In geometry, a circle is a part of a plane that is bounded by a circle. The word denoting a 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 every spill of the Nile River, people had to re-mark areas of fertile land on its banks. The circle is a closed curve, and all points lying on it are equidistant from the center by a distance called the radius (it corresponds to half the diameter - a 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 cannot determine its length or cannot answer the question, βhow to calculate the area of ββa circle?β, Does not yet know geometry. Since the most beautiful, difficult and interesting theorems are connected with a circle.
A circle is considered a "wheel of geometry." Its axis is always located at the same distance from the surface on which it rolls - this is one of the main properties. Another important property of a circle is that the area outlined by it - the circle - will be maximum in comparison with the area of ββother figures outlined by broken lines whose length is equal to the length of the circle. How to find the area of ββa circle? In answering this question, one mathematical constant should be remembered: in geometry and mathematics, the number Ο is very important (the Greek letter should be pronounced as pi), which shows that the circumference is 3.14159 times its diameter: L = Ο β’ d = 2 β’ Ο β’ r (d is the diameter, r is the radius). That is, for a circle with a diameter of 1 meter, the length will be 3.14159 m. The search for the exact value of this transcendental number has its own interesting history, which went along with the development of mathematics.
The number Ο is also used to calculate the area of ββthe circle. The entire history of this number is conditionally divided into three periods: the ancient period (geometric), the classical era and the new time associated with the advent of digital computers. Even ancient Egyptian, Babylonian, ancient Indian and ancient Greek geometers knew that the ratio of circumference to diameter is a little more than 3. It was this knowledge that helped ancient scholars to establish the circle area formula. Since the value of Ο is known, we can find the area of ββthe circle by substituting in the formula: S = Ο β’ r2, the square of its radius r. Scientists at different times (but Archimedes, in the 3rd century BC, was the first in this matter) used many methods to determine the number Ο, and today the search for methods continues, it is calculated on computers. The accuracy with which it was calculated in 2011 reached ten trillion characters.
Formulas showing how to find the area of ββa circle or how to find the circumference are known to any high school student. For thousands of years, they have been used by mathematicians and skilled computer specialists, since the interest in determining the number Ο more and more has become more like a mathematical sport, with the help of which the capabilities and advantages of programs and computers are nowadays demonstrated. The ancient Egyptians and Archimedes believed that the number Ο is in the range from 3 to 3.160. Arab mathematicians have proven that it equals 3.162. The Chinese scientist Zhang Heng in the 2nd century AD clarified its meaning β 3.1622 and so on - the search continues, but today they are acquiring a new meaning. So, for example, the approximate value of 3.14 coincides with the unofficial date of March 14, which is considered the holiday of the number Ο.
The area of ββa circle, knowing the radius and using the approximate value of the number Ο, can be easily calculated. But how to find the area of ββa 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 is not suitable. Therefore, to solve the problem contained in the question βHow to find the area of ββa circle?β, Instrumental methods are used. A numerical characteristic of a two-dimensional geometric figure, showing its size, is found using a palette or planimeter.