Magic Squares *
AbstractA 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)
Cite This Page
Last edit date: 2017-07-28
- 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
Ask an ExpertThe 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
If you like this project, you might enjoy exploring these related careers:
MathematicianMathematicians 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 TeacherMath 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
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