Lattice Squares of Integer Area
This Demonstration represents the problem of drawing a square with all four vertices at lattice points such that the area of the square is an integer. This works only when the area is the sum of two squares. Since each side has a length equal to the square root of the area, there must exist a right triangle for which the hypotenuse squared equals the area of the square. The graphic shows these squares for a given area if the construction is possible.