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
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.