Claims

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1951_05_01_motzkin: Motzkin proves that n points in the plane, not all on a line, determine a number of ordinary lines that tends to infinity with n, answering the first question.

1958_01_01_kelly_moser: Kelly and Moser prove that n points in the plane, not all on a line, determine at least 3n/7 ordinary lines, a bound attained at n equal to 7.

1993_02_01_csima_sawyer: Csima and Sawyer prove that n points in the plane, not all on a line, determine at least 6n/13 ordinary lines once n is at least 8.

2012_08_23_green_tao: Green and Tao determine the least number of ordinary lines spanned by n points, not all on a line, for all large n: n/2 for even n and 3 times the floor of n/4 for odd n, both attained, proving the Dirac-Motzkin conjecture.

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