tree-planting problem

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n, k) straight rows with k trees in each row. The problem of finding the maximum number of lines of three points for n points is due to Sylvester . The following table gives max_k(r(n, k)) for various k and n.

configuration | Euclid's orchard | Grünbaum-Rigby configuration | orchard visibility problem | Sylvester's line problem | visible point