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Math Help - Dividing a line into 5 equal parts using a compass

  1. #1
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    Dividing a line into 5 equal parts using a compass

    Can anyone tell me the method to do this?
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  2. #2
    Super Member wingless's Avatar
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    1- This is the line we want to divide.
    --


    2- Draw a ray.
    --


    3- Divide the ray equally using your compasses as many as you want to divide the line segment.
    --


    4- Draw the line that passes through the last intersection point and the end point of the line segment.
    --


    5- Draw lines parallel to the line we've just drew.
    --

    I divided it to 3 equal parts. You can do it with 5 parts, it's the same idea.
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  3. #3
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    Um... does step 3 not require being able to answer the aforementioned question?
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  4. #4
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    Quote Originally Posted by Unenlightened View Post
    Um... does step 3 not require being able to answer the aforementioned question?
    No. In step 3 we can choose any length as the compass (radius) to cut into equal parts. Whereas for the given line(whose length is fixed), the radius of the compass should be fixed. And the trouble is we do not know the length of this divided part, geometrically.
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  5. #5
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    Hello, gwen01!

    Divide a line segment into five equal parts using a compass and straightedge.

    Given a line segment AB diagonally (say, to the upper-right).
    Draw a horizontal line AC to the right.
    Code:
                              B
                              *
                            *
                          *
                        *
                      *
                    *
                  *
                *
              *
            *
        A * - - - - - - - - - - - - - - - - - C

    On AC, mark off five equal segments: . AP = PQ = QR = RS = ST
    Code:
                              B
                              *
                            *
                          *
                        *
                      *
                    *
                  *
                *
              *
            *
        A * - - + - - + - - + - - + - - + - - C
                P     Q     R     S     T

    Draw segment BT.
    Code:
                              B
                              *
                            *  \
                          *     \
                        *        \
                      *           \
                   *               \
                  *                 \
                *                    \
              *                       \
            *                          \
        A * - - + - - + - - + - - + - - + - - C
                P     Q     R     S     T

    Through P, Q, R, S construct lines parallel to BT,
    . . intersecting AB at W, X, Y, Z.
    Code:
                              B
                              *
                         Z  *  \
                          o     \
                     Y  *  \     \
                      o     \     \
                 X  *  \     \     \
                  o     \     \     \
             W  *  \     \     \     \
              o     \     \     \     \
            *  \     \     \     \     \
        A * - - + - - + - - + - - + - - + - - C
                P     Q     R     S     T

    Then: . AW = WX = XY = YZ = ZB



    Nice job, wingless!
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  6. #6
    Super Member wingless's Avatar
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    Thanks, Soroban
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  7. #7
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    Thanks Guys!

    This helps alot, and i remember now how to do it.
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  8. #8
    Global Moderator

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    But it seems this uses a non-collapsable compass.
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  9. #9
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    problem

    These constructions all assume that the lines you are making are in fact parallel. What is the method of proof to determine that these segments are in fact all equal?

    Caesar
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