degrees now play with this formula who out of you can can find the rational fraction of pi
You make this thread over and over - you think we're all too stupid to understand your point? We get it, if something actually moves in a trajectory around something then Pi must have a final rational value. What you don't get it is the fidelity for calculating that orbit can increase infinitely...this is why Pi is irational and the radius is not. By the way I think there's an easy mathematical way to show this... \(\pi = lim_{n\to \infty} n (sin^{-1}(\frac{360}{2n}))\) Where n is the theoretical number of sides.
http://en.wikipedia.org/wiki/Proof_that_π_is_irrational Proof pi is irrational. It is not rational, no ifs, no buts.
That Wikipedia article needs to be improved. Why don't you tackle that? I had been under the impression that the irrationality of Pi had been known to the ancient Greeks. The article asserts the first proof wasn't known until more modern times.
No, the Greeks did not know it was irrational, they certainly wouldn't have been able to prove it even if they had. Typically the proof is covered in a university undergrad course in Analysis. The best the Greeks could do is come up with recursive formulas to bound pi between two values and to make these bounds as tight as desired.
Mmmmm.... delicious irony. You complaining the Wiki page is poor and then demonstrating your own knowledge is poor. The irrationality of \(\sqrt{2}\) was known to the Pythagoreans and it was a major issue to them since it violated their notion that all umbers can be written as a quotient of integers. Their proof can be applied to all \(\sqrt{n}\) where integer n is not a perfect square but it doesn't apply to pi. The irrationality of pi is less trivial and hence resisted a proof for a long time. As for me 'tackling that' I generally find that when it comes to mathematics pages its not worth editing unless you have a very very clear and precise plan of what you're going to say. Generally there are people who have much more details knowledge of any given area of mathematics than myself on Wikipedia and hence why so much detail is found in mathematical pages. Hell, even my quite niche area of research is done in vastly greater detail than anything I'd write, someone already got there and they know their stuff. I prefer to correct wordy explanations and leave the lengthy algebra to those who want to do it. But if you feel Wiki is a little light on the details and accuracy you could always try opening a book. They are the things found in libraries which contain sheets covered in text which forms coherent narratives and provide information. Sound familiar? Probably not....
I suppose I was extending the Greek knowledge of irrationals ( http://en.wikipedia.org/wiki/Irrational_number ) to Pi as well, which they never attempted to express as a ratio. So they likely believed it was irrational, but did not come up with the proof other than that it was bounded between two values?
No, they liked to use 22/7 quite often as an approximation, so I don't see any evidence that anyone thought a fraction for pi didn't exist. All Archimedes did was to limit the value between upper and lower bounds. The Greeks' knowledge of irrationals was mostly limited to roots of prime numbers as far as I can tell. Mind you, it's funny the Egyptians thought pi was precisely equal to 3, yet conspiracy theorists like to attribute wonderous technological feats to them.
Thanks, Cpt.Bork. I'm not a strong ancient-Greek scholar, and in particular as to the maximum extent of their mathematical knowledge. Did they have more than one proof of the Pythagorean theorem, or did they just have the cumbersome one developed by Pythagoras? I suppose a good Wiki article on ancient-Greek mathematics would be welcome, and in particular how it compared to the knowledge of mathematics in other ancient civilizations would also be welcome.
While we're just mentioning early pi's. Jews had 1/6th of the circumference as being equal to 111/106 which brings it to 3.141509 some time between 6th and 10th century BCE.
Listen, for you all are greater than you realise, Archimedes and others in your history have created foundational errors likened to prison bars that will inhibit the evolution of your existences. The reason why you will always get an irrational number for pi is because the method that is used the calculate it. That method spawned by your predeccesors is fatally flawed, for pi is not an approximation it is an exact ratio as long as long as the Tari continue with this illogical process the aproximate pi they will never realise what it is they are looking at. Pi is a contract of conscious minds "Objectivity" it is the true center of gravity in existence, it is the foundamental basis for objectivity, it is alot more than that but it is enough to isolate my point of view.
Well that answered my question. It's obviously theoneiuse that's the more irrational. Thanks for the prompt confirmation.
So when you have realized this ratio this will shift the center of gravity of your existences. Then finally a new point of view can emerge as the correct centerpiece to objectivity and at least if not accuracy in other things but the appreciation of it.
Yeah, he was. But I always thought that his proof contained in his Elements was Pythagoras' proof. Did Pythagoras have some other proof? As I mentioned, I'm not real strong on ancient Greek history. Even the ancient Egyptians knew of the 'Pythagorean triplets', though apparently without a proof and generic extension. See: http://en.wikipedia.org/wiki/Pythagorean_theorem where the pythagorean theorem proof as presented by Euclid is given. As I mentioned, I always thought that that was the proof developed initially by Pythagoras; but perhaps not?
Aren't there as many ways to approximate Pi as there are to approximate e? I mean, duh, just count the neurons, you know?
