8 Franklin Square

In search for Eight Franklin Square?

By now you may have found out that 8 Franklin Square does not exist. At least not on Franklin Square. “It’s not an address”, Robert Langdon revealed to Mal’akh.

Indeed, its a Magic Square, similar to the one he discovered on Albrecht Duerer’s engraving of “Melencolie”.

Magic squares received their name because there are so many relationships between the sums of the numbers filling the squares.

Benjamin Franklin was a scientist , an inventor, a statesman , a printer, a philosopher, a musician, and an economist. It is easy to see how a person of such diverse talents could have invented this interesting magic square.

Eight Franklin Square

“I was at length tired with sitting there to hear debates, in which, as clerk, I could take no part and which were often so unentertaining, that I was induc’d to amuse myself with making magicsquares or circles, or anything to avoid weariness.”

Benjamin Franklin Autobiography

In a letter to Peter Collinson he describes four properties of the 8 × 8 square F1 as follows:

     1. The entries of every row and column add to a common sum called the magic sum.

     2. In every half-row and half-column the entries add to half the magic sum.

     3. The entries of the main bent diagonals and all the bent diagonals parallel to it add to the magic sum.

     4. The four corner entries together with the four middle entries add to the magic sum.

of the Department of Mathematics, University of California, Davis, in this work is defined 8 × 8 Franklin squares to be squares with nonnegative integer entries that have the properties listed by Benjamin Franklin and the additional property that every 2 × 2 subsquare adds to one-half the magic sum. The 8 × 8 squares constructed by Franklin have this additional property (this might be one of the unstated curious properties to which Franklin was alluding in his letter). It is worth noticing that the fourth property listed by Benjamin Franklin becomes redundant with the assumption of this additional property.

Franklin mentions that the square has five other curious properties but fails to list them.

In Paul Pasles of the Department of Mathematical Sciences, Villanova University, Pennsylvania says: “… readers of the Autobiography may recall the passage wherein, bored with proceedings at the Assembly, Franklin says he drew “magic squares or circles” to occupy his mind. Van Doren’s Pulitzer-prize winning biography Benjamin Franklin goes into greater detail. It includes an account of visits to the home of James Logan, with whom Franklin perused several mathematical classics. The first of these volumes was Frenicle de Bessy’s encyclopedic listing of the 4 by 4 magic squares (all 880 of them!) …”

Is of highlighting that the additional property confers to the 8 x 8 Franklin squares the structure a (alpha) of Frenicle for the 4 x 4 magic squares .-

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