Proof that π is irrational - Wikipedia, the free encyclopedia
Although the mathematical constant known as π (pi) has been studied since ancient times, and so has the concept of irrational number, it was not until the 18th century that π was proved to be irration...
en.wikipedia.org/wiki/Proof_that_π_is_irrational
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π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to ... Main article: Proof that π is irrational ...
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en.wikipedia.org/wiki/Pi
en.wikipedia.org/wiki/Pi
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The first proof of the irrationality of PI was found by Lambert in 1770 and published by Legendre in his "Elements de Geometrie". A simpler proof, essentially due to Niven, goes like this: For any integer n and real number r we can define a quantity A[n] by the definite integral / 1 A[n] = | (1 - x^2)^n cos(rx) dx / x=
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www.mathpages.com/HOME/kmath313.htm
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Archived thread of Looking for "Easy" proof of Pi Irrational from the physics forums community for science discussion and specifically Looking for "Easy" proof of Pi Irrational General Math ... I was trying to get a proof of Pi^2 irrational out of the series 1 + 1/4 + 1/9 + ... 1/n^2 + ...
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www.physicsforums.com/archive/index.php/t-8193.html
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Next we prove that Pi is irrational, which is a lot harder to do. We need a preliminary result: ... Aside from the assumption that Pi is rational (leading to the contradiction) the only other properties of Pi that are really involved in this proof are that...
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pirate.shu.edu/~wachsmut/ira/infinity/irrat_nm.html
pirate.shu.edu/~wachsmut/ira/infinity/irrat_nm.html
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I think it was from a photocopied page from some book, given to me by a professor who thought I would be interested in it. If anyone can inform me as to the author of the proof, I'd gladly ... But f_n(x) sin x are strictly positive, except for the two points 0 and pi, and these functions are bounded above by 1 / pi for all...
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www.math.clemson.edu/~rsimms/neat/math/pi/piproof.html
www.math.clemson.edu/~rsimms/neat/math/pi/piproof.html
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science and technology Forum: Question About Proof that Pi is Irrational ... From what I have read so far, the proof that pi is irrational is the same proof that pi is transcendental. Lindemann's theory implied that any algebraic power of the number e ; (where e is the base of the exponential function that is its...
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sci4um.com/post-285564.html
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In 1794, Legendre proved the stronger result that is irrational . Proof that is transcedental was made in 1882 by C. Lindeman.1 Here, I present an elementary proof that is irrational based on its Gregory series expansion.
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www.coolissues.com/mathematics/Pi/pi.htm
www.coolissues.com/mathematics/Pi/pi.htm
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It all started when I offered my original proof that Pi was rational, using induction on the number of significant digits! ... This page is listed in The Useless Pages, under The Uselessness of Pi and its Irrational Friends.
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webonastick.com/pi/
webonastick.com/pi/
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