3 part question here. In terms of n, what is the maximum amount of regions that can be made by overlapping n circles? Does circle size count? Do both of the answers to the previous questions correlate with regular polygons as well?
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What do you mean by "sections" ? Arcs or regions ? – Jean Marie Sep 08 '17 at 19:40
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Meaning regions, sorry if that was unclear – Mathematica Extrordinaire Sep 08 '17 at 19:50
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The reference I just gave deals with your first question. I think that, if you have thick borders, the answer to your second question is clearly "at most the answer of Question 1". Regarding your last question about (regular ?) polygons, I think that you have to treat separately overlapping (equilateral) triangles, overlapping squares, etc... I do not have references for that. – Jean Marie Sep 08 '17 at 20:14