Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set. The most studied restriction is that the squaring be perfect, meaning that the sizes of the smaller squares are all different. A related problem is squaring the plane, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling.
Read more about Squaring The Square: Perfect Squared Squares, Simple Squared Squares, Mrs. Perkins's Quilt, No More Than Two Different Sizes, Squaring The Plane, Cubing The Cube
Famous quotes containing the word square:
“If magistrates had true justice, and if physicians had the true art of healing, they would have no occasion for square caps; the majesty of these sciences would of itself be venerable enough. But having only imaginary knowledge, they must employ those silly tools that strike the imagination with which they have to deal; and thereby, in fact, they inspire respect.”
—Blaise Pascal (1623–1662)