Magic Squares *
Areas of Science 
Pure Mathematics 
Difficulty  
Time Required  Average (610 days) 
*Note: This is an abbreviated Project Idea, without notes to start your background research, a specific list of materials, or a procedure for how to do the experiment. You can identify abbreviated Project Ideas by the asterisk at the end of the title. If you want a Project Idea with full instructions, please pick one without an asterisk.
Abstract
A magic square is an arrangement of numbers from 1 to n^{2} in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an algorithm for constructing a Magic Square? Can you show that the sum of the entries of any row, column, or main diagonal must be n(n^{2}+1)/2? Are there any other hidden properties of a Magic Square? Show the differences between special instances of the Magic Square, like the Lo Shu, Durer, Ben Franklin, or Sator Magic Squares. Can magic squares be constructed in 3 dimensions? You can also investigate other shapes, like magic circles and stars (Alejandre, 2006; Pickover, 2002). Or test the question, "Is there really no math in Sudoku?" (Hayes, 2006)Share your story with Science Buddies!
Yes, I Did This Project! Please log in (or create a free account) to let us know how things went.Cite This Page
General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.MLA Style
Science Buddies Staff.
"Magic Squares." Science Buddies,
22 Jan. 2019,
https://www.sciencebuddies.org/sciencefairprojects/projectideas/Math_p036/puremathematics/magicsquares.
Accessed 14 Nov. 2019.
APA Style
Science Buddies Staff.
(2019, January 22).
Magic Squares.
Retrieved from
https://www.sciencebuddies.org/sciencefairprojects/projectideas/Math_p036/puremathematics/magicsquares
Last edit date: 20190122
Bibliography
 Hayes, B., 2006. "Unwed Numbers: The mathematics of Sudoku, a puzzle that boasts "No math required!" American Scientist Online: Vol 94, number 1, page 12. [accessed: 5/1/06] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.669.9080&rep=rep1&type=pdf
 Pickover, C. A., 2002. The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions. Princeton, NJ: Princeton University Press.
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Note: A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed
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