00:01
Okay, so here we want rn to be the number of regions in a plane divided by n lines.
00:17
Okay, so for example, if we have a plane and we have, say, three lines, there are some rules here, right? so the lines, more than two of them, cannot intersect and two cannot be parallel.
00:30
And that sort of guarantees that when you add your nth line, so we're going to add an nth line here.
00:44
This nth line, since it cannot be parallel or go through a same point, it's forced to pass through n regions, right? so here was region 1, region 2, region 3, and region 4, and that was our fourth line.
01:00
So it took four regions and split it in half, meaning every line we add is going to add n regions.
01:07
So that means r of n is equal to the previous number of regions plus n.
01:16
Right, because in this instance we were able, we added our fourth line, and in doing so, we created four new regions.
01:26
Okay, now we consider case there's no lines, so in our plane, that would give us just one large region.
01:35
So this is our part a finding the recurrence relation...