On some extremal problem in discrete geometry - Florek, Jan (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2011)
Let p, q, rbe any three lines in the plane passing through a common point and suppose that O, P, Q, Rare any four collinear points such that P∈ p, Q ∈ q, R ∈ r, Pand Rare harmonic conjugates with respect to Oand Q(that is, │OP│/ │PQ│= │OR│/│QR│). For every k ≥2, we construct a set Xnof n= 4kpoints, which is distributed on the lines p, q, r, but each element of XnᵕO is incident to at most n/2 lines spanned by XnᵕO.
Mathematical Economics, 2011, Nr 7 (14), s. 65-70
Keywords: Dirac-Motzkin conjecture; Desargues' theorem