Magic Squares

The Lo Shu

The Lo Shu




How can a square be magic?  Its symmetry has an aesthetic appeal, and the shape is useful for everything from sock drawers to houses to game boards.  But when you create a square table with equal rows and columns of carefully chosen numbers, that square takes on unusual properties that for some hold sacred meaning, for others a research tool in Number Theory, and for others a pleasant diversion on a rainy afternoon.  A Magic Square is an array of cells in three rows and three columns, each containing a non-negative integer, such that the sum of each column, each row, and both of the main diagonals is the same; the magic constant or the magic number.1,2 The number of rows or columns is called the order, or N, and since the numbers are a sequence from 1 to , we can write a formula to calculate the magic constant as: or more simply: 3 The square remains magic under each of eight transformations: rotations through multiple degrees of 900, including zero, and the complementary mirror images.

Magic Squares






About gblakney

Middle School Mathematics Teacher, passionate EdTech user who loves to experiment with new methods and tools in the classroom. Following the lead of Dan Meyer and Jo Boaler, I create a safe place for kids to discover the fun and beauty of maths. I use Number Talks and Groupwork to make maths accessible for all of my students. I enjoy Mathematics and I'm enthusiastic about teaching; the kids really respond to that.
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