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Suppose we have $n$ lines in the plane. What is the maximum size of an "open convex polygon" that we can get from the intersection of lines?

For example, in the following picture, we can see an "open" triangle coming from the intersection of three lines.

Any hint would be appreciated. enter image description here

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Ken
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  • What is your definition of "general position"? Whatever it is, that should be edited into your question. – quasi Sep 17 '18 at 02:27
  • @quasi: I'm sorry, it means there are no parallel lines. – Ken Sep 17 '18 at 02:28
  • Actually, I do not that condition. So I will delete it. – Ken Sep 17 '18 at 02:30
  • Also, in your example image, I don't see a triangle. – quasi Sep 17 '18 at 02:32
  • The middle region is an open triangle, 3 sided! – Ken Sep 17 '18 at 02:34
  • If it is "lines" and no segments then the area should be $\infty$. If it is finite segments of the same length then the regular polygon would do the job. You mean something else? – dmtri Sep 17 '18 at 03:04
  • @dmtri: I mean line (unbounded). and yes the area is $\infinity.$ I wanted to know how many sides an open convex polygon could have? – Ken Sep 17 '18 at 03:07

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