Magic Square

Pronunciation: /ˈmædʒ.ɪk skwɛər/ Explain
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[2][3]. 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. McAdams, David E.. All Math Words Dictionary, magic square. 2nd Classroom edition 20150108-4799968. pg 112. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Euler, Leonhard. Translated by Jordan Bell. On Magic Squares. Translated by Jordan Bell. Petersburg Academy. Last Accessed 9/2/2018.
  3. Hermann Schubert. Mathematical Essays and Recreations. Translated by Thomas J. McCormack. The Open Court Publishing Company, Chicago. Last Accessed 9/2/2018. Buy the book
  4. magic square. Encyclopedia Britannica. Merriam-Webster. Last Accessed 9/2/2018. square. Buy the book

More Information

  • Dörmann, Michael. A Perfect Magic Square. 3/12/2009.

Cite this article as:

McAdams, David E. Magic Square. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/2/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/18/2009: Added "References". (McAdams, David E.)
9/17/2008: Initial version. (McAdams, David E.)

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