In the natural world, if there is one shape, the recurrence of which is most common is the circle. Almost all of the celestial bodies are circles, and even at times, the path of their motion is circular. No wonder from ancient times, the study of the shape of a circle has always been found more interesting and useful. It would be worth remembering that one of the earliest inventions of mankind, that is, the wheel was a circular form. As the circle was found to be a very useful form, many efforts of humankind were spent on the study of the circle and to find its properties like the area or the circumference of a circle.
Why a circle has such a frequent occurrence in the natural world is often attributed to certain physical laws, but from a mathematical standpoint, a circle is unique because of its unique definition. It is defined as the locus of a path that is equidistant to a point. This point is called the center point of the circle. And all the points in the periphery of a circle are at the same distance from this center point. This distance is called the radius of a circle which helps us in finding the area of circle. So if one needs to know anything about the circle, it would be enough to know where the center point is located and what the radius of the circle is.
When drawing a circle, especially when drawing a small circle, it’s easy to measure its circumference or length of the periphery. By definition, the circumference is the length of the path which circumscribes the circular shape. If you take a small thread and try to place it on the circumference, then measuring the length of the thread piece would give an approximate value of the circumference of a circle. Now, here comes the part which surprised the world thereafter as they drew many circles of different sizes, but every time they found that the ratio of the circumference of the circle and its radius is fixed. No matter which circle was measured, the ratio came out exactly the same as other circles. This led to the discovery of perhaps one of the greatest constants of mathematics, the value of “Pi”. The ratio of the circumference of the radius of the circle was found to be twice the value of Pi. The value of pi, which is an irrational number, is when it has got an infinite number of values in the decimal places, and they are non-recurring.
So, as the Pi was discovered, the circumference of the circle was then described as 2 * pi * radius of the circle. The value of Pi is 22/7, or when expressed in decimal, it is rounded off to 3.14.
The area of a circle was another important attribute of the circle which needed to be found out, and it is possible to imagine the area of a circle as the sum of infinite circles that can be drawn inside the circle with decreasing radius. So the area of a circle can be calculated by integrating the length of its circumference from 0 to ‘length of the radius.’ By doing so, we get the area of the circle as pi * radius * radius.
It’s important to mention that the area of a circle, as is the area of any other figure, would be expressed in square units. So if you have a radius of the circle, then square the value of the length of the radius and multiply it by the value of pi, and the result would be the value of the area of the square.
The importance of the constant pi and the ease with which the circumference or the area of a circle can be calculated using just the value of pi and the length of the radius of the circle is like a boon to mankind. Being the most commonly occurring form in the natural world, it surely helps that the ways to measure it are relatively simple and quick.
