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What is the radius of a circle and how to calculate it

What is a radius of a circle

Radius of a circle is one of the issues that geometry deals with. In fact, geometry is an aspect of mathematics that deals with questions concerning size, shape of different figures, their relative position, as well as with various properties of space. Geometry is a very old science, many problems of which were at first covered by astronomy in ancient times. Due to the fact that geometry has been studied throughout thousands of years, it has a very interesting history, consisting of a number of significant periods, each of which identifies different stages of development of this science. Studying of geometry is an integral part of education all over the world, because all the students need to have essential skills and knowledge in regard to the basic issues of geometry, as long as it is used almost everywhere in life, including even daily activities of a person. To know how to deal with calculating the radius of a circle is only one of such essential skills that you need to have. In this article, you will find information that will help you with calculating the radius of a circle and get theoretical background in regard to it.

In terms of classical geometry, when talking of the radius of a circle, whether it is a circle or a sphere, we should mean the length of the line starting in the center of the figure and ending in its perimeter. The term «radius» has originated in ancient Rome. It is the Latin word that means «ray». If you have the diameter of the circle or sphere, you can find out the radius easily, because any diameter is always defined as twice the radius.

All in all, by the radius of a circle, one should mean the distance from the center of the geometrical figure to the edge of it. As long as the diameter is considered to be the overall distance from one edge of the circle to another, it is equal to the distance of two radiuses of the figure. However, you may not always be given the diameter, so you will have to base your calculations on other data concerning the properties of the circle. Below in the article, you will learn how to measure the radius of a circle in four different ways, according to the data that you you may be given within your assignment.

Different ways to calculate the radius of a circle

One of the easiest ways to deal with calculating the radius of a circle is when you are aware of its diameter. In this case, you are going to follow the next guidelines:

  • Keep in mind the commonly accepted definition of the dimeter. The diameter of the circle is certain length of the distance that starts in the center of the figure and touches two points of two opposite edges of the figure. In fact, the diameter is the longest line in the circle and it always divides the figure into two equal parts.
  • Considering that the diameter is twice as long as the radius of a circle, you need to divide it by two. This simple step will give you the needed result.
  • Check whether your calculations right by multiplying the received number by two. If you get the number of the diameter again, then your calculation is right.

The next way to calculate the radius of a circle is helpful in case if you are aware of the circumference. Here, it is needed to do the following:

  • Make sure you know what the circumference is. By the circumference, one should mean the distance around the circle. You can think of it as of the length that you could receive if you get the circle open and flat.
  • Get the radius from the data that you have. Here, you need to divide the number indicating the circumference of the figure by 6.28.
  • Check the rightness of your calculations by multiplying the radius by 6.28. If you get the number indicating the circumference again, it means that you did everything right.

In case if the only thing that you know about the circle is the area, there is still a way to calculate the radius. Just do the following:

  • Keep in mind the formula for getting the area of the circle. You can get the area by multiplying 6.28 squared by the radius of a circle.
  • Considering the above-mentioned formula, find the radius: it is the square root of the number indicating the area of the circle and divided by 6.28.
  • Check your measurements by searching for the area having the radius. If you got the same number indicating the area that you based your calculations on, you did everything right.

Finally, there is also the fourth way to deal with calculating the radius of a circle. It will work if you are aware of the coordinates of three different points located in the given circle. Here, you will have to undertake the following steps:

  • Make sure you understand that whatever three points located on the circle you have, they may define the circle. If the figure touches all of them, they can definitely define the circle. Depending on how the given points are located, the center of the figure may be whether inside or outside of the figure and it will be called the circumcenter.
  • Make sure you’ve got the coordinates of the three points on the circle. You need to know them in order to apply the distance formula to your calculations and find the length of the sides of the triangle that is drawn by these points.
  • Once you have found the length of each side of the triangle, you need to multiply all of them together. By means of this, you will find the numerator.
  • Once you have all these numbers, you can find the radius by using the formula for the circumradius.
  • When the calculations are finished, remember checking whether you’ve got the right number indicating the radius that you were looking for by undertaking the steps in the opposite order.

Having said that, the easiest way to deal with finding the radius is, of course, if you know the diameter. But even if you don’t have such data, there’s no need to get upset since you can apply other three methods and achieve the same result.

The history of circles

The term «circle» originated in ancient Greece. In Greek language, it means a «ring». The circle as a figure and symbol had been known before the history that we know started. People tended to observe various things that had a form of a circle, such as moon, sun, etc. Circles were researched within a number of ancient sciences, such as geometry, astronomy, astrology. Different ancient scientists were researching the issue of circles, which inspired them to further achievements in different fields of science.

The earliest civilizations and cultures of the world used circles for different purposes, but mostly circles played a role of symbols. In ancient Greece, a circle considered to be a perfect shape, representing balance and absolute symmetry. The properties of a circle were the object of passionate exploration for thousands of years. Even today circles are used as a symbol of harmony in different cultures and countries of the world.

There is a number of things that were invented due to the existence and understanding of circle. For example, the wheel. The wheel is the basis of all kinds of vehicles that are known today. All kinds of the machinery that people use in contemporary world were created due to the existence and understanding of circles.

Interesting facts about circles

Many people are not aware of the fact that circles themselves are inventions, as well as all the items of contemporary world that make our lives comfortable. As a matter of fact, such geometry figure as circle is not something that has always been known about and that has always existed in the world of nature. At the same time, you cannot consider a circle to be the same kind of invention as internet or America. In other words, a circle is a symbol, it is a specific mental construct that has been invented as much as all the languages far and wide across the world that people use to communicate with.

A lot of scientists agree in the fact that a circle was invented millions of years ago to represent the sun. It could be drawn on the sand with the stick. Taking into consideration that the sun has always been the biggest circle that could ever be seen by a man’s eye, it is quite possible that the first circle was meant to represent such symbol as sun. Within the years people’s comprehension of the circle has been changing in accordance with different stages of development, including the technological development. It is important to realize that without understanding of such figure as a circle people would not be like they are today, we would not have the majority of other inventions. As a matter of fact, there are several most significant inventions in the history of humanity. Among of them, there is the invention of fire and ability to make it, the agriculture of crops and, finally, the domestication of wild animals. Even though you can rarely meet circle in the list of greatest achievements, it has still affected the life of people all over the world in the most significant way.

Without circles we would not have the possibility to drive a car. A great number of inventions that we know and use today exist due to the understanding of circles. If to look around, you will find numerous representations of circles. They are everywhere, they are an integral part of almost everything that surrounds us nowadays. Still, a circle is not something that really exists. It can be spoken about, it can be drawn, made, created over and over again, but it still exists only as a symbol in our imagination.

At the same time, there are many scientific works dedicated to the issue of circles, especially in the area of philosophy. Many researches have spent significant amounts of time to understand the concept of circles and to define, whether it can or cannot be considered to be an existing thing.

The importance of circles

It is hard to imagine a world without circles. However, if we try to do it, we will be really surprised. If there were no circles around, quite possibly that there would be only squares. We would have no bicycles and there would be no cookies ad candies; there would be no basketball, baseball, football or other games requiring the usage of ball. As a matter of fact, it is much more pleasure for the eye to look at a circle rather than at a square. For this reason, circles are very often in use in the area of commerce and public relations, as long as people tend to perceive circles more efficiently than other figures and symbols.

Circle is a universal figure that has a very broad meaning. It represents a great variety of concepts, such as totality, original perfection, eternity, unity, infinite movements and so on. In some cultures, circle is used to represent god in the meaning of an energy that can be everywhere and nowhere at the same time. Such symbolism of a circle is somehow related to the fact that there were times, thousands of years ago, when sun considered to be the only god. Thus, a circle was the only way to represent god, because it has the same shape as the sun.

As you can see, the significance of circles, their role in the history of humanity and in our everyday life is quite obvious. For this reason, it is important to be aware of basic facts about this geometry figure and to know how to deal with calculating its properties. The information provided in this article should help you deal will all the mentioned above issues and to accomplish some of geometry assignments that you may face during your studies.

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