Magic Square

Pronunciation: /ˈmædʒ ɪk skwɛər/ ?
Magic square containing three rows and three columns of numbers. First row 2, 7, 6. Second row 9, 5, 1. Third row 4,3,8.
Figure 1: Normal magic square.
Image courtesy Sam Ley, St Louis, Missouri.

A magic square is a square matrix containing numbers such that the sum of any row, column, or diagonal is the same[1][2]. A magic square using the sequential numbers 1..n where n is the number of cells is called a normal magic square. Magic squares are believed to have been discovered in China about 4th century BCE. The 3x3 normal magic square was called 'Lo Shu' by the Chinese. Magic squares were known in ancient Egypt, India, and Arabia.


  1. Euler, Leonhard. Translated by Jordan Bell. On Magic Squares. Jordan Bell. Petersburg Academy, October 17, 1776. (Accessed: 2009-03-12).
  2. Hermann Schubert. Mathematical Essays and Recreations. Translated from German by Thomas J. McCormack. The Open Court Publishing Company, Chicago. (Accessed: 2009-12-18).
  3. magic square. Encyclopedia Britannica. (Accessed: 2009-03-12). square.

More Information

  • Dörmann, Michael. A Perfect Magic Square. 2009-03-12.

Cite this article as:

Magic Square. 2009-12-18. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2009-12-18: Added "References" (McAdams, David.)
2008-09-17: Initial version (McAdams, David.)

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