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Math Help - Construction

  1. #1
    Junior Member mathfun's Avatar
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    Construction

    Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
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    Quote Originally Posted by mathfun View Post
    Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
    Is it allowed to use compasses?
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  3. #3
    Junior Member mathfun's Avatar
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    Yeap
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    Super Member TheChaz's Avatar
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    Quote Originally Posted by mathfun View Post
    Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
    Ok, I have done it. Now what?
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  5. #5
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    Quote Originally Posted by mathfun View Post
    Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
    1. I assume that the compasses open more than half of the distance between the points A and B.

    2. Draw circles around A and B with the utmost opening of the compasses. These 2 circles have to intersect in 2 points P and Q.

    3. The midpoint of PQ is the midpoint of AB too. Can you finish the construction now?
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  6. #6
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by earboth View Post
    Can you finish the construction now?
    If not, we can repeat the procedure recursively, right (between A/B and midpoint of AB)?
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  7. #7
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    Quote Originally Posted by alexmahone View Post
    If not, we can repeat the procedure recursively, right (between A/B and midpoint of AB)?
    Correct!

    It is only necessary that the 2 circle-lines intersect so that you can construct midpoints between midpoints between ...
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