![]() Surprisingly, computer investigations show that Figure 2 is just one among 4,370 distinct 3 × 3 geomagic squares using pieces with these same sizes and same target. ![]() The target is a 4 × 4 square with an inner square hole. In Figure 2, for instance, the pieces are polyominoes of consecutive sizes from 1 up to 9 units. Here the 9 pieces are all decominoes, but pieces of any shape may appear, and it is not a requirement that they be of same size. ![]() The 3 pieces occupying each row, column and diagonal pave a rectangular target, as seen at left and right, and above and below. Hitherto interest has focused mainly on 2D squares using planar pieces, but pieces of any dimension are permitted.įigure 1 above shows a 3 × 3 geomagic square. By the dimension of a geomagic square is meant the dimension of the pieces it uses. Similarly, the eight trivial variants of any square resulting from its rotation and/or reflection are all counted as the same square. As with numerical types, it is required that the entries in a geomagic square be distinct. ![]() A geomagic square, on the other hand, is a square array of geometrical shapes in which those appearing in each row, column, or diagonal can be fitted together to create an identical shape called the target shape. A traditional magic square is a square array of numbers (almost always positive integers) whose sum taken in any row, any column, or in either diagonal is the same target number. Figure 1: A geomagic square with same-sized pieces ( decominoes)Ī geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. ![]()
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