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Math Help - how to prove pi is not an algebraic number

  1. #1
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    how to prove pi is not an algebraic number

    how do you go about proving pi is not an algebric number??
    thanks for any help
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  2. #2
    Senior Member Dinkydoe's Avatar
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    Proof that ? is irrational - Wikipedia, the free encyclopedia

    Here are some proofs you might want to look at
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  3. #3
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    thanks, but i dont understand how proving that pi is irrational proves that it is not an algebraic number?
    root 2 is algebraic and yet is also irrational, thanks for any help
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  4. #4
    Senior Member Dinkydoe's Avatar
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    You're right.

    Pi is Transcendental
    pi is transcendental

    The last link provides a proof for the fact that pi is transcendental. However it's quite a difficult proof. To proof a number is transcendental is often hard.
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  5. #5
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Dinkydoe View Post
    You're right.

    Pi is Transcendental
    pi is transcendental

    The last link provides a proof for the fact that pi is transcendental. However it's quite a difficult proof. To proof a number is transcendental is often hard.
    There is a proof using "elementary" calculus. I'll try to find it and post it up later.
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  6. #6
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    AMM March 2001

    There is an article
    "Similarities in Irrational Proofs for ..."
    in the March 2001 American Mathematical Monthly.
    Simple calculus and some, more or less, advanced algebra. There are a few typos as I recall.
    The technique is interesting but takes a lot of thought to really understand.
    They also have references to other sources.
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  7. #7
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    AMM article oops

    I just reread the article and it only covers irrationality; not transcendental.
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  8. #8
    Senior Member Dinkydoe's Avatar
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    There is a proof using "elementary" calculus. I'll try to find it and post it up later.
    I'd also be interested in it. The proofs for irrationality of \pi are allready difficult. Showing that \pi is also transcendental is even more difficult.
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