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I know $\pi$ is 3.141592653589793...... We all learn this at school.

But I haven't learned why pi is irrational number.

How can prove that pi is irrational number?

I would be grateful if you can explain it easily. :)

Maybe I didn't understand it, but this answer didn't help me anyway.

msm082919
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    Yes, the answer doesn't answer anything, but did you follow the link that says "proved" in the answer? – Blue Feb 03 '20 at 16:56
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    What kind of answer are you looking for. Do you want why we know $\pi$ is irrational, which a proof would answer, or some reason that it "should be" irrational? There are so many more irrationals than rationals that any number that doesn't "have to be" rational isn't. – Ross Millikan Feb 03 '20 at 17:02
  • Why not, there are provably more irrational than rational numbers. If $\pi$ is rational or even algebraic, then it will be a big surprise. – achille hui Feb 03 '20 at 17:08
  • Thanks for the link. The content was difficult, but it was answered. I did not see the wiki content when I searched because I am not an English speaker. – msm082919 Feb 03 '20 at 17:12
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    "Mathologer" has a proof on YouTube that you might find interesting. https://www.youtube.com/watch?v=Lk_QF_hcM8A – awkward Feb 03 '20 at 21:16
  • Irrationality proofs are usually extremely difficult. For example, whether $e+\pi$ or whether $e\cdot \pi$ is irrational, is not known. The argument that "almost every real number is irrational" is the common answer to such questions if a number has "no obvious reason" to be rational or at least algebraic. Irrationality is assumed for the Euler-Mascheroni-constant, but again the character of this number is unknown. – Peter Feb 15 '20 at 15:07
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    Does this answer your question? Why is $\pi$ irrational? – Elias Zamaria Feb 14 '21 at 03:31
  • Thanks for the comment. But it's still not easy to understand. okay. I see why root 2 is an irrational number. I am not sure how this affects my question. Maybe it's because my English isn't good... – msm082919 Feb 17 '21 at 03:30

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