The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the...

In geometry, a Sylvester–Gallai configuration consists of a finite subset of the points of a projective space with the property that the line through any...

named after him: The Sylvester–Gallai theorem, on the existence of a line with only two of n given points. Sylvester–Gallai configuration, a set of points...

points of the set; this is the Sylvester–Gallai theorem. Because the Hesse configuration disobeys the Sylvester–Gallai theorem, it has no Euclidean realization...

configurations with this property are known as Sylvester–Gallai configurations due to the Sylvester–Gallai theorem that shows that they cannot be given...

two points. The Fano plane has no such line (that is, it is a Sylvester–Gallai configuration), so it is not realizable. A complete quadrangle consists of...

triples in the system. Sylvester matroids of rank three may also be formed from Sylvester–Gallai configurations, configurations of points and lines (in...

subspaces. Constant weight code Kirkman's schoolgirl problem Sylvester–Gallai configuration This property is equivalent to saying that (xy)y = x for all...

result is a consequence of the Sylvester–Gallai theorem, by an induction on the number of points. Let P be a configuration of n points in a projective plane...

OCLC 28661687. Nwankpa, Sonde Ndubeze (1970). Generalized Sylvester Gallai configurations. East Lansing, Michigan: Michigan State University. OCLC 25362816...

equivalent dual form about arrangements of lines. For instance, the Sylvester–Gallai theorem, stating that any non-collinear set of points in the plane...