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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
VividD
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Chume
  • 23
  • related http://math.stackexchange.com/questions/190914/do-circles-divide-the-plane-into-more-regions-than-lines – VividD Apr 28 '15 at 00:30

1 Answers1

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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.

kmbrgandhi
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  • Thank you. I had arrived at the equation C_n= n*(n-1)+2 and was having a hard time finding a source to confirm it. – Chume Mar 04 '14 at 03:35