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 first calculated π value by exhaustive method in the book Measurement of Circle. The so-called "exhaustive method" is to start from the unit circle, find out that the lower bound of pi is 3 by inscribed regular hexagon, and then find out that the upper bound of pi is less than 4 by circumscribed regular hexagon with the help of Pythagorean theorem. Then, he doubled the number of sides of inscribed regular hexagon and circumscribed regular hexagon to inscribed regular hexagon 12 and circumscribed regular hexagon 12 respectively, and then improved the upper and lower bounds of pi with the help of Pythagorean theorem. 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.