# Observations and Computations in Sylvester-Gallai Theory

@inproceedings{Lenchner2005ObservationsAC, title={Observations and Computations in Sylvester-Gallai Theory}, author={Jonathan Lenchner and Herv{\'e} Br{\"o}nnimann}, booktitle={CCCG}, year={2005} }

We bring together several new results related to the classical Sylvester-Gallai Theorem and its recently noted sharp dual. In 1951 Dirac and Motzkin conjectured that a configuration of n not all collinear points must admit at least n/2 ordinary connecting lines. There are two known counterexamples, when n = 7 and n = 13. We provide a construction that yields both counterexamples and show that the common construction cannot be extended to provide additional counterexamples.

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