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Magic Squares *

Time Required Average (6-10 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.


A magic square is an arrangement of numbers from 1 to n2 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(n2+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)

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Science Buddies Staff. "Magic Squares" Science Buddies. Science Buddies, 30 June 2014. Web. 20 Oct. 2014 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p036.shtml>

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Science Buddies Staff. (2014, June 30). Magic Squares. Retrieved October 20, 2014 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p036.shtml

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Last edit date: 2014-06-30


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