The dissection of rectangles into squares

We consider the problem of dividing a rectangle into a finite number of non-overlapping squares, no two of which are equal. A dissection of a rectangle R into a finite number n of non-overlapping squares is called a squaring of R of order n; and the n squares are the elements of the dissection. The term “elements” is also used for the lengths of the sides of the elements. If there is more than one element and the elements are all unequal, the squaring is called perfect, and R is a perfect rectangle.