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{{Short description|Set of marks on a 2d square grid such that no two pairs of marks are the same distance apart}}
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In mathematics, a '''Costas array''' can be regarded [[geometry|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 (vector)|displacement]] [[Euclidean vector|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.
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