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How did Zu Chongzhi study pi?
As early as the Wei and Jin Dynasties, Liu Hui put forward the method of "cutting the garden" (inscribed with regular polygons) to measure the perimeter of the garden. He said: "If you cut it carefully, you won't lose much. If you cut it again, you won't be able to cut it any more. Then you can encircle it and lose nothing." It's a pity that he lacks contradictory ideas and can't put forward the idea of "tangent circle" (regular polygon outside tangent circle) to solve the measurement of the circumference of a circle. Zu Chongzhi followed Liu Hui's method. I don't know that a large number of "cuts" tend to infinity, and a large number of "cuts" also tend to infinity. The closer the sum of the side lengths of the "incision" is to the circumference, the closer the sum of the side lengths of the same "incision" is to the same circumference. This reality can easily lead to the concept of "limit". Without the concept of limit, differential calculus cannot be invented! What a pity! There is a "cut" first. If there are profound opposing thoughts, we should think of "cutting". "Cut" and "cut" tend to be the same number, and it is easy to get the concept of "limit"! Ah! Missed! Let the latecomers Newton and Leibniz take the lead!