A circle arrangement is a configuration of circles in the plane. One enumeration considers distinct, unlabeled circles of arbitrary positive radii, with no tangencies and no point belonging to three circles. Each pair is therefore disjoint or meets in two points. Two configurations are equivalent when one can be continuously deformed into the other while the curves remain circles, without creating or removing intersections or passing a circle through an intersection point. Reflection of the whole configuration is also allowed (OEIS A250001; Numberphile 2019).
For 
,
1, 2, 3, 4, the numbers of arrangements under this convention are 1, 1, 3, 14, 173,
respectively (OEIS A250001). For two circles,
the three possibilities are external disjointness, two-point intersection,
and one circle inside the other. These count distinct
arrangements, not the regions within a single arrangement. In particular, the convention
does not require all possible membership regions of a Venn
diagram to occur.
