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Math Help - surface of a group of curves

  1. #1
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    Question surface of a group of curves

    Hi all,

    Assuming you have two points in an Euclidian plane, with a distance D between the two.
    If you would take the union of all possible curves connecting the two points, with a length smaller or equal to M, with M > D, what kind of shape would that give (and with what parameters) ?

    Intuitively I would think it to be an ellipse.

    Thx

    (I'm sorry if this post is in the wrong sub-forum)
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  2. #2
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    Re: surface of a group of curves

    Right that will be a solid ellipse with boundary |z-a|+|z-b|=M
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  3. #3
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    Re: surface of a group of curves

    Thank you !
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