🔖 Sylvester’s Problem, Steinberg’s Solution | Cut the Knot

Bookmarked Sylvester's Problem, Gallai's Solution (cut-the-knot.org)

T. Gallai's proof has been outlined by P. Erdös in his submission of the problem to The American Mathematical Monthly in 1943. Solution Given the set Π of noncollinear points, consider the set of lines Σ that pass through at least two points of Π. Such lines are said to be connecting. Among the connecting lines, those that pass through exactly two points of Π are called ordinary.