Whats So Magical About Magic Squares?
All your troubles would be over if you had a magic square! At least that’s what people believed long ago in China, India, Greece, and Rome. A magic square is an arrangement of numbers in the shape of a square. The numbers are arranged so that the sum of each horizontal row, each vertical column, and each diagonal line are all eq
COPYRIGHT 2002 Cobblestone Publishing, Co. A magic square is a square array of numbers in which the values of each row–horizontal, vertical, and diagonal–add up to the same sum. Read on to see what makes them special. Orders and Magic Constants A magic square’s order is the number of cells in each row. For example, a 3-by-3 (or 3×3) magic square is order-3. Mathematicians trace an order-3 magic square back to ancient China (see “Animal Angles,” p. 49), Babylonia, and Mayan culture. Some cultures have even treated magic squares as having mystical or religious powers. The magic constant is the sum of each row’s values. For a magic square of consecutive natural numbers (counting numbers) starting with 1, let n equal the magic square’s order and C equal the magic constant. Then, for example, for an order-3 magic square starting with 1, C = [n([n.sup.2] + 1)]/2 = [3(9 + 1)1/2 = 3(10)/2 = 30/2 = 15. Some people use a broad definition of magic squares so that the magic square values don’t h
” pg. 13 • Magic squares may seem like mathematical madness, but anyone who knows the rules can produce them. Explore the history of this ancient pastime and discover the shortcuts that make constructing them a little less magical. • Vocabulary, Deductive Reasoning “Magic Square Mix-Up” (Brain Strain) pg. 17 • Help Susie rebuild her magic square and save her cat from a scolding. Stuck? Reread the prior article! • Following Directions, Inductive Reasoning “Tesseracts: Cubes Get Hyper,” pg. 18 • Author Madeleine L’Engle uses tesseracts for space travel in her novel A Wrinkle in Time. Although "real" tesseracts may not serve as transportation, these four-dimensional hypercubes are a "trip" nonetheless. • Spatial Relations, Extrapolation “John Hendricks: Math Magician” (People to Discover) pg. 19 • He worked as a meteorologist and as a forest ranger, but even after nearly perishing in a forest fire, John Hendricks was grateful that his math notes didn’t burn. Hendricks look
