# Construction of the correct hexagon

Hexagon construction can be done in several ways. The most convenient way is to use a standard set of drawing tools: a compass, a ruler. However, in the absence of a compass, a figure of this type can be drawn using a T-square, a factory-made square with angles of 90/60/30 °. Hexagons are used to loosen and tighten the bolts during the repair and assembly of furniture.

In both cases, the construction feature is an elementary knowledge of the fundamentals of geometry. In a regular hexagon, the length of its side is always equal to the radius of the circle described around it, the opposite sides are parallel, the faces are mated at an angle of 60 °.

## The way of drawing the hexagon with compass, ruler

To construct a hexagon in the presence of a compass, it is enough to draw a circle, find 6 points on its arc, connecting them with segments. To do this, simply set the compass once, setting aside the value of the side of the polyhedron. The line will be required for the construction of auxiliary, main lines.

The method is as follows: The first way to draw a hexagon with a compass: 1,2,3,4,5,6 - angles, 0 - center, D - radius of hexagon.

• the compass draws a circle - the radius is the size of the side;
• radius is drawn along the ruler - the intersection points of this segment will be the angles of the polygon;
• the two angles of the polygon are located — the compass is rearranged to one of the intersection points of the segment (the diameter carried out at the previous stage), marks are made on the arc;
• the remaining two angles are located — the compass moves to the opposite point of intersection of the segment with the arc of a circle; the intersection marks on the second side of the circle are created.

The construction of the correct hexagon is completed by connecting the resulting angles along the ruler. This is the most accurate method, requiring a minimum number of drawing tools. With a significant size of the sides (for example, cutting sheet metal, wooden blanks) you can use a cord with a pencil. One edge of the cord is attached to a pencil / marker, the second one is fixed at the center of the circle, then at the points of intersection of the diameter with the arc of a circle.

The construction takes a minimum amount of time, the accuracy depends entirely on the sharpening of the pencil, the presence of the lock on the compass.

## The way to draw a hexagon without compass

The construction of a regular hexagon without a compass requires the obligatory presence of a tarp, a special tool in the form of a ruler, inside of the case of which there is a massive shaft with rubber elements that prevent slipping. It is designed for the rapid manufacture of parallel lines, ensuring high accuracy of construction. The quality of tracing in this method completely depends on the accuracy of the angle of 60 ° in the factory-made square, the graduation of the ruler scale.

The method of construction is as follows: The second way of drawing a hexagon with a compass: 1,2,3,4,5,6 - angles, 0 - center, D - radius of hexagon.

• A square is applied to one side of the segment - the short side is aligned with the line, the angle of 60 ° is adjacent to the end of the segment from the inside, and the hypotenuse of the square is drawn by a line of arbitrary size, which is subsequently corrected on a ruler scale;
• a line is drawn on the sheet / blank - its length is equal to two dimensions of the side of the polygon, the edges automatically become the centers of the polyhedron;
• the operation is repeated when the square is turned - the angle of 60 ° moves to the opposite side of the segment, the center of rotation is the long leg of the square;
• turn of the square - now the short leg of the square becomes the center of rotation, two more faces are drawn;
• specifying the sizes of the sides — on the four resulting sides of the polygon, their exact size is plotted along the ruler;
• construction of the two remaining sides - they are located parallel to the line from which the drawing was started, are carried out along a ruler, then their size is specified;
• control of parallelism - the scale of the square gauge is combined with the line from which the construction of the figure began, then the tool moves up / down to verify the parallelism of the two opposite faces between themselves, with this segment

The hexagon in this case is drawn longer than in the first method. However, it is possible to construct the necessary figure, in the absence of a compass, with a square. The technology is based on the parallelism of opposite sides of a regular hexagon, the same internal angles of 60 °.

The industry produces squares with both sharp corners, convenient for this method, and with rounded. The third way of drawing a hexagon with a compass: a is the diameter, b is the side of the hexagon.

In the latter case, it is more convenient to change the technology somewhat:

• after drawing the central segment along it the reishin is aligned;
• the instrument rolls back down by an arbitrary value;
• the short hypotenuse of the square is combined with the rugsha line, and not with the central segment;
• the rounded edge of the instrument does not participate in the construction; the line is drawn along the whole part of the hypotenuse.

The operation is repeated on the opposite side of the segment, after which the T-square is rotated 180 °, again combined with the central line, rolled up to build the two other sides of the polyhedron.

These are standard ways of drawing an equilateral polygon with six corners, edges. They are convenient for cutting blanks of all sizes from different materials, in standard drawing on Whatman paper. Both techniques are of purely practical importance, as in professional graphic editors (AutoCAD, Compass-3D) such figures are created automatically by setting the necessary parameters.