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Math Help - "Rice Problem"

  1. #1
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    "Rice Problem"

    This problem is assumed by me, but I have no answer.....


    Let us suppose that we have two absolutely same sacks.
    The first sack is full with rice with round beans
    The second sack is full with ellipse beans.
    Let us suppose that volumes of round and ellipse beans are same
    The question is: which sack contains more beans?
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  2. #2
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    Quote Originally Posted by Ilia Tutberidze View Post
    This problem is assumed by me, but I have no answer.....


    Let us suppose that we have two absolutely same sacks.
    The first sack is full with rice with round beans
    The second sack is full with ellipse beans.
    Let us suppose that volumes of round and ellipse beans are same
    The question is: which sack contains more beans?
    What does: "Let us suppose that we have two absolutely same sacks." mean?

    Exactly the same would imply same mass, in which case the number of beans is the same.

    If you mean the same volume, then assuming the packing fraction (I think that is the right term) is the same then again the number is the same.

    However if you are asking about the packing fraction, then ..

    CB
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  3. #3
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    I mean, that the saks are absolutely same: i.e., same forms, and same volume.
    Yes, this problem is problem of packing of different forms in same area.....
    I can prefear the 2 dimention variant of this problem:

    We have two absolutely same tables. The surfase of first table is covered by circules (cutted of paper), and second table is covered by ellipses (also cutted of paper). the question is: which table is more covered? (figures do not cover each other, no part of same figure is out of table)
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Ilia Tutberidze View Post
    I mean, that the saks are absolutely same: i.e., same forms, and same volume.
    Yes, this problem is problem of packing of different forms in same area.....
    I can prefear the 2 dimention variant of this problem:

    We have two absolutely same tables. The surfase of first table is covered by circules (cutted of paper), and second table is covered by ellipses (also cutted of paper). the question is: which table is more covered? (figures do not cover each other, no part of same figure is out of table)
    Some experimental results are here, The MathWorld article is here, but you could find these and more using Google for yourself.

    CB
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  5. #5
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    Quote Originally Posted by Ilia Tutberidze View Post
    This problem is assume by me, but I have no answer.....


    Let us suppose that we have two absolutely same sacks.
    The first sack is full with rice with round beans
    The second sack is full with ellipse beans.
    Let us suppose that volumes of round and ellipse beans are same
    The question is: which sack contains more beans?
    I think this would make your problem a bit clearer:

    just use "beans"; leave rice out

    use identical rectangular boxes instead of sacks
    (sacks can end up in different shapes depending on what they contain)

    the width and length and height of the boxes should be such that they
    are multiples of both the circles and ellipses

    all round beans are identical; all elliptical beans are identical

    And I think that if you went filling a rectangle with circles versus filling
    same rectangle with ellipses (circle and ellipse same AREA), you would
    get same results.
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