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Math Help - Geometric Interpretations..

  1. #1
    MHF Contributor kalagota's Avatar
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    Geometric Interpretations..

    can someone give geometric interpretations on this..

    |z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2+|z_2|^2)

    thanks..
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by kalagota View Post
    can someone give geometric interpretations on this..

    |z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2+|z_2|^2)

    thanks..
    What exactly do you mean by geometric interpretation? Is it something like writing the above equation in the form of a geometrically meaningful statement?
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by kalagota View Post
    can someone give geometric interpretations on this..

    |z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2+|z_2|^2)
    Geometrically it's an equation which links the sides of a parallelogram to its diagonals : OC^2+OE^2=2(OA^2+AC^2)=\frac{1}{2}(OD^2+EC^2)
    Attached Thumbnails Attached Thumbnails Geometric Interpretations..-parallelogram.png  
    Last edited by flyingsquirrel; July 2nd 2008 at 03:23 AM. Reason: OD^2 = 4OA^2 != 2OA^2 :(
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    You can find it here.
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