Magic Squares
What are Magic Squares?
Magic squares have intrigued people for centuries. In ancient times they were connected with the supernatural and the magical world. Archeological excavations have turned them up in ancient Asian cities. In fact, the earliest record of the appearance of magic square is about 2200 B.C. in China. I was called lo-shu.
Emperor and the Tortoise
Over four thousand years ago the Emperor Yu of China was standing on the banks of the Yellow River when he saw a tortoise. On its back was a magic square of numbers. The square was magic because, no matter which way the Emperor added up its lines, the numbers came to the same total.
In ancient China numbers were used in government and religious rituals. Can you make magic squares?
Some Properties of Magic Squares
Properties |
Examples from Emperor Yu's Magic Square |
| Each row, column, and diagonal total the same number | The Magic Number of Emperor Yu's Magic Square is 15 |
| Any two numbers that are equidistant from the center are complements. Numbers of a magic square are complements if their sum is the same as the sum of the smallest and largest numbers of a magic square. | This magic square has complements- 9 and 1, 3 and 7, 6 and 4, 8 and 2 |
| Any number may be either added or multiplied to every number of a magic square and it will remain a magic square. |  Here, we have multiplied every number in
Emperor Yu's magic square by two. The magic number is 30. |
| If two rows and two columns, equidistant from the center, are interchanged the resulting square is a magic square. |  Here, the first and last columns are reversed by it is still a magic square. |