The Pythagorean Theorem - Educational Outreach

4.2) Pythagorean Magic SquaresA magic square is an array of counting numbers(positive integers) geometrically arranged in a square.Figure 4.2 shows a 4X4 magic square. Where is the magicin this square?1 15 6 128 10 3 1311 5 16 214 4 9 7Figure 4.2: Pure and Perfect 4X4 Magic SquareAnswer: if one adds the four numbers in any one row, anyone column, or along any one of the two diagonals—totaling10 different ways—one will obtain the same number 34 foreach sum so done, called the magic sum.Normal or Pure Magic Squares are magic squares where thenumbers in the little squares are consecutive countingnumbers starting with one. Perfect 4X4 Magic Squares aremagic squares having many additional four-numberpatterns that sum to 34 , such as the four corners of anysmaller square embedded in the 4x4 square. Figure 4.3depicts a sampling of four-number patterns that sum to 34for the magic square shown in Figure 4.2.141