Do you have a pencil nearby?Take a look at his section - it is a regular hexagon, or as it is called, hex.This form also has a cross-section of the nut, the hexagonal field of chess, the crystal lattice of certain complex carbon molecules (such as graphite), snowflake, honeycombs and other objects.Giant regular hexagon was recently discovered in the atmosphere of Saturn.Does not it seem strange as the frequent use of nature for their creations designs of this particular form?Let's look at this figure in more detail.
regular hexagon is a polygon with six equal sides and equal angles.From the school course we know that it has the following properties:
- length of its sides corresponds to the radius of the circumscribed circle.Of all geometric shapes, this property is a regular hexagon.
- angles are equal and the value of each of 120 °.
- perimeter of the hexagon can be found by the formula R = 6 * R, if you know the radius of the circle around him, or F = 4 * √ (3) * r, if it is inscribed in a circle.R, r - radius of the circumscribed and the inscribed circle.
- area occupied by the regular hexagon is defined as follows: S = (3 * √ (3) * R2) / 2.If the radius is unknown, instead substitute length of one of the sides - as is known, it corresponds to the length of the radius of the circle.
have regular hexagon has one interesting feature, through which he received in nature is widespread - it is able to fill any surface plane without overlaps and gaps.There is even a so-called Pala lemma, according to which the correct hex side is equal to 1 / √ (3), is a versatile tire, that is, can cover any set with a diameter of one unit.
Now consider the construction of a regular hexagon.There are several ways, the simplest of which involves the use of compasses, pencil and ruler.First draw an arbitrary circle compass, then any place on this circle makes a point.Without changing the compass solution, put the tip to that point, mark the circle next to the notch, so to continue until we get all 6 points.It remains only to connect them by straight line segments, and obtain the desired shape.
In practice, there are times when you want to draw a large hexagon.For example, two-level gypsum ceiling, around the site of attachment of the central chandelier, set at the lower level six small lamps.The compass of this size find will be very, very difficult.What to do in this case?How could draw a big circle?Very simple.We need to take strong thread of the desired length and tie one of its ends in front of a pencil.Now you only find a mate who would be pinned to the ceiling at the point where the second end of the thread.Of course, in this case there are minor errors, but they are unlikely to even be noticeable to a stranger.
