Zu Chongzhi, an ancient mathematician in China, approximated the circumference of a circle with the circumference inscribed by a regular polygon, thus obtaining the value of π accurate to the seventh decimal place.
π = perimeter/diameter ≈ inscribed regular polygon/diameter. When the side length of a regular polygon is longer, its circumference is closer to a circle. The π value calculated by Zu Chongzhi has been very accurate in most practical applications.
Throughout history, the calculation methods of π can be roughly divided into experimental period, geometric period, analytical period and computer calculation period.
Experimental period: A stone tablet in Babylon, made from 1900 BC to 1600 BC, recorded pi = 25/8 = 3. 125, while the Egyptians seemed to know pi earlier. British writer john tyler (1781–65438). For example, the ratio of the circumference to the height of a pyramid is equal to twice the pi, which is exactly equal to the ratio of the circumference to the radius of a circle.
Geometric method period: Archimedes (287–2 BC12 BC), a great mathematician in ancient Greece, initiated the theoretical calculation of approximate value of pi in human history. He gradually doubled the number of sides inscribed with regular polygons and circumscribed with regular polygons until inscribed with regular polygons and circumscribed with regular polygons. Finally, he came to the conclusion that 3. 14 185 1 is the approximate value of pi.
This method was later developed by two ancient mathematicians in China. In 263 AD, Chinese mathematician Liu Hui calculated the area of 3072 polygons by secant method, and obtained a satisfactory pi ≈3. 14 16.
Zu Chongzhi, a mathematician in the Northern and Southern Dynasties, further calculated the areas inscribed by the regular 12288 polygon and the regular 24576 polygon, and got 3. 14 15926.