1.1.3 Example C Consider a plane that has lying in it k nonparallel lines. Into how many sepa- rate compartments will the plane be divided if not more than two lines inter- sect in the same point? Let N be the number of compartments. Therefore, the (k+ 1)th line will be cut by the k previous lines in k points and, consequently, divides each of the k +1 prior existing compartments into two. This gives Nk+1 = Nk + (k +1). (1.15) Note for k = 0, No = 1, since the plane is then undivided. For k = 1, N1 = 2, because a single line divides the plane into two compartments, etc. %3D %3D %3D

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