The document discusses research conducted on the maximum and minimum number of intersections between lines and between vertical planes. It presents formulas to calculate the minimum and maximum number of intersections for a given number of lines N. The minimum is 1 intersection, while the maximum is (N-1)N/2 intersections. It then generalizes this concept to vertical planes in 3D space, showing the same formulas apply by treating the planes as lines. Examples are given to illustrate the formulas.