# Magic Square

Science EncyclopediaScience & Philosophy: *Macrofauna* to *Mathematics*

Magic **square** is an unusual numerical configuration containing consecutive **integers** in arrangements so that the sum of numbers in any row, column, or diagonal are identical. Such squares were known approximately 4,000 years ago in China.

The basic magic square is a square containing consecutive integers starting with number 1. Three of the basic magic squares are shown in Table 1.

2 | 9 | 4 | 12 | 7 | 9 | 6 | 9 | 2 | 25 | 18 | 11 | ||

7 | 5 | 3 | 13 | 2 | 16 | 3 | 3 | 21 | 19 | 12 | 10 | ||

8 | 11 | 5 | 10 | 22 | 20 | 13 | 6 | 4 | |||||

6 | 1 | 8 | 1 | 14 | 4 | 15 | 16 | 14 | 7 | 5 | 23 | ||

15 | 8 | 1 | 24 | 17 |

Other magic squares can be constructed by starting with one of the basic squares shown above and adding the same whole integers to each integer; equals added to equals, the sums are equivalent. Likewise subtracting the same value from each integer can result in other magic squares. In a similar manner, **multiplication** or **division** can be used to create other magic squares.

A general equation for constructing basic magic squares is:

where X equals the sum of integers in any row, column, or diagonal, and n equals the number of rows.

Jeanette Vass

## Additional topics

- Magic - Magic, Religion, And Science, The Functions And Effects Of Magic In Classic Anthropological Works
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