A single line divides a plane into two regions. Two lines (by crossing) can divide a plane into four regions, three lines can divide it into seven regions. Let psubn be the max number of regions into which n lines divide a plane where n is a positive integer.© BrainMass Inc. brainmass.com February 24, 2021, 2:06 pm ad1c9bdddf
In order for n lines to divide the plane into a maximum number of regions first any of the lines is parallel to another and no three of them intersect at the same point. Let R(n) ...
This shows how to find the max number of regions divided in a plane.