The correct hexagon: how interesting it is and how to build it
Is there a pencil around you? Look at its section - it is a regular hexagon or, as it is also called, hex. This shape also has a cross-section of the nut, a hexagonal chess field, a crystal lattice of some complex carbon molecules (eg graphite), a snowflake, honeycombs and other objects. A giant regular hexagon was recently discovered in the atmosphere of Saturn. Does not it seem strange to use so often the nature of this form for its creations? Let's look at this figure in more detail.
- The length of its sides corresponds to the radius of the circumscribed circle. Of all the geometric figures, this property has only a regular hexagon.
- The angles are equal to each other, and the value of each is 120 °.
- The perimeter of the hexagon can be found by the formula P = 6 * R,if the radius of the circumscribed circle is known, or P = 4 * √ (3) * r, if the circle is inscribed in it. R and r are the radii of the circumscribed and inscribed circle.
- The area occupied by a regular hexagon is defined as follows: S = (3 * √ (3) * R2) / 2. If the radius is unknown, instead of it we substitute the length of one of the sides - as is known, it corresponds to the length of the radius of the circumscribed circle.
Now consider the construction of the correcthexagon. There are several ways, the simplest of which involves the use of a compass, a pencil and a ruler. First, draw an arbitrary circle with a compass, then in a random place on this circle make a point. Without changing the solution of the compass, put the point at this point, mark the next incision on the circle, continue until until we get all 6 points. Now it remains only to connect them with each other by straight lines, and the desired figure will be obtained.