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i have found a formula for the number of regions created by n lines. The only condition is that no three lines are concurrent. Parallels are permitted. The formula is R=1+n+p where n is the number of lines and p is the number of points created by these n lines. Can someone show me how to prove this formula? Maybe with a proof by induction on l or with a sweep-line argument. Can someone explain me in detail how a proof containing a sweep-line argument works?

Schubertliszt
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  • Not true, consider three lines that intersect in the same point. – naslundx Aug 25 '16 at 14:18
  • but i said no three lines are concurrent – Schubertliszt Aug 25 '16 at 14:19
  • Ah, sorry, my bad. – naslundx Aug 25 '16 at 14:20
  • I've closed this as duplicate since that other question does have understandable proofs of the formula. If you prefer you can edit this question here to focus on this sweep-line idea of yours, and write a comment containing @MvG and asking for it to be reopened. But in that case please include more details on the expected outline of the proof, and what parts you find missing. (I actually wasn't aware that I had gained the power to close duplicates all by myself. Any other users disagreeing with that decision, please let me know.) – MvG Aug 26 '16 at 09:40

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