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In this paper, it is shown that by arranging the elements of a beam-scanning planar antenna array in a triangular pattern rather than a rectangular pattern, the number of elements needed in the array is reduced. (The number of elements needed in an array is determined from the requirement that no spurious beams form in the array pattern.) The reduction in the number of elements depends upon the solid angle over which the main beam is positioned. If the main beam is positioned within a constant angle about the array normal, then the number of elements can be reduced by 13.4 per cent by arranging the elements in a pattern of equilateral triangles rather than in a square pattern. If the main beam is positioned within a "pyramid," centered about the array normal, then the reduction is usually less than 13.4 per cent. Graphs are included showing for both element arrangements the solid angle over which the main beam can be scanned without the formation of spurious beams.