Arrangements of lines with a minimum number of triangles are simple (Q1100442)

The author proves the following conjecture of \textit{B. Grünbaum} [Arrangements and spreads. Providence, R. I.: American Mathematical Society (AMS) (1972; Zbl 0249.50011)]: Any arrangement of \(n\) (straight) lines in the real projective plane defining exactly \(n\) triangular faces, the minimum possible number, is a simple arrangement. The proof runs by contradiction showing that any nonsimple arrangement of \(n\) (pseudo-)lines with \(n\) triangular faces necessarily contains a configuration which is not realizable by straight lines. In fact (as already known) the assertion is not true for arrangements of pseudolines.