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[parent] Franklin magic square (Example)

One day in 1771, Benjamin Franklin, tired of hearing political debates, amused himself by creating the following magic square, now called a Franklin magic square:

$\displaystyle \begin{bmatrix} 52 & 61 & 4 & 13 & 20 & 29 & 36 & 45 \ 14 & 3 &... ... & 18 & 31 & 34 & 47 \ 16 & 1 & 64 & 49 & 48 & 33 & 32 & 17 \ \end{bmatrix}$

The magic constant is 260. Furthermore, half any row or column (positions 1 to 4 or 5 to 8) equals half the magic constant. Two centuries later, Joseph Madachy realized that some half diagonals from the corner to the center also give 260.

Some other 8 by 8 magic squares with these properties are also called Franklin magic squares.



"Franklin magic square" is owned by CompositeFan.
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Other names:  Franklin square

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Cross-references: properties, center, diagonals, column, row, magic constant, magic square, Benjamin Franklin
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This is version 1 of Franklin magic square, born on 2006-11-16.
Object id is 8563, canonical name is FranklinMagicSquare.
Accessed 1019 times total.

Classification:
AMS MSC05B15 (Combinatorics :: Designs and configurations :: Orthogonal arrays, Latin squares, Room squares)
 01A50 (History and biography :: History of mathematics and mathematicians :: 18th century)

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