The shape of the circle is interesting from the point of view of occultism, magic and ancient meanings given to it by people. All the smallest components around us - atoms and molecules - are round. The sun is round, the moon is round, our planet is also round. Water molecules - the basis of all living things - also have a round shape. Even nature creates its life in circles. For example, you can think of a bird's nest - birds also make it in this form.
This figure is in the ancient thoughts of cultures
The circle is a symbol of unity. It is present in different cultures in many minute details. We don't even attach as much importance to this shape as our ancestors did.
For a long time, a circle is a sign of an endless line, which symbolizes time and eternity. In the pre-Christian era, it was an ancient sign of the wheel of the sun. All points in this figure are equivalent, the circle line has neither beginning nor end.
And the center of the circle was the source of the endless rotation of space and time for the Masons. The circle is the end of all figures, it was not for nothing that it containedthe secret of creation, according to Freemasons. The shape of the watch face, which also has this shape, means an indispensable return to the point of departure.
This figure has a deep magical and mystical composition that many generations of people from different cultures have endowed it with. But what is a circle 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 not surprising, because they are very closely interconnected. Even their names are similar, which causes a lot of confusion in the immature minds of schoolchildren. Let's take a closer look at these questions to understand who is who.
By definition, a circle is a curve that is closed, and each point of which is equidistant from a point called the center of the circle.
What you need to know and be able to use to build a circle
To build a circle, it is enough to choose an arbitrary point, which can be designated as O (this is how the center of the circle is called in most sources, we will not deviate from traditional designations). The next step is the use of a compass - a tool for drawing, which consists of two parts with either a needle or a writing element attached to 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 very parts. With this device,an arbitrary point O is set to the point of a compass, and a curve is already outlined with a pencil, which eventually turns out to be a circle.
What are the dimensions of the circumference
If we connect the center of the circle and any arbitrary point on the curve obtained as a result of working with a compass using a ruler, we will get the radius of the circle. All such segments, called radii, will be equal. If we connect two points on the circle and the center with a straight line, we will get its diameter.
It is also typical for a circle to calculate 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 Pi is a constant value of 3, 14.
By the way, the Pi constant was calculated just from the circle.
It turns out that no matter what the diameter of a circle is, the ratio of circumference to diameter is the same, about 3.14.
What is the main difference between a circle and a circle
Basically, a circle is a line. It is not a figure, it is a curved closed line that has neither end nor beginning. And the space that is located inside it is emptiness. The simplest example of a circle is a hoop or, in other words, a hula hoop, which children use in physical education classes or adults in order to create a slender waist for themselves.
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 is the circle discussed 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 in space. If we pull a fabric over a hula hoop, then we will no longer be able to twist it, because it will no longer be a circle - its emptiness is replaced by a fabric, a piece of space.
Let's go directly to the concept of a circle
Circle is a geometric figure that is part of a plane bounded by a circle. It is also characterized by such concepts as radius and diameter, discussed above when defining a circle. And they are calculated in exactly the same way. The radius of a circle and the radius of a circle are identical in size. Accordingly, the length of the diameter is also similar in both cases.
Since a circle is part of a plane, it is characterized by the presence of an area. You can calculate it again using the radius and Pi. The formula looks like this (see the picture 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 for a circle, which can also be calculated using the diameter, changes and takes the form shown in the following figure.
One fourth comes from the fact that the radius is 1/2 of the diameter. If the radius is squared, it turns out that the ratioconverted to the form:
rr=1/2d1/2d;
rr=1/4dd.
A circle is a shape in which you can select individual parts, such as a sector. It looks like a part of a circle, which is limited by a segment of the arc and its two radii drawn from the center.
The formula that allows you to calculate the area of a given sector is shown in the figure below.
Using a figure in problems with polygons
Also, a circle is a geometric figure that is often used in conjunction with other figures. For example, such as a triangle, trapezoid, square or rhombus. Often there are problems where you need to find the area of an inscribed circle or, conversely, circumscribed around a certain figure.
An inscribed circle is one that is in contact with 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 determination of the radius of the inscribed circle is calculated according to separate rules, which are clearly explained in the geometry course.
Some of them can be cited as an example. The formula for a circle inscribed in polygons can be calculated as follows (the photo below shows a few examples).
A few simple examples from life in order to consolidate the understanding of the difference between a circle andcircle
There is a manhole in front of us. If it is open, then the iron border of the hatch is a circle. When closed, the lid acts as a circle.
A circle can also be called any ring - gold, silver or jewelry. The ring that holds the bunch of keys is also a circle.
But a round fridge magnet, a plate or pancakes baked by grandma is a circle.
The neck of a bottle or can when viewed from above is a circle, but the lid that closes this neck is a circle when viewed from above.
There are many such examples, and in order to assimilate such material, they must be given so that children better grasp the connection between theory and practice.
