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Why god? why e?

  1. Sep 29, 2004 #1

    quasar987

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    oops there's an extra m in my topic title, I was going for why e. :wink:

    I believe most the the exponential equations in physics come from the fact that a^[f(x)] = a^[f(x)] * lna * df/dx but the book I had in my first calculus class didn't had a proof for that.

    Does anybody have one? And most importantly, why e? Does that number represent anything special; is it a certain ratio like pi or anything like that? It really seem to be coming out of nowhere for me. The only definitions I've seen are all unintuitive: "e is defined as the integral from there to there of this" or "e is the number such that [such and such]", etc. But why does it appear in nature so often??

    (If you know a similar thread exists, tell me because I didn't find one.)
     
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  3. Sep 29, 2004 #2

    Integral

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    I think that there is significance in this relationship

    [tex] 1 = \int ^e _1 \frac {dx} x [/tex]

    Edit, fixed typo, now I'll add a bit of verbiage.

    Think about that, the area under the inverse curve between 1 and e is equal to 1. This is a pretty fundamental definition of e.
     
    Last edited: Sep 29, 2004
  4. Sep 29, 2004 #3

    Integral

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    Please do not double post.

    See this thread.
     
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