Suppose I draw 20 circles in the plane, all passing through the origin, but no two tangent at the origin. Also, except for the origin, no three circles pass through a common point. How many regions are created in the plane?
Answer
A hint:
Move the origin to ∞ using the map z↦1z. Then the circles become lines, no two of them parallel, and no three of them going through the same point.
Denote the number of regions created by n lines by an, and find a recursion for the an.
Attribution
Source : Link , Question Author : laser01 , Answer Author : Christian Blatter
