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 in shape. 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 recall the bird's nest - birds also fly 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.
Since ancient times, a circle is a sign of an infinite line that 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 no beginning or end.
And the center of the circle was the source of the endless 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 it, according to the Masons. The shape of the watch dial, which also has this shape, means an indispensable return to the point of departure.
This figure has a deep magical and mystical composition, which has been endowed with it by many generations of people from different cultures. But what is a circle like 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. To understand “who is who”, we will consider these questions in more detail.
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 how to use to build a circle
To construct 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 depart from the traditional notation). The next step is the use of a compass - a 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, the point of the compass is set to an arbitrary point O, and a curve is already outlined with a pencil, which ultimately turns out to be a circle.
What values is characterized by a circle
If we connect with the help of a ruler the center of the circle and any arbitrary point on the curve obtained as a result of working with the compasses, we get the radius of the circle. All such segments, called radii, will be equal. If we connect two points on a circle and a center with a straight line using a ruler, we will get its diameter.
A circle 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 is the circumference, r is the radius of the circle, d is the diameter, and Pi is a constant with a value of 3.14.
By the way, the constant Pi was calculated just from the circle.
It turned out that no matter what the diameter of the circle, the ratio of the circumference and diameter is the same, equal to about 3.14.
What is the main difference between a circle and a circle?
In fact, a circle is a line. She is not a figure, she is a curved closed line with no end or beginning. And the space that is located inside it is a void. The simplest example of a circle is a hoop, or, in a different way, a hula-hoop, which children use in physical education 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 is the circle considered above. It turns out that a circle is a circle in the middle of which is not a void, but a set of points in space. If you pull the fabric over the hula-hoop, then we will not 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.
A 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 determining the circle. 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 diameter length is also similar in both cases.
Since the circle is part of the plane, it is characterized by the presence of area. It can again be calculated 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 Pi number is again the same constant, equal to 3.14.
The circle formula, 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 of the diameter. If the radius is squared, it turns out that the ratio is converted to the form:
r * r = 1/2 * d * 1/2 * d;
r * r = 1/4 * d * d.
A circle is a figure 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 this sector is presented in the following figure.
Using a shape in polygon problems
Also, a circle is a geometric shape, which is often used in conjunction with other shapes. For example, such as a triangle, a trapezoid, a square or a rhombus. Often there are problems where you need to find the area of an inscribed circle or, conversely, described around a specific figure.
An inscribed circle is one that is in contact with all sides of the polygon. A circle should have a point of contact with each side of any polygon.
For a certain type of polygon, the definition of the radius of the inscribed circle is calculated according to separate rules, which are easily explained in the course of geometry.
We can cite several of them as an example. The formula of a circle inscribed in polygons can be calculated as follows (several examples are given in the photo below).
A few simple life examples to reinforce the understanding of the difference between a circle and a 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, 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 refrigerator, a plate or pancakes baked by grandma is a circle.
The top of a bottle or can when viewed from above is a circle, but the lid that closes this neck is a circle with the same top view.
There are many such examples, and for the assimilation of such material they need to be cited so that children better understand the connection between theory and practice.