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Magic squares

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Magic squares.


As a topic for Mathematics Internal Assessment, I chose magic squares.

First thing that is impressive is its name. It seems like there is a mystery

and actually, there is. Even sometimes, I have faced with these magic squares in

different situations and I wonder, “How they’re created?” “Why are they

created?” “Do they have any relations with real life?” or “Is it useful in

different areas?”. Magic squares are the

combination of math, myth and magic. In addition, one reason why I chose this

topic is that because it seems mysterious and I think there are some things to

investi­gate and reveal. It may seem like basic topic but it has deep history

and other roots. My aim is to find, analyse, explain those mysteries, go deep

as much as I can and try to give this information to you.

We can find enough information about the history of those magic squares”,

which are also transformed into magic cubes. If we look at roots of magic

squares, it takes us back to 2800 B.C China.

There was a river called “Lo River”. And its flood has destroyed many

crops in that area. In those years, people really believed that there was a

river god and they decided to give something to god in order to make him calm.

When the river flooded there always were a turtle that walked around, and one

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day a child found out a drawing under the turtle. These pattern was 3 by 3

square and the sum of the numbers of dots were same for each column, diagonal

and row was equal. It was called Lo Shu Square.

In addition to this the oldest magic square was found in India nearly in

12th century, and this was 4 x 4 square.

The sum for each row, column and interestingly diagonals(no matter how)

the sum is 34.

Magic squares are squares that include

different numbers from 1 to n2 and here n is numbers of rows (or we

can say columns, they have to be equal). For example if the square is 5 x 5 the

greatest number in the square can be

. If we call

the sum as M, then


is directly related with sum of numbers in a sequence. For example, the sum of

1, 2, … , n2

There are not lots of ways to

construct these magic squares. Until today, three general ways are invented to

create magic square. By adding two preliminary squares, by bordering method and

by making composite magic squares we can create that. There are some different

specific ways for different situations like if n is odd or even.


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