The area of a circle refers to the size of the plane space occupied by the circle, which is often expressed by S. The circle is a regular plane geometry figure, and there are many calculation methods, such as Kepler method and cavalli method.

The Egyptian pyramid of khufu, built more than 4,000 years ago, has a square base and covers an area of 52,900 square meters. The calculation of its base length and angle is very accurate and the error is very small. It can be seen that the technical level of measuring a large area was already very high at that time. And the circle is the most important curved edge shape. The ancient Egyptians regarded it as a sacred figure given by God.

How to find the area of a circle is a test of human wisdom by mathematics. The general derivation of the formula of circle area is: firstly, divide a circle into several parts evenly, then put it into an approximate rectangle, and finally derive the formula of circle area according to the relationship between rectangle and circle. At that time, people thought that since the square area was easy to find, all they had to do was to find a way to make the square area and the circle area exactly equal.

But how to make such a square has become another difficult problem. One of the three major geometric problems in ancient times was to turn a circle into a square. This geometric drawing problem, which originated in ancient Greece, has been puzzling many geniuses for more than 2000 years. It was not until the19th century that people proved that this geometric drawing problem could not be made by the ruler and ruler drawing method of the ancients.

Deductive history of circle area;

Zu Chongzhi, an ancient mathematician in China, started with a circle inscribed with a regular hexagon, multiplied the number of sides, and approximated the area of a circle with the inscribed area of a regular polygon. Mathematicians in ancient Greece started with regular polygons inscribed in a circle and circumscribed at the same time, increasing the number of their sides and approaching the area of the circle from the inside out.

Mathematicians in ancient India cut a circle into many small petals similar to watermelons, and then butted these small petals into a rectangle, replacing the area of the circle with the area of the rectangle. Many ancient mathematicians worked hard on the area of a circle and made valuable contributions. It opens the way for future generations to solve this problem.