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I found an answer from www.quora.com

How to prove that \pi^2 is irrational - Quora


This proof is an adaptation of Chapter 16 of Spivak's Calculus. To prove that \pi^2 is irrational, we need to first introduce the function ...


For more information, see How to prove that \pi^2 is irrational - Quora

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I found an answer from en.wikipedia.org

Proof that π is irrational - Wikipedia


This proof uses the characterization of π as the smallest ... of the cosine function and it actually proves that π2 is irrational.


For more information, see Proof that π is irrational - Wikipedia

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I found an answer from en.wikipedia.org

Square root of 2 - Wikipedia


The square root of 2, or the (1/2)th power of 2, written in mathematics as √2 or 2 12, is the .... A short proof of the irrationality of √2 can be obtained from the rational root theorem, that is, if p(x) is a ...... √2 appears in Viète's formula for π: 2 m 2 ...


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I found an answer from crypto.stanford.edu

Pi - Proof that Pi is Irrational


Proof that Pi is Irrational. Suppose π=a/b π = a / b . Define. f(x)=xn(a−bx)nn! f ( x ) = x n ( a − b x ) n n ! and. F(x)=f(x)−f(2)(x)+f(4)(x)−...+(−1)nf(2n)(x) F ( x ) = f ( x ) ...


For more information, see Pi - Proof that Pi is Irrational

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I found an answer from math.stackexchange.com

Homework 8th grader: $\pi^2$ is irrational - Mathematics Stack ...


May 22, 2015 ... comes from the Euler series acceleration method and it can be used to prove the irrationality of π 2 and even more, for instance providing a ...


For more information, see Homework 8th grader: $\pi^2$ is irrational - Mathematics Stack ...

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I found an answer from www.quora.com

How do we know Pi and sqrt(2) is irrational and not just have ...


How do we know Pi and sqrt(2) is irrational and not just have EXTREMELY long part ... We either show two integers whose ratio is equal to the given number or ...


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I found an answer from math.stackexchange.com

Is this a valid proof that e π 2 is irrational?


But π 2 isn't a natural number, so that result doesn't apply. ... The answers to that question only show that e n is irrational for any positive integer ...


For more information, see Is this a valid proof that e π 2 is irrational?