How to find the area of a circle

In geometry, a circle is a part of a plane that is bounded by a circle. The word for the section of mathematics, according to descriptions left by the ancient Greek historian Herodotus, came from the Greek words "geo" - earth and "metrio" - I measure. In ancient times, after each flood of the Nile River, people had to re-mark the areas of fertile land on its banks. The circle is a closed curve, and all the points lying on it are equidistant from the center by a distance called the radius (it corresponds to half the diameter - the line connecting two points of the circle and passing through its center). It is believed that one who has not studied the properties of a circle, does not know how to determine its length, or can not answer the question "how to calculate the area of a circle?" Does not yet know geometry. Since the most beautiful, difficult and interesting theorems are connected with the circle.

A circle is considered to be a "wheel of geometry". Its axis is always from the surface on which it rolls, at one distance - this is one of the main properties. Another important property of the circle is that its area delineated - a circle - will be the maximum in comparison with the area of other figures outlined by broken lines, the length of which is equal to the length of the circle. How to find the area of a circle? When answering this question one should remember one mathematical constant: in geometry and mathematics the number π (the Greek letter should be pronounced like pi) is of great importance, which shows that the circumference is 3.14159 times its diameter: L = π • D = 2 • π • r (d is the diameter, r is the radius). That is, for a circle with a diameter of 1 meter, the length will be 3.114159 m. The search for the exact value of this transcendental number has its own interesting history, which went in parallel with the development of mathematics.

The number π is also used to calculate the area of a circle. The entire history of this number is conventionally divided into three periods: the ancient period (geometric), the classical era and the new time associated with the advent of digital computers. Even the ancient Egyptian, Babylonian, ancient Indian and ancient Greek geometers knew that the ratio of the circumference and diameter is slightly greater than 3. It was this knowledge that helped scientists of antiquity establish the formula of the area of the circle. Since the value of π is known, we can find the area of the circle by substituting in the formula: S = π • r2, the square of its radius r. Scientists at different times (but Archimedes, as far back as the 3rd century BC, were the first in this issue) used a variety of ways to establish the number π, and today the search for methods continues, it is computed on computers. The accuracy with which it is calculated in 2011 reached ten trillion signs.

Formulas showing how to find the area of a circle or how to find the circumference of a circle are known to any high school student. They have been used for thousands of years by mathematicians and qualified calculators, since the interest in an increasingly accurate definition of the number π has become like a mathematical sport, with which modern opportunities and advantages of programs and computers are demonstrated. The ancient Egyptians and Archimedes believed that the number π is in the range from 3 to 3,160. Arab mathematicians have been shown to be 3,162. Chinese scientist Zhang Heng in the 2nd century of our era specified its meaning ≈ 3,1622 and so on - the searches continue, but today they acquire a new meaning. So, for example, the approximate value of 3.14 coincides with the unofficial date of March 14, which is considered a holiday of the number π.

The area of the circle, knowing the radius and using the approximate value of the number π, can easily be calculated. But how to find the area of a circle if its radius is unknown? In the simplest case, if the area can be divided into squares, then it is equated to the number of squares, but in the case of a circle this method does not fit. Therefore, to solve the problem contained in the question "how to find the area of the circle?", Use the instrumental methods. The numerical characteristic of a two-dimensional geometric figure, showing its size, is found using a pallets or a planimeter.