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magic circle

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.

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This page © 2001 Paul C. Pasles