The basic idea of cyclotomy is to divide a circle into several small sectors, and then add the areas of these small sectors to get the approximate area of the circle. For example, if a circle is divided into six equal sectors, and the angle of each sector is 60 degrees, then the approximate area of the circle can be obtained by calculating the sum of the areas of these sectors.
With the development of science and technology, secant is gradually replaced by more accurate methods, such as finding the area and circumference of a circle with infinite series. However, the historical and cultural value of cyclotomy should not be underestimated. It is not only an important concept in mathematics, but also one of the important milestones in the development of human civilization.
In modern mathematics, secant is also widely used in circles and other curves and surfaces. For example, if you divide a circle into smaller parts and treat it as a straight line, you can calculate its circumference more accurately. At the same time, by dividing the circle more finely, the area and other geometric quantities of the circle can be calculated more accurately.
The characteristics of cyclotomy:
1. Circumcision is a simple extreme idea. It gradually approximates the circumference and area of a circle by increasing the number of edges inscribed with a regular polygon, thus obtaining the approximate value of the circumference and area of a circle. This kind of limit thought is one of the foundations of modern mathematical thoughts such as calculus and has important mathematical value.
2. Secant embodies the combination of mathematics and art. When calculating the inscribed regular polygon of a circle, it is necessary to divide the circle into equal parts, and the position of each equal part is calculated according to the equal angle passing through the center of the circle. Therefore, when calculating the inscribed regular polygon of a circle, secant is actually simulating the basic characteristics and curve beauty of the circle. This combination of mathematics and art not only makes secant have higher aesthetic value, but also makes mathematics more practical and expressive.
3. The secant circle method has strong approximate calculation ability. By increasing the number of sides of a circle inscribed with a regular polygon, secant technology can gradually improve the approximate accuracy of the circumference and area of a circle. This approximate calculation ability has important application value in scientific calculation and engineering design, which can help people better understand the nature and laws of things.
4. Circumcision also has strong cultural value. It is one of the important achievements of ancient mathematics in China and represents the unique characteristics and wisdom of ancient mathematics in China. The cultural connotation and thinking method in the art of cyclotomy are also widely used in China's traditional culture and philosophy, and become an important part of China's traditional culture and philosophy.