The first way - on this side S using a protractor.
We draw a straight line and put AB \u003d S on it; we take this line as a radius and with this radius we describe arcs from points A and B: then, using a protractor, we construct angles of 108 ° at these points, the sides of which intersect with the arcs at points C and D; from these points with a radius AB \u003d 5 we describe arcs that intersect at E, and with straight lines we connect points L, C, E, D, B.
The resulting pentagon - the desired one.
Second way. Let's draw a circle with radius r. From point A with a compass, draw an arc of radius AM to the intersection at points B and C with a circle. Connect B and C with a line that crosses the horizontal axis at point E.
Then from point E we draw an arc that will intersect the horizontal line at point O. Finally, from point F, we describe an arc that will intersect the circle at points H and K. Putting the distance FO \u003d FH \u003d FK around the circle five times and connecting the dividing points with lines, we get a regular pentagon.
Third way. Inscribe a regular pentagon in this circle. We draw two mutually perpendicular diameters AB and MC. Divide the radius of AO by point E in half. From point E, as from the center, draw an arc of a circle of radius EM and mark it with the diameter AB at point F. The segment MF is equal to the side of the required regular pentagon. With a compass solution equal to MF, we make the serifs N 1, P 1, Q 1, K 1 and connect them with straight lines.
The figure shows a hexagon on this side.
Straight line AB \u003d 5, as a radius, from points A and B we describe arcs that intersect in C; from this point, with the same radius, we describe a circle on which side A B is deposited 6 times.
Hexagon ADEFGB- the desired one.
"Decorating rooms during renovation",
N.P. Krasnov
The basis for the painting is the completely finished painting of the surface of walls, ceilings and other structures; painting is done using high quality glue and oil paints, made for trimming or fluting. When starting to develop a sketch for finishing, the master must clearly imagine the whole composition in a domestic setting and clearly understand the creative intention. Only if this basic condition is met is it possible to correctly ...
Measurement of the work performed, with the exception of specially stipulated cases, is carried out according to the area of \u200b\u200bthe actually processed surface, taking into account its relief and minus the untreated places. To determine the really treated surfaces during painting work, use the conversion factors given in the tables. A. Wooden window devices (measurement is made according to the area of \u200b\u200bopenings along the outer contour of the boxes) Name of devices Coefficient at ...
We have already said that to perform some types of painting work, you need to be able to draw. And the ability to draw, in turn, presupposes knowledge of the rules of construction geometric shapes... Sketches on paper are drawn using triangles, rails, transporters and compasses, and on the plane of walls and ceilings, constructions are made using a weight, a ruler, a wooden compass and a cord. In this case, it is necessary ...
This shape is a polygon with a minimum number of corners that cannot be paved with an area. Only a pentagon has the same number of diagonals as its sides. Using the formulas for an arbitrary regular polygon, you can determine all the necessary parameters that the pentagon has. For example, to inscribe it into a circle with a given radius, or build it on the basis of a given lateral side.
How to draw the beam correctly and what drawing accessories do you need? Take a piece of paper and mark a point in an arbitrary place. Then attach a ruler and draw a line from the indicated point to infinity. To draw a straight line, press the Shift key and draw a line of the desired length. Immediately after drawing, the Format tab opens. Remove the selection from the line and you will see a dot appear at the beginning of the line. To create a label, click the "Draw Label" button and create a field where the label will be located.
The first way to construct a pentagon is considered more "classic". The resulting shape will be a regular pentagon. The dodecagon is no exception, so its construction will be impossible without the use of a compass. The task of constructing a regular pentagon is reduced to the task of dividing a circle into five equal parts. You can draw a pentagram using the simplest tools.
I struggled for a long time trying to achieve this and independently find proportions and dependencies, but I did not succeed. It turned out that there are several different options for constructing a regular pentagon, developed by famous mathematicians. An interesting point is that this problem can be solved arithmetically only approximately exactly, since you will have to use irrational numbers. But it can be solved geometrically.
Division of circles. The points of intersection of these lines with the circle are the vertices of the square. A vertical diameter should be drawn in a circle of radius R (Step 1). At the conjugation point N of a straight line and a circle, the straight line is tangent to the circle.
Receiving with a strip of paper
A regular hexagon can be built using a rail and a 30X60 ° square. The vertices of such a triangle can be built using a compass and a square with angles of 30 and 60 °, or just one compass. To build side 2-3, set the raceway to the position shown by dashed lines, and draw a straight line through point 2, which will define the third vertex of the triangle. We mark point 1 on the circle and take it as one of the vertices of the pentagon. We connect the found vertices in series with each other. A heptagon can be constructed by drawing rays from the F pole and through odd divisions of the vertical diameter.
And on the other end of the thread set a pencil and obsessed. If you know how to draw a star, but don't know how to draw a pentagon, draw a star with a pencil, then connect the adjacent ends of the star together, and then erase the star itself. Then put a sheet of paper (it is better to fix it on the table with four buttons or needles). Pin these 5 stripes to a piece of paper with buttons or needles to keep them stationary. Then circle the resulting pentagon and remove these stripes from the sheet.
For example, we need to draw a five-pointed star (pentagram) for a picture of the Soviet past or the present of China. True, for this you need to be able to create a drawing of a star in perspective. Likewise, you can draw a shape with a pencil on paper. How to draw a star correctly, so that it looks smooth and beautiful, you cannot immediately answer.
From the center, lower 2 rays to the circumference, so that the angle between them is 72 degrees (protractor). The division of the circle into five parts is carried out using a conventional compass or protractor. Since the regular pentagon is one of the figures that contains the proportions of the golden ratio, painters and mathematicians have long been interested in its construction. These principles of construction with the use of a compass and a ruler were set forth in the Euclidean Principles.
