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 90^{0}, including zero, and the complementary mirror images.

Magic Squares

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## 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.