Perfect Squared Squares
A "perfect" squared square is a square such that each of the smaller squares has a different size.
It is first recorded as being studied by R. L. Brooks, C. A. B. Smith, A. H. Stone and W. T. Tutte at Cambridge University. They transformed the square tiling into an equivalent electrical circuit — they called it "Smith diagram" — by considering the squares as resistors that connected to their neighbors at their top and bottom edges, and then applied Kirchhoff's circuit laws and circuit decomposition techniques to that circuit.
The first perfect squared square was found by Roland Sprague in 1939.
If we take such a tiling and enlarge it so that the formerly smallest tile now has the size of the square S we started out from, then we see that we obtain from this a tiling of the plane with integral squares, each having a different size.
Martin Gardner has published an extensive article written by W. T. Tutte about the early history of squaring the square.
Read more about this topic: Squaring The Square
Famous quotes containing the words perfect, squared and/or squares:
“The work of art assumes the existence of the perfect spectator, and is indifferent to the fact that no such person exists.”
—E.M. (Edward Morgan)
“Dreams are toys.
Yet for this once, yea, superstitiously,
I will be squared by this.”
—William Shakespeare (1564–1616)
“And New York is the most beautiful city in the world? It is not far from it. No urban night is like the night there.... Squares after squares of flame, set up and cut into the aether. Here is our poetry, for we have pulled down the stars to our will.”
—Ezra Pound (1885–1972)