Corpus ID: 16437438

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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