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A circle is a flat geometric figure consisting of all points located at the same distance from another point, called the center, as well as all points that lie within this perimeter. On the other hand, the circumference is the curved line formed by all the points that are at the same distance from the center. By virtue of this, the circumference consists of the line that delimits the circle.
Like any line, one of the characteristics of the circumference is its length. This length is what is commonly called “the circumference of a circle”. We can imagine the circumference as a ring made of a thread, and its length refers to the length that this tape would have if we cut it and stretched it in the form of a straight line, as shown in the following figure.
the elements of the circle
Now that we know what the circumference is, we are going to define other parts or elements of the circles that will allow us to calculate its length.
the center of the circle
In a circle, the center is a single point that is inside it and that is at the same distance from all the points that are on the outer edge, that is, on the circumference.
Rope
A chord is a line segment that is inside a circle and that joins any two points of the circumference that delimits it. Infinitely many strings of different lengths can be drawn around a circle.
The diameter
It is a chord that passes through the center of the circle, that is, it is any segment that includes the center and that joins two opposite points on the circumference. The diameter is the longest chord that can be inside a circle, its length is unique and is related to the length of the circumference.
The radio
It is a line segment that joins the center of the circle with any point on the circumference. Its length is half the diameter.
In addition to the elements of the circle, the calculation of the circumference also involves a very special number or mathematical constant, which is described below.
The number π (pi)
The number π (Greek letter pi) is a special type of number called an irrational number. It is a mathematical constant whose value is approximately 3.141593 that has infinite decimal numbers which do not follow any pattern.
Pi is closely related to the circumference of a circle. In fact, this number represents the ratio between the circumference and the diameter of a circle, so if you want to calculate that circumference, you inevitably have to use it.
Tip on the use of π
We have all probably heard that pi is 3.14, or 3.1416, however, this is not strictly correct. Those values are just approximations to the value of pi which makes it easier to use when doing calculations with it. This opens the question of how many decimal places to use in a particular case.
For many simple cases, simply using 3.14 will suffice. However, using more decimal places for pi makes our calculations more accurate, so it is preferable to use as many decimal places as possible.
As a general rule of thumb, if you are using a calculator to perform math on pi, it is best to use the value of pi that scientific calculators have stored in their memory. This is usually as simple as pressing the SHIFT key followed by the EXP key.
Calculation of the circumference of a circle
The circumference is calculated by means of the diameter of the circle or by means of its radius. In the first case, the formula is:
In this equation C represents the length of the circumference, π is the constant pi that we talked about before and d is the diameter of the circle. That is, if we want to calculate the circumference, all we have to do is multiply the diameter by 3.1416 or by the value of pi that the calculator brings.
Although it is very easy to use the diameter to calculate the circumference, most of the calculations related to circles and circumferences are made based on their radius, and not on the diameter. The only thing to do in this case is replace the diameter by twice the radius, and you’re done. The result is:
Note: In mathematics, the coefficients or numerical factors such as 2 are usually placed first, then the constants that are represented with letters, such as π, and at the end the variables, such as the radius. This is why the formula is written 2.π.r instead of π.2.r, even though the result is exactly the same.
Examples of circumference calculation
Example 1:
Determine the circumference of a coin whose diameter is 2.09 cm.
Solution
Since the diameter is given, we must use the first formula:
So, the circumference of the coin is approximately 6.57cm.
Note that the result was rounded to the same number of significant figures as the diameter of the coin, which is the data provided by the exercise.
Example 2
What will be the circumference in centimeters of a cylindrical column that has a radius of 0.500 meters at its base?
In this case the radius is given so we can use the second circumference formula, or multiply the radius by 2 to get the diameter and then use the first formula as we did before. To reduce the number of steps, we will use the second formula.
It should be taken into account that the circumference is requested in centimeters, but the radius is given in meters. For this reason we must convert the units from meters to centimeters either before or after calculating the circumference. In our case, we will do it before:
Now, we apply the circumference formula:
Again, the result was rounded to the same number of significant figures as the original radius. This has 3 significant figures since there are 3 figures that are not leading zeros.
References
Easy Classroom, AF (2015, March 6). The Circumference and the Circle – Mathematics Sixth Primary (11 years). Retrieved from https://www.aulafacil.com/cursos/matematicas-primaria/matematicas-sexto-primaria-11-anos/la-circunferencia-y-el-circulo-l7465
Garcia, ML (sf). Circumference and circle | Math. Retrieved from http://www.bartolomecossio.com/MATEMATICAS/circunferencia_y_crculo.html
Khan Academy. (nd). Radius, diameter and circumference (article). Recovered from https://es.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/a/radius-diameter-circumference
