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Mathematics Experiment #9

Order Out of Chaos?

On two arbitrary linesl1 and l2 select six points P1,...,Q3 at random, three on a line. Then draw P1Q2, P2Q1, P1Q3, P3Q1, P2Q3, and P3Q2. What do you notice? Is there any pattern?

 





Is this true in other cases? Try at least twenty different random configurations of lines and points.