What is the equation for the maximum number of regions into which N circles can partition a plane? Is there a name for this equation?
A single circle partitions the plane into two regions, inside and out.
First few outputs:
- 1 circle 2 regions
- 2 circles 4 regions
- 3 circles 8 regions
- 4 circles 14 regions
The equation is $C_{n} = n^2 - n + 2$. See here: http://mathworld.wolfram.com/PlaneDivisionbyCircles.html.
I don't know a specific name for this, but I assume "Plane Division by Circles Equation" might work.
If you want me to prove why this equation is correct, let me know.