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Why is the more sides of a regular polygon, the closer it is to a circle?
This is an approximate method called cyclotomy. The circle is relative, just a visual effect. When the number of sides of a regular polygon increases indefinitely, the length of the regular polygon gradually shortens and finally approaches a point. At this time, it is a circle in visual effect. Just like watching a movie, continuous action is formed by countless single pictures under the illusion of visual persistence.

In the middle of the 3rd century AD, Liu Hui, a mathematician in Wei and Jin Dynasties, initiated secant technique, and established a strict theory and a perfect algorithm for calculating pi. Secant method is a method to find the circumference of a circle by multiplying the number of edges inscribed in a regular polygon.

Secant is the infinite approximation of the area of a circle inscribed with a regular polygon to the area of a circle. Liu Hui described his "tangent circle" as follows: If you cut it carefully, you won't lose much. If you cut it again, it will be combined with the circle and nothing will be lost.

That is, the circle is inscribed with a regular polygon, and the circumference of the regular polygon is infinitely close to the circumference of the circle, thus obtaining more accurate pi.