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Math Help - Divide a square into 7 equal parts

  1. #1
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    Divide a square into 7 equal parts

    Can you help me devide a square into seven equal parts? Each having the same amount of perimeter and the same area? It seems like everything I do I just end up with 8 peices. Is this not possible? And if it isn't possible how do I prove that it's not possible?


    Thank you!
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  2. #2
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    Quote Originally Posted by angels_symphony View Post
    Can you help me devide a square into seven equal parts? Each having the same amount of perimeter and the same area? It seems like everything I do I just end up with 8 peices. Is this not possible? And if it isn't possible how do I prove that it's not possible?


    Thank you!
    Definition of part? Why don't you slice it into seven rectangles?
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  3. #3
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    Part being equal in perimeter and area. Hmm in the question it's a pizza...or it wants to be devided into 7 equal parts each having the same amount of pizza and same amount of crust. (crust = perimeter)
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    Quote Originally Posted by angels_symphony View Post
    Part being equal in perimeter and area. Hmm in the question it's a pizza...or it wants to be devided into 7 equal parts each having the same amount of pizza and same amount of crust. (crust = perimeter)
    Hello,

    I don't know when you have eaten a pizza but the crust and the perimeter of a part of a pizza is only equal if you eat the whole pizza.

    I've attached a sketch of a qudratic pizza with seven equal parts and each part has the same amount of crust.
    Attached Thumbnails Attached Thumbnails Divide a square into 7 equal parts-pizza_crust.gif  
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  5. #5
    Super Member angel.white's Avatar
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    "Quadratic pizza"
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by earboth View Post
    Hello,

    I don't know when you have eaten a pizza but the crust and the perimeter of a part of a pizza is only equal if you eat the whole pizza.

    I've attached a sketch of a qudratic pizza with seven equal parts and each part has the same amount of crust.
    how did you know how to divide it? did technology do it for you, or did you actually work something out?
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  7. #7
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    Hmmm Yea. How did you know how to divide it up?
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  8. #8
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    Quote Originally Posted by Jhevon View Post
    how did you know how to divide it? did technology do it for you, or did you actually work something out?
    Good morning,

    here are the steps I took:

    1. I divided the perimeter of the square into 7 equal distances.
    2. I played with some geometric shapes (rectangle, triangle, ...)
    3. I noticed that a triangle would fit best if I take the center of the square as common vertex.

    4. Only the quadrilateral shapes bothered a me a lot until I noticed that I can divide them into 2 triangles and that they actually have the same area as the simple triangles too.

    Or, to quote topsquark: I was hit by a particle of inspiration.
    Last edited by earboth; December 8th 2007 at 10:03 PM.
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  9. #9
    Super Member angel.white's Avatar
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    Quote Originally Posted by earboth View Post
    Good morning,

    here are the steps I took:

    1. I divided the perimeter of the square into 7 equal distances.
    2. I played with some geometric shapes (rectangle, triangle, ...)
    3. I noticed that a triangle would fit best if I take the center of the square as common vertex.

    4. Only the quadrilateral shapes bothered a me a lot until I noticed that I can divide them into 2 triangles and that they actually have the same area as the simple triangles too.

    Or, to quote topsquark: I was hit by a particle of inspiration.
    So you actually used ten triangles to calculate? I'm impressed ^_^
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by earboth View Post
    Or, to quote topsquark: I was hit by a particle of inspiration.


    -Dan
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