The ancient Egyptians had a measure for the diagonal of a one cubit square (the double remen). They knew that the area of a square on the double remen was twice the area of the one cubit square and they used the diagonal measure to double the area of a square while retaining the shape of a square area. This is another example of ancient Egyptian awareness of the area of the two shorter sides being equal to the area of the diagonal. In this case the sidelengths are 1:1:1.414 and the areas are 1:1:2.