Article révisé par les pairs
Résumé : An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328ℓ2 points in the plane contains an empty pentagon or ℓ collinear points. This is optimal up to a constant factor since the (ℓ - 1) x (ℓ - 1) square lattice contains no empty pentagon and no ℓcollinear points. The previous best known bound was doubly exponential.