During repairs, it often has to deal with circles, especially if you want to create interesting and original decor elements. Also often have to share them on equal parts. To make it there are several methods. For example, you can draw the correct polygon or use tools known to everyone from school. So, in order to divide the circle on the equal parts, the circumference itself will be needed with a clearly defined center, pencil, transport, as well as a ruler and a circula.

Dividing circumference with the help of transport

The separation of the circle to equal parts with the aforementioned tool is perhaps the most simple. It is known that the circle is 360 degrees. By dividing this value to the desired number of parts, you can find out how much each part will occupy (see photo).

Further, starting from any point, you can make a mark that correspond to the calculated calculations. This method is good when the circle needs to be divided into 5, 7, 9, etc. Parts. For example, if the shape must be divided into 9 parts, the marks will be 0, 40, 80, 120, 160, 200, 240, 280, and 320 degrees.

Division of 3 and 6 parts

To properly divide the circle on 6 parts, you can use the property of the correct hexagon, i.e. Its longest diagonal should be two lengths of it. To begin with, the circulor must be stretched for a length equal to the radius of the figure. Next, leaving one of the tool legs at any point of the circle, the second must be seed, after which repeating the manipulation, it will turn out to make six points, connecting which you can get a hexagon (see photo).

By connecting the vertices of the shape through one, you can get the right triangle, and accordingly, the figure can be divided into 3 equal parts, and by connecting all the vertices and spending diagonally through them you can divide the figure on 6 parts.

Division of 4 and 8 parts

If the circle needs to be divided into 4 equal parts, first of all, it is necessary to draw the diameter of the shape. This will allow you to get two of the necessary four points at once. Next, you need to take a circuit, stretch its legs in diameter, after which one of them is left at one of the ends of the diameter, and the other to make a seat outside the circle below and from above (see photo).

The same must be done for the other end of the diameter. After that, the points obtained outside the circle are connected using a ruler and pencil. The resulting line will be a second diameter that will go clearly perpendicular to the first, as a result of which the figure will be divided into 4 parts. In order to obtain, for example, 8 equal parts, the resulting straight angles can be divided by half and spend diagonally through them.

And the construction of the right inscribed polygons

Division of circumference 3, 6 and 12 equal parts. Building the correct included triangle, hexagon and twelve-broth.

To build a proper inscribed triangle, it is necessary to BUTcrossing the center line with a circle to postpone the size equal to the radius R,in the same way. We get vertices 1 and 2 ( fig. 26, A.). Vertex 3 lies at the opposite point BUTlate diameter.

1/3 1/6 1/12

a B C)

Fig. 26.

The hexagon side is equal to the circle radius. Decision on 6 parts is shown in Fig. 26, b.

In order to divide the circle on the 12 parts, the size equal to the radius is to postpone the circumference into one and the other side of the four centers (Fig. 26, in).

Division of circumference 4 and 8

inserted quadrangle and octagon.

Fig. 27.

On 4 parts, the circle is divided into two mutually perpendicular centers. To divide on 8 parts it is necessary an arc equal to a quarter of the circle, divided by half ( fig.27.)

Division of circumference 5 and 10 equal parts. Building the right one

inserted pentagon and a decidagon.

1/5 1/10

a) b)

Fig. 28.

Half of any diameter (radius) divide in half ( fig. 28, A.) get a point N.From the point N,like from the center, conduct an arc with a radius R 1equal to the distance from the point N.to the point BUT, before crossing from the second half of this diameter, at the point R.Section ARequal to chore, a tightening arc, the length of which is 1/5 of the length of the circle. Making serifs on circle by radius R 2,equal to cut Armake a circle on five equal parts. The starting point is chosen depending on the location of the pentagon. ( ! It is impossible to perform serifs in one direction, since the error ragging occurs and the last side of the pentagon turns out to be powered.)

The division of the circle at 10 equal parts is performed similarly to dividing the circle to five equal parts ( fig. 28, B.), but first divide the circle for five parts, starting constructing from point A, and then from the point B, located at the opposite end of the diameter. Can be used to build a segment OR - The length of which is equal to chord 1/10 of the circumference length.

Division of circumference 7 equal parts.

1/7

a B C)

Fig. 29.

From any point (for example, BUT) circumference, radius of a given circumference RPOsOw arc before intersection with a circle at points IN and D (Fig. 29, a).Connecting Points IN and D. straight, get a segment Sun,equal of chord, which is tightened by an arc that makes 1/7 of the circumference length. Serifs are performed in the sequence specified on fig. 29 B..

Conjugation

Often in the design of parts one surface goes to another. Usually these transitions make smooth, which increases the strength of the parts and makes them more convenient in their work. Conjugation - This is a smooth transition from one line to another. Conjugation conjugation comes down to three moments: 1) Definition of the pairing center; 2) finding pairing points; 3) Building an arc conjugation of a given radius. To construct the conjugation, the conjugation radius is most often set. The center and the pairing point are defined graphically.

Today in the post I lay out several pictures of ships and schemes for embroidering to embroider (clickable pictures).

Initially, the second sailboat is made on cloves. And since the carnation has a certain thickness, it turns out that there are two threads from each. Plus to this layering of one sail on the second. As a result, a certain effect of splitting the image occurs in the eyes. If you embroider a ship on cardboard, I think it will look more attractive.
The second and third ships to embroider somewhat easier than the first. In each of the sails there is a central point (on the underside of the sail), from which the rays go to the points around the perimeter of the sail.
Joke:
- Do you have a thread?
- There is.
- And harsh?
- Yes, a nightmare is simple! I'm afraid!

Master Class: Embroide Peacock

I have a debut - the first master Class. I hope not the last. We will embroider peacock. Product scheme. The situation of punctures, pay special attention to their closed circuits even number. SOFT PICTURE - Tight cardboard (I took a brown density of 300 g / m2, you can try on black, then the colors will look even brighter), better scorched on both sides (For Kiev, I took in the department of stationery in TsUM on Khreshchatyk). Thicks - Moulin (any manufacturer, I had DMC), in one thread, i.e. Bunches unwind on separate fibers. How to transfer the scheme to the base. Embroidery consists of three layers Thread. First We embroider the first layer in the pile on the head of the peacock, the wing (light blue color of the thread), as well as dark blue tails circles. The first layer of the torso embroidered with chords with a variable step, trying so that the threads pass on the tangent to the circuit of the wing. Then Embroide the sprigs (seam-snake, mustard threads), leaves (first dark green, then remaining ...

Dividing circle on equal parts

Division of 3 parts (Fig. 12, but). From the end of the diameter of the circumference, an arc is carried out by a radius R.equal to the radius of the circle. The arc forms two necessary points on the circle. The third point is at the opposite end of the diameter.

Division of 4 and 8 parts. When dividing a circle on 4 parts, a circulation and a ruler will be helped, with which it is necessary to carry out two mutually perpendicular diameters (Fig. 12, b.). If you spend one diameter and from one end to describe the arc is somewhat big than the radius R., and from the opposite end of the diameter to carry out another arc of the same radius, then by connecting the points of their intersection of the straight line (which will be held through the center), we obtain the second diameter perpendicular to the first. The intersection points perpendicular diameters with a circle divide it into 4 equal parts.

To divide the circle on 8 equal parts (Fig. 12, in) It is necessary to construct two pairs of mutually perpendicular diameters.

Fig. 12. Dividing circle to equal parts: but - for three parts; b. - for four parts; in - for eight parts; g. - for five parts (1st way); d. - for five parts (2nd method); e. - by six parts; j. - Seven parts.

5-piece division. The division of the circle on 5 parts can be performed in several ways. First method (Fig. 12, g.) implies the use of a circulation and a ruler. First, a known method must be carried out two mutually perpendicular diameters. After that, radius R. It is necessary to divide in half: from the extreme point of intersection of the horizontal diameter it is necessary to carry out an arc of radius R. And after two points formed when crossing this arc with a circle, spend a straight line - it will split the horizontal line of the radius R. in half. From the division point (? R.) conduct an arc with a radius r. (equal distance from the point? R. to the intersection point of the circle with a vertical diameter). This arc cross the second half of the horizontal diameter at the point FROM. Cut equal to the distance from the point FROM The point of intersection of the circle with a vertical diameter will correspond to the part of the sought-in pentagon circumference. It is necessary to establish a circuit for a value equal to the length of this segment, and from the upper point of crossing the circle with a vertical diameter to carry out an arc of a given radius - the point of its intersection with the circle will be the next peak of the pentagon. From the found vertex you need to spend another arc of a given radius - it will be the third top of the pentagon, from which, in turn, it will be necessary to carry out the following arc, and so far the circle is not divided into 5 equal parts. If after this is to carry out the next five arcs of a given radius, but starting from the lower point of intersection of the circle with a vertical diameter, the circle is divided into 10 equal parts. In addition, in fig. 12, g., segment allocated SO On the horizontal diameter corresponding to the 1/10 circumference, that is, if there are 10 arcs on the circle to carry out 10 arcs by a radius corresponding to the length of the segment SO, The circle is also divided into 10 equal parts.

In the second method (Fig. 12, d.) On the diameter of the circle using the already known reception, it is necessary to find a point that will divide the radius R. in half. From this point spend a straight line to the intersection with the end of the diameter (points FROM). Then from the point R./ 2 conduct an arc with a radius equal to? R., before its intersection with the conducted line at the point E.. Next Circle from point FROM conduct an arc with a radius equal to the segment CE, before its intersection with a circle at points BUT and IN. Section AU - Grand Pentagon. Now it remains to spend out of points BUT and IN arc radius equal to the magnitude of the segment AUTo sequentially divide the circle on 5 parts.

There is also a way of dividing the circle on 5 parts using the transport. To radius R. Circle must be attached to the transportation, construct a central angle of 72 ° (360: 5 \u003d 72) and spend from the center a direct line to the point of its intersection with a circle. The resulting point must be connected to the radius intersection point. R. On the circle - this segment is a pentagon side. After conducting from both arc points with a radius corresponding to the length of this segment, a circle on 5 parts can be divided.

Division of 6 and 12 parts (Fig. 12, e.). From the points of crossing the circle with a vertical diameter, two arcs are carried out, the radius of which is equal to the radius of the circle. Crossing arcs on the circle forms points that are consistently connected by chords. As a result, the hexagonist is part of the circle inscribed. To divide the circle on 12 parts, the same construction is made, but only on two mutually perpendicular diameters.

Division into 7 pieces (Fig. 12, j.). From the end of any diameter, auxiliary arc radius is carried out R.. Through the points of its intersection with a circle, chord is carried out, equal to the side of the correctly inscribed triangle (as in Fig. 12, but). Half chords equates to the side inscribed in the circumference of the sevenginous. Now it is enough to sequentially postpone the circumference of several arcs with a radius equal to half of the chord to divide the circle on 7 parts.

Division on any number of parts (Fig. 13). In this case, the circle is divided into 9 parts.

Through the center of the circle, two mutually perpendicular straight lines are carried out. One of the diameters, for example CDThe line is divided into the desired number of equal parts (in this case 9), the points are numbered. Next from the point D. conduct an arc with a radius equal to the diameter of this circle (2 R.), before intersection with perpendicular direct AU. From the intersection points BUT and IN Rays are carried out, but so that they passed only through even or only through odd (as in this case) the rooms. When crossing with a circle, the rays form points that divide the circle to the desired number of parts (in this case 9).

Fig. 13. Dividing the circle on any given number of parts.

From the book of loggia and balconies Author Cereshser Natalia Gavrilovna

The build of the triple part in Figure 27 shows the general design, the method of the material cutting and the order of the assembly of parts. The frame consists of longitudinal front and rear CARGs, as well as from the exterior and internal Tsarg. They glued together and are additionally recorded with

From the book of the cottage. Construction and finishing by Mayer Ronald.

Assembling the double part Assembling the dialing section of the sofa (Fig. 28) is performed in the same way as the build triple. It remains to note that the rear wall with the corner table should speak to the right side edge for docking with the first part of the sofa. Of course, if you allow

From the book Tree carving [Installations, Takes, Products] Author Podolsky Yuriy Fedorovich

Construction of "light" part of the house: the first floor construction work is moving now faster than in the basement, since the blocks of the external walls of the first floor due to the necessary thermal insulation is much easier than the blocks used for the construction of the basement. Great

From the book of cosmetics and handmade soap Author Zgur Maria Pavlovna

Construction of a large diameter circumference Construction of a small diameter circumference is made using a circulation, which does not cause difficulties. At the same time, the possibility of constructing a large diameter circumference is limited to the size of the circulation. Get out of difficulty will help

From the book of the author

Definition of the center of the circle One of the ways to determine the center of the circle is presented in Fig. 14, B: On the circle, any three points (A, B, and C) are chosen, connect them to two or three segments and divide these segments in half with the help of perpendicular to them. Intersection point

From the book of the author

It turns out too soft soap, disintegrating on the part with cutting if the soap during cutting disintegrates into parts and at the same time it is also very soft, oily, but you did everything right and on the right recipe, your soap, most likely, could not pass the gel phase. For solutions

The circle is called a closed curve line, each point of which is located at the same distance from one point O, called the center.

Straight lines connecting any point of the circle with its center, call radius R.

Direct AV connecting two circumference points and passing through its center Oh, called diameter D.

Parts of circles are called arcs.

Straight CD connecting two points on the circle called chordoy.

Straight Mn, which has only one common point with a circle called tangent.

Part of a circle limited by chord CD and arc, called sigment.

Part of the circle bounded by two radius and arc is called sector.

Two mutually perpendicular horizontal and vertical lines intersecting in the center of the circle are called axes of the circle.

Angle formed by two radii cola called central angle.

Two mutually perpendicular radius Make up an angle of 90 0 and limit 1/4 of the circle.

Dividing circumference

We carry out a circle with a horizontal and vertical axes, which divide it on the 4r equal parts. Circulated or coal conducted under 45 0, two mutually perpendicular lines divide the circle on the 8th equal parts.

Dividing circle on 3 and 6 equal parts (multiple 3 three)

For dividing the circle to 3, 6 and multiple them, the number of parts, we carry out the circumference of the specified radius and the corresponding axis. The division can be started from the intersection point of the horizontal or vertical axis with a circle. The specified radius of the circle is sequentially postponed 6 times. Then the obtained points on the circle are sequentially connected by the straight lines and form the correct inscribed six-square. The connection of points through one gives an equilateral triangle, and dividing the circle into three equal parts.

The construction of the correct pentagon is performed as follows. We carry out two mutually perpendicular axis of the circle equal to the diameter of the circle. We divide the right half of the horizontal diameter in half with the arc R1. From the obtained point "A" in the middle of this segment R2, we carry out an arc of the circle to the intersection with a horizontal diameter at the point "b". R3 radius from the point "1" conduct an arc of the circumference to the intersection with a given circle (T.5) and get the side of the correct pentagon. The distance "B-o" gives the side of the right decagon.

Dividing the circumference on the N-number number of the same parts (building the right polygon with N sides)

It is performed as follows. We carry out horizontal and vertical mutually perpendicular axis of the circle. From the upper point "1" circle, carry out an arbitrary angle to the vertical axis direct line. On it laying equal segments of arbitrary length, the number of which is equal to the number of parts into which we divide this circle, for example 9. The end of the last segment connect with the lower point of the vertical diameter. We carry out lines parallel to the resulting sections of the deferred segments before intersection with a vertical diameter, thus separating the vertical diameter of this circle to the specified number of parts. Radius equal to the diameter of the circle, from the lower point of the vertical axis, we carry out an arc Mn to the intersection with the continuation of the horizontal axis of the circle. From points M and N, we carry out the rays through which (or odd) points of dividing the vertical diameter to intersection with the circle. The resulting segments of the circle will be the desired, because Points 1, 2, .... 9 divide the circle to 9 (n) equal parts.

To find the center of the Arc Circle, you need to perform the following constructions: on this arc, we mark four arbitrary points A, B, C, D and connect them in pairwise chords of AV and CD. Each of the chord with the help of a circulation divided in half, thus obtaining a perpendicular passing through the middle of the corresponding chord. The mutual intersection of these perpendicular gives the center of this arc and the corresponding circumference.