A Magic Square is a square grid
arrangement, where each square is filled with a number such that each column,
each row and both diagonals sum to the same number. In the case of the magic square shown above each
row, each column and each diagonal sums to 15.
The grids do not have to have consecutive numbers (like the example
above) but they do have to have different numbers in each square. The square grids can be of different sizes:
3x3, 4x4, 5x5, etc.

The Lo Shu magic square is the oldest
know magic square, discovered in Chinese literature date to about 650 B.C. It is basically the same magic square as the
one shown above.

Many magic squares have been created
that have additional properties. They
may be created with just prime numbers, or us multiplication instead of
addition, or have multiple magic squares inside the main magic squares.

Magic squares were popular evening
entertainment years ago (before radio, TV and the internet). Benjamin Franklin (the $20 bill guy) created
many magic squares with additional properties.
In fact there is a recently published book about Benjamin Franklin and
his magic squares: “Benjamin Franklin's Numbers” by Paul C. Pasles. (This would be a good place of an Amazon.com
add to make a little change.)

The largest magic square that I have
found was a 3559 x 3559 magic square created by Peter Weber and Tassilo Herbig
in Germany in 2012. (I won’t reprint it
here. That magic square requires
12,666,481 different numbers!) The largest
magic square that I am aware of that was created by hand was a 1111 x 1111
magic square created by Norbert Behnke, also from Germany, in 1990. This magic square only requires 1,234,321
different numbers.

My personal favorite magic squares is a
13 x 13 magic square that contains 12 other magic squares inside it (well
almost – I think one diagonal did not add up to the correct number in one of
the smaller magic squares, and a 3 x 3 alphamagic square the was created by the
MBIOM faculty, staff, and student that we believe is the first alphamagic
square to use Pig Latin (I will explain some of the newer special versions soon
in other posts.

REFERENCES:

David

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