Magic squares
Have you ever seen a magic square? At one time, people gave all kinds of
meanings to magic squares. But of course there is nothing really magic
about them. They are just a special arrangement of numbers.
To the left is a magic square that someone in China figured out
thousands of years ago. When you add up any three numbers across, or
down, or diagonally (slantwise), you always get the same answer! Try it
and see.
Below is a different kind of magic square. To use this square, pick any
number in it—say 5. Cross out, or cover up, all the numbers above
and below it, and to the right and left of it.
Next, pick any number that is left—let’s say 9. Now cover up the
numbers above and below, and to the right or left of the 9.
Now you have three numbers left—1, 5, and 9. Add them up and you’ll
see that they total 15. No matter what number you start with, you’ll
always end up with three numbers that total 151 Try it a few times and
see.
The magic square above is a famous one by the German artist Durer. It is
only a small part of a large picture. But this magic square is more
marvelous than most. With all magic squares, you can add up the numbers
across, down, or diagonally and the total is the same—in this case 34.
But this is only the beginning. Look at some of the other ways you can
get 34.
The numbers in the four corners total 34. The four numbers in the center
add up to 34. The two middle numbers in the top row, 3 and 2, and the
two middle numbers in the bottom row, 15 and 14, total 34. The two
numbers in the middle of the first column (5 and 9) and the two in the
middle of the last column (8 and 12) add up to 34. And the four numbers
in each quarter—such as 16, 3, 5, and 10—total 34!
Why did Durer pick the number 34 for his magic square? We can’t be sure,
but there is something very curious about it. He made the engraving when
he was 43 years old. This was in the year 1514. Look at the date. Take 1
from 5 and you get 4. Take 1 from 4 and you get 3. So, you get the
number 43—the same as his age. Turn 43 around and you get—34!
