I´ve been wondering for a while now if it exists and if so, how it looks like. By elementary I mean something like: completely (elementary) number theoretically. Because I know there are a few easy proofs that is not rational, but all of the ones I’ve seen, make use of some calculus (like computing an integral or so). So, my question: Can anyone show me the irrationality of with just the very basics of number theory or tell me why it is/shouldn’t be possible? For example, a few years ago I tried to prove it using the the formula: along with basic arguments which you may find in some proofs of the irrationality of . Although (obviously) I wasn’t able to prove the desired result, I did not find a reason why it shouldn’t be possible *in principle. *Even more, I had the gut feeling I was almost there. So I might give it another shot it the future, but hopefully that doesn’t stop you, my dearest reader, from helping me if you’ve got some info on this.

## An elementary proof of the irrationality of Pi

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June 30, 2010 at 15:45 |

Dear prof Math

I want a question but I think I can wrong

pi=4/(1+(1^2)/(2+(3^2)/(2+(5^2)/(2+(7^2)/(….)))))).?

I read it in a book in past but I think my memory can wrong

June 30, 2010 at 16:22 |

Dear My idea,

I think you mean the following:

4/Pi = 1 + 1/(2 + 9/(2 + 25/(2 + 49/(2 + 81/(2 + 121/(2 + ..))))))

Found on: http://functions.wolfram.com/Constants/Pi/10/0008/MainEq1.L.gif

June 30, 2010 at 15:45 |

😉

June 30, 2010 at 17:33 |

thank you,prof Math

June 30, 2010 at 17:39 |

I like your blog very much,it’s great