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Math Help - Geometry Help Please Help

  1. #1
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    Exclamation Geometry Help Please Help

    I have a diagram of 25 congruent circles in a 5 x 5 pattern, but all touching, somewhat like this:

    OOOOO
    OOOOO
    OOOOO
    OOOOO
    OOOOO

    Just forget the spaces between the lines, imagine they are all bunched up together to form a perfect square. The question says I am to shade at least one circle so the figure has rotational symmetry of 90 degrees, but no line of symmetry. After looking at this, I fail to see how it's possible, but obviously it must be. Thank you all for your time and answers
    Rocker 1414
    Last edited by Rocker1414; August 25th 2008 at 06:24 PM.
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  2. #2
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    OO#OO
    OO#OO
    #####
    OOOOO
    OOOOO


    The #'s are the circles you should shade in.
    That's the answer. No line symmetry whatsoever, but it has 90 degree rotational symmetry.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by desperatesoul View Post
    OO#OO
    OO#OO
    OO#OO
    #####
    OOOOO
    OOOOO


    The #'s are the circles you should shade in.
    That's the answer. No line symmetry whatsoever, but it has 90 degree rotational symmetry.
    ok, what do we mean by rotational symmetry? because rotating this 90 degrees, say clockwise, yields:

    OO#OO
    OO#OO
    OO###
    OO#OO
    OO#OO
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Hello,
    Quote Originally Posted by desperatesoul View Post
    OO#OO
    OO#OO
    #####
    OOOOO
    OOOOO


    No line symmetry whatsoever.
    As Jhevon said, it seems there is no 90 rotational symmetry. Plus, there is a line of symmetry :

    Code:
      |
      |
    OO#OO
    OO#OO
    #####
    OOOOO
    OOOOO 
      |
      |
    A solution without line symmetry is
    Code:
    OOO#O
    #OOOO
    OOOOO
    OOOO#
    O#OOO
    Another possibility is to shade circles so that they form a swastika.
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  5. #5
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    Oh sorry about that! Must have had a brain fade.
    Last edited by mr fantastic; December 8th 2009 at 01:00 PM. Reason: rt --> de
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