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Math Help - Ellipse Geometry

  1. #1
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    Angry Ellipse Geometry

    Hi All

    Can anyone help me with regards ellipse geometry.

    I have an issue were i have to be able to calculate the major and minor axis of an ellipse when i have the circumference.

    I know Ellipse Circumference = pi*sqrt((major^2+minor^2)/2)

    My relation from major to minor is: major = minor + constant (say 2.5 to start)

    This now leaves me with:
    Ellipse Circumference = pi*sqrt(((minor + 2.5)^2+minor^2)/2)

    I have re-arranged the equation to give me:
    2*((ellipse circumference/pi)^2) = (minor + 2.5)^2 + minor^2

    Continuing to manipulate I get:
    2*((ellipse circumference/pi)^2) = 2*minor^2 + 5*minor + 6.25

    I am now stuck on where to go to calculate minor if i know the circumference as using a quadratic equation -b (+/-) sqrt(b^2-4ac)/2a I am left with a negative square root which i can not solve.

    Can anyone HELP, where do i go from here?
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  2. #2
    Eater of Worlds
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    I may be misunderstanding, but the length of an ellipse circumference is not

    gotten by that formula. As a matter of fact, the circumference of an ellipse is

    rather difficult to calculate. That is where Elliptic integrals come in.
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  3. #3
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    Ellipse Geometry

    Hi Galactus

    I got the approximation formula from the following link

    www.csgnetwork.com/circumellipse.html

    Ive done an initial bit of re-arranging which i why my formula stated looks different to that in the link.
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  4. #4
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    For a closed ellipse , the length of the ellipse circumference is

     2a\pi [ \sum_{n=0}^{\infty} (\frac{k}{16})^{n} \frac{ [\binom{2n}{n}]^2}{1-2n} ]

    with major a and minor b (a>b) ,  k = \frac{a^2 - b^2}{a^2}
    Last edited by simplependulum; July 11th 2009 at 01:58 AM.
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  5. #5
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    simplependulum
    Given that formula you have can you tell were it came from?,

    Given that formula you have stated, what is "n", and how would i solve to get a or b, i will still be left with having to solve 2*minor^2 + 5*minor + 6.25 were i replace a with b + constant (2.5)


    Cheers
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