
Here is Ben Franklin's famous magic circle. Some of its
properties:
Each radius (including the center entry) sums to 360, as does each
annulus
(again, only if one includes the center too). Franklin has also
highlighted
20 "excentric" annuli, each of which, together with the central 12,
sums
to 360. He also refers to 28 half-magic half-annuli; these and other
nifty
properties are described in my paper, "The Lost Squares of
Dr. Franklin"
(Amer. Math. Monthly, June-July 2001). There you will find
the first
published construction of the magic circle, as well as the first
publication
of Franklin's handwritten correction to James Ferguson's printed
description.
The graphic here is taken from Sparks, and it preserves a couple of
his typos. The corrected version can be found in my paper, and I will
post that on this page soon.