In mathematics, a Costas array can be regarded geometrically as a set of "n" points, each at the center of a square in an "n"×"n" square tiling such that each row or column contains only one point, and all of the "n"("n" − 1)/2 displacement vectors between each pair of dots are distinct. This results in an ideal "thumbtack" auto-ambiguity function, making the arrays useful in applications such as sonar and radar. Costas arrays can be regarded as two-dimensional cousins of the one-dimensional Golomb ruler construction, and, as well as being of mathematical interest, have similar applications in experimental design and phased array radar engineering.