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Math Help - pi vs e

  1. #1
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    pi vs e

    First of all, pi is an approximation, right?

    Why is pi only an approximation?

    Secondly, what exactly is the meaning of the number e?

    Why is e only an approximation or is it?

    Question:

    pi^(pi) times e^(e) =
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    First of all, pi is an approximation, right?
    No its not an approximation. It is transcendental, that is its not a
    root of a polynomial with rational (or integer) coefficients.

    Being transcendental it is irrational which means that it cannot be
    writen as a ratio of integers, nor can it be written as a terminating
    or periodic decimal.

    Why is pi only an approximation?
    see above

    Secondly, what exactly is the meaning of the number e?
    It has no meaning, but it is important in mathematics because it
    has interesting and usefull properties.

    Specificaly it the the number which has the property that e^x is the solution of:

    \frac{d}{dx}f(x)=f(x)

    satisfying f(0)=1.

    Why is e only an approximation or is it?
    see comments above about \pi

    RonL
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by symmetry View Post
    First of all, pi is an approximation, right?

    Why is pi only an approximation?
    \pi is irrational, so know matter how many decimal places you write, there will always be more. So whatever number you use for it will be an approximation.

    Secondly, what exactly is the meaning of the number e?

    Why is e only an approximation or is it?
    I was told that e is just a number that appears frequently in calculus...

    It too is irrational, so \pi^\pi\times e^e is irrational.

    Although, e^{i\pi}=-1
    Last edited by Quick; January 12th 2007 at 01:37 PM.
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  4. #4
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    Quote Originally Posted by symmetry View Post
    First of all, pi is an approximation, right?

    Why is pi only an approximation?

    Secondly, what exactly is the meaning of the number e?

    Why is e only an approximation or is it?

    Question:

    pi^(pi) times e^(e) =
    \pi and e are both numbers that appear a lot in Calculus/Analysis. Because of their appearances they are important.
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