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Math Help - Perimeter of an Ellipse

  1. #1
    Super Member Aryth's Avatar
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    Perimeter of an Ellipse

    I need to know how one would evaluate this expression given:

    h = \frac{(a - b)^2}{(a + b)^2}

    Here's the expression for the major radius a and minor radius b of an ellipse:

    P = \pi (a + b) \sum_{n = 0}^\infty \left[{\frac{1}{2} \choose n}^2 h^n\right]

    Where:

    a = 405407

    b = 338246
    Last edited by Aryth; March 7th 2008 at 10:25 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Aryth View Post
    I need to know how one would evaluate this expression given:

    h = \frac{(a - b)^2}{(a + b)^2}

    Here's the expression for the minor radius a and major radius b of an ellipse:

    P = \pi (a + b) \sum_{n = 0}^\infty {\frac{1}{2} \choose n}^2 h^n

    Where:

    a = 405407

    b = 338246
    Here is what Wikipedia has to say about it:
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  3. #3
    Super Member Aryth's Avatar
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    Those are all approximations (With the exception of the sum/product), I'm familiar with those and I have my own approximation whose error cannot exceed:

    \delta = \frac{0.4e^8}{(1 - e^2)}

    Where e is eccentricity and for my particular case, it is:

    e = 0.05

    So, the approximation is very close, yet I wish to have an exact measurement, and according to my research, this is one of four exact methods.

    I was wondering how to use the series above. I'm not very experienced with infinite series, which is why I posted it.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Aryth View Post
    Those are all approximations (With the exception of the sum/product), I'm familiar with those and I have my own approximation whose error cannot exceed:

    \delta = \frac{0.4e^8}{(1 - e^2)}

    Where e is eccentricity and for my particular case, it is:

    e = 0.05

    So, the approximation is very close, yet I wish to have an exact measurement, and according to my research, this is one of four exact methods.

    I was wondering how to use the series above. I'm not very experienced with infinite series, which is why I posted it.
    It is exact untill you want to evaluate it when (except for a few special cases) you will have to used an approximation to the sum. There is no general finite closed form expression for this in terms of elementary functions

    RonL
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