It is well known that a circle cut by n chords gives at most (n^2 + n + 2 )/2 regions eg.
http://mathworld.wolfram.com/CircleDivisionbyLines.html
Questions:- How close to equal area regions can we achieve? ... For 1, 2 chords, equality is easily seen. But what about 3 chords (7 regions)? ... Can they be made all equal? There must be a smallest region and a biggest one. The interesting question is what is the Biggest Smallest region to Smallest Biggest region ratio and do they co-exist in the same construction or are there 2 distinct constructions, one for each?
If we consider the circle edge as a side we have:-
n=1 gives 2 x 2-gons (2 regions),
n=2 gives 4 x 3-gons ("triangles"),
n=3 gives 4 x 3-gons + 3 x 4-gons,
Is this decomposition unique? ... Is there a formula to give how many of each?
