The geometry of the circle is called the plane, which is bounded by a circle.The word for a branch of mathematics, the descriptions left by ancient Greek historian Herodotus, is derived from the Greek words "geo" - the land and the "metro" - measure.In ancient times, after each flood of the Nile people I had to re-mark areas of fertile land on its shores.The circumference of the closed curve is the same, and all points thereon lie equidistant from the center by a distance called the radius (it corresponds to half the diameter of the - line connecting two points of the circle and passing through its center).It is believed that the one who has not studied the properties of a circle, is not able to determine its length or can not answer the question, "how to calculate the area of a circle?", Does not know geometry.Since the most interesting, challenging and interesting theorem connected with the circle.
Circle is considered a "wheel geometry."Its axis is always located on the surface on which it is rolling, at the same distance - this is one of the main properties.Another important property of the circle lies in the fact that the area circumscribed by it - circle - is compared with the maximum area of the other figures outlined with broken lines, the length of which is equal to the circumference.How to find the area of a circle?In answering this question we should remember about a mathematical constant: in geometry and mathematics is critical number π (Greek letter should be pronounced as pi), which shows that the circumference at 3.14159 times its diameter: L = π •d = 2 • π • r (d - diameter, r - radius).That is, for a circle with a diameter of 1 meter, the length will be equal to 3.14159 m. Find the exact value of transcendental numbers has an interesting story that ran parallel with the development of mathematics.
number π is also used to calculate the area of a circle.Throughout the history of the number conventionally divided into three periods: the ancient period (geometric), the classical era and a new time associated with the advent of digital computers.Even ancient Egyptian, Babylonian, ancient Indian and Greek geometers knew that the ratio of the circumference and diameter of a little more 3. It is this knowledge has helped scientists to establish the ancient formula for the area of a circle.Since the value of π is known, it is possible to find the area of a circle, substituting into the formula: S = π • r2, the square of its radius r.Scientists at different times (but Archimedes, even in the 3rd century BC, in this matter was the first) used a variety of methods to determine the number π, and today continues to search for methods, it is calculated on the computers.The accuracy with which it is designed in 2011, has reached ten trillion marks.
Formula showing how to find the area of a circle, or how to find the circumference, known to any high school students.They have been used for millennia by mathematicians and calculators, qualified as interest more accurately determine the number π began to resemble a mathematical sport, with which today demonstrates the possibility and benefits of programs and computers.The ancient Egyptians, and Archimedes believed that the number π is in the range of 3 to 3,160.Arab mathematicians, it was proved that it is equal to 3,162.Chinese scientist Zhang Heng in the 2nd century AD, said the value ≈ 3,1622 and so on - the search continues, but now they take on a new meaning.For example, the approximate value of 3.14 coincides with the unofficial date of March 14 is considered a holiday of π.
area of a circle, the radius of knowing and using the approximate value of π, is easy to find.But how to find the area of a circle if the radius is unknown?In the simplest case, if the area can be divided into squares, then it equates to the number of squares, but in the case of the circle, this method is not suitable.Therefore, to solve the problem contained in the question "how to find the area of a circle?", Using instrumental techniques.Numerical characteristics of two-dimensional geometric figures, showing its size, are using the palettes or planimeter.
