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In Euclidean geometry, is there some set of lines in s.t. there are at least 2 intersections, but every intersection contains at least 3 lines, and no lines in the set are parallel?

I tried for a long time to construct this by hand but couldn't find a way, so I'm looking for a construction or a proof that one doesn't exist.

Thanks!

simonzack
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  • Interesting problem. I am curious, what led you to it? Although tagged (euclidean-geometry), it might help clarify the problem if you state explicitly that you are talking about lines in the Euclidean plane (if that is the case). – Jonas Meyer Nov 30 '13 at 09:54
  • Thanks, I've updated my post, what led me to it wasn't anything interesting, it was just something I thought of when I tried to find the maximum intersection of n lines. – simonzack Nov 30 '13 at 10:19

1 Answers1

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This is not possible. See the Sylvester-Gallai theorem and in particular Melchior's proof.

WimC
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