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Math Help - I'm so frustrated!!! Can someone please help??

  1. #1
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    Angry I'm so frustrated!!! Can someone please help??

    I have to make a Cairo Tessellation with these steps:

    1: On another sheet of paper, construct segment AB, with midpoint M.
    2: In the same half plane, construct two 45 degree angles with vertex M. Call them (angle)AMX and (angle)BMY.
    3: Locate C on ray MY such that C lies on the circle having center B and radius AB.
    4: Locate E on ray MX such that E lies on the circle having center A and radius AB.
    5: Locate D, the intersection of the circle having center C and radius AB and the circle having center E and radius AB.
    6: Pentagon ABCDE is the Cairo tile. Recopy it and create the Cairo tessellation!
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  2. #2
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    What are we supposed to do? We can't possibly construct it for you, and the instructions are pretty straightforward. I don't know how to improve on the step-by-step instructions you've provided.

    Have you started? What have you done? Have you constructed a segment and found the midpoint?

    I would suggest using a geometry textbook with a section on constructions - most geometry books have a chapter or at least a few sections. Any diagrams they have there will most likely be more helpful than a description found here.
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  3. #3
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    Quote Originally Posted by Mathnasium View Post
    What are we supposed to do? We can't possibly construct it for you, and the instructions are pretty straightforward. I don't know how to improve on the step-by-step instructions you've provided.

    Have you started? What have you done? Have you constructed a segment and found the midpoint?

    I would suggest using a geometry textbook with a section on constructions - most geometry books have a chapter or at least a few sections. Any diagrams they have there will most likely be more helpful than a description found here.
    i found midpoint M and i'm assuming that you just bisect the angle to get a 45 on each side but after that, i'm totally lost... "Locate C on ray MY such that C lies on the circle having center B and radius AB" how am i supposed to do that?
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  4. #4
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    Quote Originally Posted by MUSICismyBOYFRIEND View Post
    I have to make a Cairo Tessellation with these steps:

    1: On another sheet of paper, construct segment AB, with midpoint M.
    2: In the same half plane, construct two 45 degree angles with vertex M. Call them (angle)AMX and (angle)BMY.
    3: Locate C on ray MY such that C lies on the circle having center B and radius AB.
    4: Locate E on ray MX such that E lies on the circle having center A and radius AB.
    5: Locate D, the intersection of the circle having center C and radius AB and the circle having center E and radius AB.
    6: Pentagon ABCDE is the Cairo tile. Recopy it and create the Cairo tessellation!
    I've done the construction according to your description (and I can't imaging why you can't do it)

    I then reflected the pentagon about the midpoint of oneside to get a garland of pentogons.
    Attached Thumbnails Attached Thumbnails I'm so frustrated!!!  Can someone please help??-cairotile1.gif  
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  5. #5
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    You can't cover the plane completely what I would presume by the word "tesselation". If you try to cover the plane there'll be some "holes".

    I've marked them lightgrey.
    Attached Thumbnails Attached Thumbnails I'm so frustrated!!!  Can someone please help??-cairotile2.gif  
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  6. #6
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    FYI: This is the origin of things like, in Mathematics, Penrose tiling, and in the physical sciences, quasicrystals.

    -Dan
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