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This drawing shows a few lines connecting a few points such that each two lines intersect
each other exactly once - when one counts common endpoints
as intersections.
Can one have more lines than points in this way? In this case the number is the same: there are six points and six lines. And in this case it is not possible to add a line between two points which intersects all other lines just once! (Try it) This problem is known as John Conway's Thrackle Problem. A short write-up explains most of what is known about it! (Additions, anyone?) |