Science Projects

Magic Squares

195 reviews

Summary

Areas of Science

Pure Mathematics

Difficulty

Time Required

Average (6-10 days)

Credits

*Note: For this science project you will need to develop your own experimental procedure. Use the information in the summary tab as a starting place. If you would like to discuss your ideas or need help troubleshooting, use the Ask An Expert forum. Our Experts won't do the work for you, but they will make suggestions and offer guidance if you come to them with specific questions.

If you want a Project Idea with full instructions, please pick one without an asterisk (*) at the end of the title.

Abstract

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)

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. Retrieved 5/1/06.
Pickover, C. A., 2002. The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions. Princeton, NJ: Princeton University Press.

Ask an Expert

Do you have specific questions about your science project? Our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.

Post a Question

Careers

If you like this project, you might enjoy exploring these related careers:

Mathematician

Career Profile

Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more

News Feed on This Topic

, ,

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, 20 Nov. 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p036/pure-mathematics/magic-squares. Accessed 28 May 2023.

APA Style

Science Buddies Staff. (2020, November 20). Magic Squares. Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p036/pure-mathematics/magic-squares

Last edit date: 2020-11-20

Explore Our Science Videos

Underwater Color Bursts – STEM Activity