Did you know a Hexagon can be constructed using the angle pi/3 a lot of times? This is because a hexagon is made of 6 triangles with equal side length - the radius of the hexagon. The inner angles of these triangles is pi/3. Using this information and the trigonometric functions sin and cos can be used to draw such a picture.
interesting point. My program draws 6 red hexagons, and in the one a blue one "overdraws" the others at the border.