When a Magic Square Is Not Square
Seymour S Block, Santiago A Tavares · 2009
Abstract The magic triangle shown in Figure 6.1 is presented by Mochalov [105]. It is constructed with the numbers 1, 2, 3, ... , 9. The four magic triangles shown in Figure 6.2 are constructed with the numbers 1, 2, 3, 4, 5, and 6. Each triangle has a different magic number, as can be verified by adding each number along each side of each triangle. When is a square nota square? When itis a rectangle? After all, a rectangle is a square that has grown too much in one dimension. If we can have magic squares, why notmagic rectangles? A magic rectangle is defined as an array of rc integers, where r is the number of rows and c the number of columns, with the following properties (Jelliss [103], Nakamura [106]):