Area of a circle inscribe a hexagon. Cut the hexagon into six triangles by splitting it from the center. Two opposite triangles both touch two common diameters; slide them along one so the radial edges are adjacent. They now form a parallelogram, with the hexagon sides making two opposite edges, one of which is the base, "s". Two radial edges form slanted sides, and the height, "h" is equal to its apothem (as in the Archimedes proof). In fact, we can assemble all the triangles into one big parallelogram by putting successive pairs next to each other. The same is true if we increase
Magic hexagon can be called a T-hexagon and it has many more properties than the hexagon of hexagons. As with the above, the rows of triangles run in three directions and there are 24 triangles in a T-hexagon of order 2. In general, a T-hexagon of order "n" has formula_10 triangles. The sum of all these numbers is given by: If we try to construct a magic T-hexagon of side "n", we have to choose "n" to be even, because there are rows so the sum in each row must be For this to be an integer, "n" has to be even.