Suppose that n straight lines in the plane are positioned so that no two are parallel an no three pass throught the same point. Show that they divide the plane into 1/2(n^2 + n + 2) distinct regions.
First we prove that how many distinct regions will be created if the n+1th line show up in the plane where there are n lines exist already.
That's will be easy to find that there will be n+1 distint regions created if the n+1th line show ...
A proof linking lines, planes and regions is provided.