A set of
magic circles is a numbering of the intersections of the circles such that the sum over
all intersections is the same constant for all circles. The above sets of three and
four magic circles have magic constants 14 and 39 (Madachy 1979). For circles, the constant is , for , 2, ... corresponding to 3, 14, 39, 84, 155, 258, ... (OEIS
A027444).

Another type of magic circle arranges the number 1, 2, ..., in a number of rings, which each ring containing the same
number of elements and corresponding elements being connected with radial lines.
One of the numbers (which is subsequently ignored) is placed at the center. In a
magic circle arrangement, the rings have equal sums and this sum is also equal to
the sum of elements along each diameter (excluding the central number). Three magic
circles using the numbers 1 to 33 are illustrated above.