# Magic Squares *

***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*, 28 July 2017, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p036/pure-mathematics/magic-squares. Accessed 19 Oct. 2018.### APA Style

Science Buddies Staff.
(2017, July 28).

*Magic Squares.*Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p036/pure-mathematics/magic-squaresLast edit date: 2017-07-28

## Bibliography

- Alejandre, S., 2006. "Magic Squares," The Math Forum, University of Drexel School of Education. [accessed: 5/1/06] http://mathforum.org/alejandre/magic.square.html
- 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.

## News Feed on This Topic

*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

## 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.## Ask an Expert

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, 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.Ask an Expert

## Related Links

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

### Mathematician

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### Math Teacher

Math teachers love mathematics and understand it well, but much more than that, they enjoy sharing their enthusiasm for the language of numbers with students. They use a variety of tools and techniques to help students grasp abstract concepts and show them that math describes the world around them. By helping students conquer fears and anxieties about math, teachers can open up many science and technology career possibilities for students. Teachers make a difference that lasts a lifetime! Read more## News Feed on This Topic

*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

## Looking for more science fun?

Try one of our science activities for quick, anytime science explorations. The perfect thing to liven up a rainy day, school vacation, or moment of boredom.

Find an Activity