Saturn's hexagon change in season. These changes were observed by the Cassini spacecraft. One hypothesis, developed at Oxford University, is that the hexagon forms where there is a steep latitudinal gradient in the speed of the atmospheric winds in Saturn's atmosphere. Similar regular shapes were created in the laboratory when a circular tank of liquid was rotated at different speeds at its centre and periphery. The most common shape was six sided, but shapes with three to eight sides were also produced. The shapes form in an area of turbulent flow between the two different rotating fluid bodies with dissimilar speeds. A
Magic hexagon gave a less intricate constructive proof. The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887). The numbers in the hexagon are consecutive, and run from 1 to formula_1. Hence their sum is a triangular number, namely There are "r" = (2"n" − 1) rows running along any given direction (E-W, NE-SW, or NW-SE). Each of these rows sum up to the same number "M". Therefore: This can be rewritten as Multiplying throughout by 32 gives which shows that formula_6 must be an integer,