Hexagon Hexagon In geometry, a hexagon (from Greek ἕξ "hex", "six" and γωνία, "gonía", "corner, angle") is a six-sided polygon or 6-gon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. A "regular hexagon" has Schläfli symbol {1} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius
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,