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Thread: Points and line segments

  1. #1
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    Points and line segments

    Draw 6 points on a plane. Can you connect each of them with 4 other points, in such a way that the line segments do not intersect?
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    Re: Points and line segments

    Quote Originally Posted by Alderamin View Post
    Draw 6 points on a plane. Can you connect each of them with 4 other points, in such a way that the line segments do not intersect?
    You are looking for a planar graph of order six in which each vertex is of degree four.
    Good luck. Tell us what you find.
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    Re: Points and line segments

    I think I got it. Thanks for the help.Points and line segments-geometry-6.jpg
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    Re: Points and line segments

    Quote Originally Posted by Alderamin View Post
    I think I got it. Thanks for the help.Click image for larger version. 

Name:	geometry-6.jpg 
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    well damn...

    nicely done. Did you come up with that yourself?
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    Re: Points and line segments

    Quote Originally Posted by Alderamin View Post
    I think I got it. Thanks for the help.Click image for larger version. 

Name:	geometry-6.jpg 
Views:	2 
Size:	36.9 KB 
ID:	36771
    Yes, well done indeed. This exercise is getting you ready to be asked if $\bf{K}_6$ is planar?
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    Re: Points and line segments

    Quote Originally Posted by romsek View Post
    well damn...

    nicely done. Did you come up with that yourself?
    No, I followed Plato's hint.
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    Re: Points and line segments

    Quote Originally Posted by Plato View Post
    Yes, well done indeed. This exercise is getting you ready to be asked if $\bf{K}_6$ is planar?
    Yes, if I understood well, it is planar, since "it can be drawn on the plane in such a way that its edges intersect only at their endpoints" (wiki).
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