The circle is ... The circle is a geometric figure

The shape of the circle is interesting from the point of view of occultism, magic and ancient values attached to it by people. All the smallest components around us - atoms and molecules - have a round shape. The sun is round, the moon is round, our planet is also round. Molecules of water - the basis of all living things - also have a round shape. Even nature creates its life in circles. For example, you can remember about the bird's nest - birds also catch it in this form.

This figure in the ancient thoughts of cultures

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

Long since the circle is a sign of an infinite line, which symbolizes time and eternity. In the pre-Christian era, he was an ancient sign of the wheel of the sun. All points in this figure are equivalent, the line of the circle has neither a beginning nor an end.

And the center of the circle was the source of infinite rotation of space and time for masons. The circle is the end of all figures, it was not for nothing that the secret of creation was concluded in him, according to the Masons. The shape of the dial, which also has this form, means an indispensable return to the point of departure.

This figure has a deep magical and mystical composition, which it gave many generations of people from different cultures. But what is the circle like as a figure in geometry?

What is a circle

Often the concept of a circle is confused with the concept of a circle. This is no wonder, because they are very closely interrelated. Even their names are similar, which causes a lot of confusion in the immature minds of schoolchildren. To understand who is who, let us consider these issues in more detail.

By definition, a circle is a curve that is closed, and each point of which is equidistant from the point called the center of the circle.

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

To construct a circle, it is sufficient to choose an arbitrary point, which can be designated as O (this is the name of the center of the circle in most sources, we will not depart from the traditional notation). The next stage is the use of a circular drawing tool, which consists of two parts with either a needle or a writing element fixed on each of them.

These two parts are interconnected by a hinge, which allows you to choose an arbitrary radius within certain boundaries associated with the length of these same parts. With the help of this device an edge of the compass is placed at an arbitrary point O, and a curve is already drawn with a pencil, which is the result of a circle.

What are the values of the circle

If we connect with the ruler the center of the circle and any arbitrary point on the curve obtained by working with the compass, we get the radius of the circle. All such segments, called radii, will be equal. If we connect two points on the circle and center by means of a straight line with a straight line, we get its diameter.

The circumference is also characterized by the calculation of 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 is the circumference, r is the radius of the circle, d is the diameter, and the number Pi is a constant with a value of 3.14.

By the way, the constant Pi was calculated from the circle.

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

What is the main difference between a circle and a circle

In fact, the circle is a line. It is not a figure, it is a curve of a closed line, which has neither end nor beginning. And then the space that is located inside it is empty. The simplest example of a circle is a hoop or, in a different way, hula-hoop, which children use for physical training or adults, in order to create a slender waist.

Now we come to the concept of what a circle is. This is primarily a figure, that is, a certain set of points bounded by a line. In the case of a circle, this line represents the circle considered above. It turns out that a circle is a circle, in the middle of which there is not a void, but a set of points of space. If we stretch the fabric on a hula-hoop, then we can no longer twist it, because it will no longer be a circle - its emptiness is replaced by a cloth, a piece of space.

We proceed directly to the concept of a circle

A circle is a geometric figure that is part of a plane bounded by a circle. It is also characterized by such concepts as the radius and diameter, considered above when determining the circumference. And they are calculated in exactly 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 a square. You can calculate it again using the radius and the number Pi. The formula is as follows (see the figure below).

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

The formula of a circle, for the calculation of which it is also possible to use the diameter, changes and takes the form shown in the following figure.

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

R * r = 1/2 * d * 1/2 * d;

R * r = 1/4 * d * d.

A circle is a figure in which it is possible to distinguish separate parts, for example a sector. It looks like a part of a circle that is bounded by a segment of an arc and its two radii drawn from the center.

The formula that allows us to calculate the area of this sector is shown in the following figure.

Using a shape in tasks with polygons

Also a circle is a geometric figure, which is often used in conjunction with other figures. For example, such as a triangle, a trapeze, a square or a rhombus. Often there are problems where it is necessary to find the area of an inscribed circle or, conversely, described around a certain figure.

The inscribed circle is one that touches all sides of the polygon. With each side of any polygon, the circle must have a point of contact.

For a certain type of polygon, the definition of the radius of the inscribed circle is calculated according to individual rules, which are explained in the geometry course.

For example, there are several of them. The formula of a circle inscribed in polygons can be calculated as follows (below, several examples are given in the photo).

A few simple examples from life, in order to consolidate the understanding of the difference between the circle and the circle

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

A circle can also be called any ring - gold, silver or jewelry. A ring that holds a bunch of keys on itself is also a circle.

But a round magnet on the fridge, a plate or pancakes, baked by a grandmother, is a circle.

The neck of a bottle or a jar when viewed from above is a circle, but the lid that closes this neck, with the same view from above, is a circle.

There are many such examples, and to assimilate such material, they must be brought up so that the children better grasp the connection between theory and practice.