Roberts's triangle theorem

Roberts's triangle theorem, a result in discrete geometry, states that every arrangement of ${\displaystyle n}$ lines, with no parallel lines and no crossings of more than two lines, has at least ${\displaystyle n-2}$ triangular faces. Thus, three lines form a triangle, four lines form at least two triangles, five lines form at least three triangles, etc. It is named after Samuel Roberts, a British mathematician who published it in 1889.