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Simply put, a rectangle is the easiest shape to cut versus some other layout such as circles or pentagons. Bills are printed on large sheets of paper in a grid layout, which allows them to be cut apart mechanically with no waste paper.

As far as being rectangular versus square, a rectangular layout means it's easier to orient bills in stacks because they can only be oriented in one of two directions as opposed to four, which simplifies sorting and counting.

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