What is a circle and circle, what their differences and examples of data figures are from life. The meaning of the word & laquokurg

Circle Circle, Circle, B, On Circle and Circle, MN. Circles, m. 1. (B, on a circle). Part of the plane limited to the circle (mat.). Calculate the area of \u200b\u200bthe circle. Circle quadrature. 2. (in a circle). Playground, land plot forming a circle figure (collapse). Running circle. Orchestra played on a circle. Evolution. 6. (in a circle) over. Closed as-n. borders sphere whether. (Book.). Circle classes. This is not included in the circle of my 3. (B, on the circle). Circle. Move in a circle. Draw a circle. Polar circle. (Imaginary line, for k-swarm lies the polar region; geogr.). Circle on water. At a huge height, the eagles soak, smoothly describing the big circles. Chekhov. 4. (B, on the Circle). The object having a circle. Lifebuoy. Circle of cheese. 5. (In a circle), over. A closed chain of events exhausting in its totality development of any, process (book.). Circle of development. Circle of life. By the end of the 19th century, Russian naturalism completed the circle of its 7. (in a circle). A group of people united in social or everyday life. In favorites circle. Numerous circle of friends. Decided to discuss it in a family circle. With friends. 8. Only MN. Wednesday of persons united by the community of professional interests and classes and forming a separate public group (book.). Literary circles. In political circles, the English note caused many senses. In circles close to the ministry. Party circles. On the circle (progress) - on average, by approximate counting. On the circle was 200 rubles. per month. Middle peasant can be

Song sentences

• Schooner described the circle and swam right on me.
• It was necessary to make an angle closer, inside the circle.
• Mustangi all continued their run in a circle.
• He walked, looking around scattered and viciously.
• In the circle of dancers, something unusual happened.
• Rose and went ahead of Cherubim in a circle.
• People that stand far above him, the people of her circle.
• And not for me was in this circle, too, much.
• Many trees grew around in the valley.
• In the circle, weather definitions were indicated.
• There was a vicious circle, the exit from which was not.
• The center of this circle was the place where the snake was lying.
• Yes, much in this circle was just nice to me.
• Everything else is still reminiscent of yesterday's holiday.
• Tell the conversation in the circle of the interests of your interlocutor.
• We all took turns on the car around the yard.
• Then, with all his might struck with all the body to the center of the circle.
• The hunter also dismounted and walked over to the circle itself.
• The sea around, as I saw the eye, it was deserted.
• People on the rotating circle are discarded behind his edges.
• Again full circle - Early morning in the winter of the twenty-fifth year.
• Inside the circle of several dozen huts burned fire.
• Sasha walked in a circle, along the track running in the snow.
• It was unthinkable to count all the people visible around the circle.
• And over each lamp sleeping in a light circle of a lid.
• True, he knew that this was not the most narrow elected circle.
• Behind the feature of this circle were women and children.
• But he was discussed in a close circle of two - three people.
• From the palace, it was nowhere to come out, the swamps, streams.
• The loyalty of the revolution and admire it was also in this circle.

The shape of the circle is interesting from the point of view of the occult, the magic and the ancient values \u200b\u200battached to her. All the smallest components around us are atoms and molecules - have a round shape. The sun round, the moon is round, our planet is also round. Water molecules - the basics of all living things - also have a round shape. Even nature creates its life in circles. For example, you can remember the bird's nest - the birds are screwed in this form.

This figure in the ancient thoughts of cultures

The circle is a symbol of unity. It is present in different culturesah in many smallest details. We do not even attach so much value to this form, as our ancestors did.

A round has long been a sign of an endless line that symbolizes time and eternity. In the pre-Christian era, he was an ancient sign of the Wheel of the Sun. All points in equivalent, the line of the circle has no beginning, no end.

And the center of the circle was the source of the infinite rotation of space and time for the masons. Circle - the end of all the figures, no wonder in it was concluded the secret of creation, according to Masons. The form of the clockball clock, which also has such a form, denotes an indispensable return to the point of departure.

This figure has a deep magic and mystical composition, which has been given many generations of people from different cultures. But what is the circle as a figure in geometry?

What is a circle

Often the concept of a circle is confused with the concept of circle. This is not wonderful, because they are very closely interrelated. Even the names of their similar, which causes a lot of confusion in the immature minds of schoolchildren. To figure out, "who is who", consider these questions more.

By definition, the circle is such a curve that is closed, and each point of which is equal to the point, called the center of the circle.

What you need to know and how to use how to use to build a circle

To build a circle, it is enough to choose an arbitrary point, which can be designated as oh (this is how the center of the circle is called in most sources, we will not move away from traditional designations). The next step is to use a circulation tool for drawing, which consists of two parts with each of them either with a needle or a writing element.

These two parts are interconnected by a hinge, which allows you to choose an arbitrary radius in certain boundaries associated with the length of these most parts. With the help of this device in an arbitrary point, the tip of the circular is established, and the pencil is already outlined by the curve, which is from the result obtained by a circle.

What values \u200b\u200bis characterized by a circle

If you combine the center of the circle and any arbitrary point on the curve obtained as a result of the circulation, we will get all these segments referred to as radius, will be equal. If you connect with a line of a straight line two points on the circle and the center, we get its diameter.

For the circle, it is also characterized by calculating its length. To find it, you need to know either the diameter or the radius of the circle and use the formula shown in the figure below.

In this formula C - the circumference of the circle, R is the radius of the circle, D is the diameter, and the number of Pi is a constant with a value of 3.14.

By the way, the PI constant was calculated just from the circle.

It turned out that no matter what the diameter of the circle, the ratio of the circumference length and the diameter is the same, equal to about 3.14.

What is the main difference between the circle from the circle

In fact, the circle is a line. It is not a figure, it is a closed line curve that does not have the end nor the beginning. And the space that is located inside it is emptiness. The simplest example of the circle is the hoop or, in a different, Hula-HUP, which children use in class physical culture Or adults, in order to create a slim waist.

Now we approached the concept of what a circle is. This is primarily a figure, that is, a variety of points, limited line. In the case of a circle, this line acts a circle discussed above. It turns out that the circle is a circle, in the middle of which is not emptiness, but many points of space. If you pull the cloth on hula-chup, then we can no longer twist it, because it will not be circumference - its emptiness is replaced by a cloth, a piece of space.

Let's go directly to the concept of a circle

The circle is a geometric shape, which is part of a plane limited by a circle. It is also characterized by such concepts as the radius and the diameter discussed above when determining the circle. And they are calculated in the same way. The radius of the circle and the radius of the circle are identical in size. Accordingly, the length of the diameter is also similar in both cases.

Since the circle is part of the plane, it is characterized by the presence of an area. It can be calculated again with radius and pi. The formula looks in the following way (see Figure below).

In this formula S - the area, R is the radius of the circle. The number Pi is the same constant, equal to 3.14.

The circle formula, to calculate which it is also possible to use the diameter, changes and takes the view shown in the following figure.

One fourth appears from the fact that the radius is 1/2 diameter. If the radius is in the square, it turns out that the ratio is converted to the form:

r * R \u003d 1/2 * D * 1/2 * D;

The circle is a figure in which individual parts can be distinguished, for example, the sector. It looks like a part of a circle, which is limited by the segment of the arc and its two radius spent from the center.

The formula that allows you to calculate the area of \u200b\u200bthis sector, is presented at the following figure.

Using the figure in problems with polygons

Also a circle is a geometric shape, which is often used complete with other figures. For example, such as a triangle, a trapezoid, square or rhombus. Often there are tasks where you need to find an inscribed circle or, on the contrary, described around a certain figure.

The inscribed circle is such that comes into contact with all the sides of the polygon. With each side of any polygon near the circle there should be a point of contact.

For a certain type of polygon, the definition of the infected circle is calculated by separate rules that are available in the course of geometry.

It can be brought to an example several of them. The formula of the circle inscribed in polygons can be calculated as follows (several examples are given below in the photo).

Some simple examples of life in order to consolidate the understanding of the difference between the circle and the circle

Before us if it is open, then the iron cut of the hatch is a circle. If it is closed, the lid acts as a circle.

A circle can also be called any ring - gold, silver or jewelry. The ring that keeps the key ligament is also a circle.

But a round magnet on the refrigerator, a plate or pancakes, baked with a grandmother, is a circle.

The neck of the bottle or banks at the sight is from above - this is a circle, but the lid that closes it with the neck, with the same video from above is the circle.

Such examples can be brought by many, and to assimize such material they need to be given to ensure that children will better catch the connection of the theory with practice.

a common sign of cult symbolism "means unity, infinity, co-vertex and completeness. As a symbol means a process that has no beginning, no end, harmonious and centered. IN ancient mythology It was distributed, for example, in the form of a snake, which keeps his tail in the mouth, there is a ball in its reality and development. In cosmogonic myths, the universe was often portrayed in the shape of a ball. In a temporary terms, the circle is embodied in the idea of \u200b\u200ba cycle, closely connected with the calendar.

Excellent definition

Incomplete definition ↓

A CIRCLE

Primary symbol of unity and infinity, the sign of absolute and perfection. As an endless line, the circle symbolizes the time in eternity, and how the macro-space mark forms a zodiac circle. He is an ancient mystical symbol, traditionally denoting the sky, universe and eternity. Sometimes it is depicted in the form of a typoros - a snake that bows his own tail. The emptiness in the middle of the circle rarely remains blank: most often the square, or cross, or an equilateral triangle, or a pentagram fit into it. In any case, the figure, inscribed in the circle, symbolizes the relationship between the concept denoted by the figure, and eternity. Such, in particular, the mystical meaning of the ancient task of the "quadrature of the circle": having decided her, the adept comprehends the equivalence of the Earth and the sky, space and time, the person and the universe. In Egypt, a circle with a point in the center was a symbol of a person. Circle - an ancient pre-Christian sign of the Sun Wheel. A complex symbol connecting the idea of \u200b\u200bperfection and eternity, the circle is superior to all other geometric shapes. The circle line is the only line that has no beginning, no end and all points of which are equivalent. Circle Center - source of infinite rotation of time and space. That is why in the understanding of Masons a circle - the end of all the figures, as the secret of creation is concluded. The circle is one of the most widely used figures to express the idea of \u200b\u200beternity, as the movement in a circle symbolically means a constant return to itself. The circle that the arrow passes in the clock dial or on the scale in the compute, also denotes the return to the point of departure. In Buddhism, the unity of the internal and external worlds is symbolized by three circles. The first round is depicting a demon holding in its mouth 12 of the initial root causes. In the inner circle, chicken (sweet bypass), snake (wrath) and pig (dullness) were clung to. And the middle circle accommodates the pictures of six categories: the kingdoms of people, gods, demons, animals, hell and suffering spirits. In Zen-Buddhism, concentric circles mean higher degrees of enlightenment and perfection in unity: therefore, Yin and Yang are depicted in the circle. The temple of the pagan God, which he appears, in particular, in Italian painting since the XVI century, is, as a rule, round construction. The columns that form a round colonnade support the Cathedral arch - this form was traditional in ancient architecture. Renaissance architects who followed the principles for the first time formulated by the Italian scientist Leon Alberti in the XV century. , returned to a circle as the main form of a church building. The circle and the sphere were considered a perfect form that consistent with the Renaissance concept of God, according to which he was a cosmic mind that made the form of the sphere, which enters the entire space, the spirit, mind and matter in the descending concentric spheres. In Christianity, concentric circles represent spiritual hierarchies or different stages Creation. For example, the circle is used symbolically in the images of the sky in the form of concentric choirs of angels and at the location of students standing around Christ. Three intersecting circles mean a trinity, and isosceles triangle With three circles is a monogram of three hatters of one God. The circle represents the sky as opposed to the square of the Earth. Perfect circle geometry is a volume of imperfection in the temporary world, arising over time. The circle in the square is a common Kabbalistic sign, meaning the divine spark, hidden in matter. Adam Cadmmon in the Kabbalistic Pictogram is depicted in a circle. In turn, the square in the circle means the world of physical elements. The circle, as a monogram of God, denotes not only his perfection, but also its borrics. A series of concentric circles one inside the other means space. The magic circle is an element of the traditional markup of the place for magical operations. Usually, special view The annular structure consists of three circles, i.e., two limbs and the central circle, inside of which the magician cargo is located. Most theorists and practical magicians claim that the circle has protective function. Therefore, pentagram and other signs, stoping evil spirits, certainly fit into the limbs. It is known a lot of legends that spirits do not see a magician located in a circle, but can be confused by violating the magic circle. SEM .: Hall J. Dictionary of plots and symbols in art. M., 1999; Encyclopedia of mystical terms. M., 1998; Encyclopedia characters, signs, emblems. M., 1999; Sheynina E. Ya. Encyclopedia of characters. M., 2001.

Are there many items around us that are similar to geometric figures? Yes it's true! In particular, many of them have a circle form. For example, the circus isna, the bottom of the pan, we can easily cut it out of fabric or cardboard.

Consider what a circle is

Figure that is limited to a circle. It has a center, so all the points that are located from the center to the circle are the plane of the circle. The radius of the circle is the distance from its center to the circle.

Many do not distinguish what circumference and a circle. Circle will succeed, if we circle a glass, and we can also lay it out of the thread. All points of the plane that are placed at the same distance from this point form a figure, which is called a circle. If you connect two points of the circumference, then we will get a segment called the chord. If the chord is passing through the center of the circle, then we already call it a diameter that is equal to two radius. The circle can be divided into sectors using two radius. And the circle divides the chord to segments.

Look! And you will see around yourself a circle and a circle! It is only a little fantasy.

AND a circle - Geometric shapes, interrelated. There is a boundary broken line (curve) circle,

Definition. The circle is a closed curve, each point of which is equal to the point called the center of the circle.

To build a circle, an arbitrary point O, adopted for the center of the circle, and with the help of a circular is a closed line.

If the point is about the center of the circle to connect with arbitrary dots on the circle, then all the segments obtained will be equal to each other, and they are called such sections with radii, abbreviated with the Latin small or large letter "ER" ( r. or R.). Radius in a circle can be carried out as much as the dots have a circumference length.

A segment connecting two circumference points and passing through its center is called a diameter. Diameter Consists of two radiuslying on one straight line. The diameter is indicated by the Latin little or large letter "DE" ( d. or D.).

Rule. Diameter Circle is equal to two radius.

d \u003d 2r.
D \u003d 2r.

The length of the circle is calculated by the formula and depends on the radius (diameter) of the circle. The formula contains the number ¶, which shows how many times the circumference is greater than its diameter. The number ¶ has an infinite number of semicolons. For calculations, it is accepted ¶ \u003d 3.14.

The circumference of the circle is indicated by the Latin large letter "CE" ( C.). The length of the circle is proportional to its diameter. Formulas for calculating the length of the circle by its radius and diameter:

C \u003d ¶d.
C \u003d 2¶r.

• Examples
• Danched: d \u003d 100 cm.
• Circle Length: C \u003d 3.14 * 100 cm \u003d 314 cm
• Danched: D \u003d 25 mm.
• Circle Length: C \u003d 2 * 3,14 * 25 \u003d 157 mm

Singing circle and arc circumference

Any sequential (straight line) crosses the circle at two points and divides it into two arcs. The magnitude of the circumference arc depends on the distance between the center and the unit and is measured according to the closed curve from the first intersection point of the sequential circle to the second.

Dougi. Circles are divided sale On a large and small, if the sequer does not coincide with a diameter, and two equal arcs, if the sequer passes along the diameter of the circle.

If the sequer passes through the center of the circle, then its segment located between the intersection points with the circle is the diameter of the circle, or the greatest chord of the circle.

The further the secant is located on the center of the circumference, the smaller the degree of the dimension of the circumference and more - greater arc of the circle, and the segment of the section, called chordoydecreases as the sequence is removed from the center of the circle.

Definition. The circle is called a part of the plane lying inside the circle.

Center, radius, circle diameter are simultaneously center, radius and diameter of the corresponding circle.

Since the circle is part of the plane, the area is one of its parameters.

Rule. Area of \u200b\u200ba circle ( S.) is equal to the product of the radius square ( r 2.) by number ¶.

• Examples
• Dano: R \u003d 100 cm
• Area of \u200b\u200ba circle:
• S \u003d 3.14 * 100 cm * 100 cm \u003d 31 400 cm 2 ≈ 3m 2
• Danched: D \u003d 50 mm
• Area of \u200b\u200ba circle:
• S \u003d ¼ * 3,14 * 50 mm * 50 mm \u003d 1 963 mm 2 ≈ 20 cm 2

If in the circle to spend two radius to different points circle, then two parts of the circle are formed, which are called sectors. If there is a chord in a circle, the part of the plane between the arc and the chord is called segment of the circle.