It is estimated that geometry was discovered by the Babylonians around 350 BC. We do not know for sure, but it is thought that one of the first shapes of geometry, which can be defined as the processing of mathematics through shapes, is a circle. Circumference has always been the most important information in circle operations, which appear in nature with similar shapes.
Sometimes it is necessary to calculate the circumference of the circle in order to grasp a whole, sometimes to find an area within the circle, or sometimes to at least form the basis of a multi-layered operation. Of course, as in all geometry operations, there is a formula that we can easily memorize and apply. Let’s see how the circumference of the circle is calculated and what the formula is in its simplest form.
Let’s get to know our shape first; What is a circle?
A two-dimensional shape formed by many different points equidistant from a stationary point on a surface is called a circle. The stationary point is defined as the center of the circle. Equal distances are defined as radius, while twice the radius is called diameter.
The center of the circle is o, the radius of the circle is r, the diameter of the circle is R, and the circumference of the circle is C. The lengths of the radius and its double diameter are considered constant. If we draw a straight line connecting two points on the circle, it is called a chord. The number of chords in a circle is infinite. When viewed from the center, the length of the line that appears symmetrical to each other and the diameter are considered equal, and the diameter of the circle is the longest chord.
Let’s take a look at the properties of the circle:
- A circle arc, also known as a circle segment, is the segment between two points.
- The part remaining in the circle and cutting it is the beam.
- It is the correct diameter that allows us to divide the circle into two equal parts.
- Diameter is the beam passing through the center.
- The line joining a point on the circle and the center is the radius.
- The diameter is twice the radius.
- Circle; It consists of three regions: the inner region, the outer region, and itself.
- The union of the inner region of the circle with itself is called the circle.
It is also necessary to pay attention to the angles of the circle:
The vertex of the central angle is the center of the circle. On the circle is the vertex of the perimeter angle. When we look between the points where the sides of the angle in the center of the circle intersect the circle, one of the arcs we see is the major circle arc. The other is called the minor circle arc, that is, the minor. The circumferential arcs are between 0 and 360 degrees, while the central angle is between 0 and 180 degrees.
Let’s come to the formula for calculating the circumference of the circle:
π = D / R = C / 2r
C = 2 . pi . r
i.e. Circumference of Circle = 2 x number of pi x radius of the circle
How is the circumference of a circle calculated?
Center of the circle = it
R is the diameter of the circle = [AB]
r is the radius of the circle = [AO] = [0B]
As a result C = 2 . pi . r
2 is already constant when calculating the circumference of the circle. Pi is generally taken as 3 or 3.14. r, that is, the radius of the circle, is a value that can be seen or easily found on the circle shape most of the time. When we put them in the right places in the formula, you can easily find the circumference of the circle.
It is possible to prove the formula for the circumference of the circle:
2 of the formula of the circumference of the circle. pi . It is a certain fact that there is r, but this is not a belief or common acceptance, on the contrary, it is an equation system that has been proven by mathematicians over and over again. If you have some time, you can try it and see.
First, draw four equilateral triangles inside the circle. It will be seen that the sum of the base lengths is less than the circumference of the circle. Delete them and draw eight equilateral triangles in their place. The sum of the base lengths will still be smaller than the circumference of the circle, but closer than in the previous case.
Now let’s expand things a little and draw a regular polygon with more sides inside the circle. Yes, we are getting closer and closer to the circumference of the circle, but no matter what we do, since the number of sides of the triangles inside will end, we cannot get a value equal to the circumference of the circle, no matter how close it gets.
When we start arranging n-sided triangles inside the circle, we get a situation like sin ( θ / 2 ) = ( L / 2 ) / r. We turn this into lim n sin ( π / n ) with the L’Hospital rule. Of course, the operations were a bit complicated before, but at the end we see that Ç = 2 . pi . Apart from the r equation, there is no result that will collect this operation.
We shared the formula that you can easily apply by answering the question of how to calculate the circumference of the circle, which is one of the most important operations of geometry. When it comes to the circle, after finding the radius, the rest feels like ripping a sock.
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