(2) Northern and Southern Dynasties: ① Liu Hui, a mathematician in Wei and Jin Dynasties, put forward a correct method to calculate pi by using limit theory. ② Zu Chongzhi in the Southern Dynasties accurately calculated pi between 3.1415926-3.1415927, which was nearly a thousand years earlier than foreign countries. His monograph seal script has made outstanding contributions to the development of mathematics.
(1) Introduction to Zhoupian Jing, an ancient arithmetic book in China: Zhoupian Jing, Jiuzhangsuan, Sunzi Suan Jing, Wucao Suan Jing, Xiahouyang Suan Jing, Sunqiu Jian suan, Shimasuan Jing, Wujing Arithmetic and Zhushu. Among them, Zhou Pi Ai suan Jing, which expounds the theory of "covering the sky", is considered to be the oldest astronomical almanac in China, which talks about both celestial bodies and mathematics. It came into being in the 2nd century BC, but it contains historical materials earlier than this. Among them, the mathematical knowledge used by Dayu in water control has become the earliest example of using Pythagorean theorem in existing literature. (2) Pythagorean Theorem The Book of Changes Shu Jing is not the original, but has been revised and supplemented by later generations. This article in Parallel Prose of Zhou Dynasty is a question-and-answer part between Duke Zhou and Shang Gao. Next, the Q&A part of Fang Rong and Chen Zi is the sequel of Zhou pian Shu Jing. According to "Zhou Kuai Shu Jing", "So I thought the sentence was three in width, four in shares and five in diameter. If it is outside the square, it will be three, four and five in half an hour, and the ring will be * * *. The two moments * * * are twenty and five respectively, which are called product moments. Therefore, the reason why Yu ruled the world was born of this number. " Convert two right-angled sides of a moment into a certain proportion. The short right-angle side length (sentence) is 3, the long right-angle side length (strand) is 4, and the chord is equal to 5, which are 3, 4 and 5 respectively (as shown in the right figure). The sum of the sentence (that is, tick) and the square of the share is 25, which is called the product moment. The method used by Dayu to govern the world (referring to water conservancy) was developed from these mathematical knowledge. In the history of mathematics in the world, Pythagoras, an ancient Greek mathematician who discovered Pythagoras around the 5th century BC, is generally regarded as the credit of Pythagoras theorem, because he put forward a general description and proof of the theorem, which is a bit late in China. But in fact, Shang Gao understood Pythagorean theorem much earlier than Pythagoras. The Classic of Parallel Calculation of Zhou Dynasty was written around the 2nd century BC, and recorded the questions and answers between Duke Zhou and Shang Gao around 1 1 century BC. This fact proves that ancient mathematicians in China independently discovered and applied Pythagorean Theorem much earlier than foreign countries. (3) (Method of Measuring Height, Depth and Distance) The altimeter was an astronomer in the Zhou Dynasty and an amateur astronomer at that time. In the concrete data calculation method taught by Chen Zi to Fang Rong, we can find that the application of Pythagorean theorem in China has reached a very skilled level 26,700 years ago. Chen Zi's method of measuring the height of the sun can be described as follows: When the sun shines directly on the Tropic of Cancer on the summer solstice, an 8-foot-high pole is erected in the north, and the shadow length is 6 feet. Then, the surveyor moves the marker to the south, and the shadow length of the marker decreases by 1 inch every 1000 Li. It can be imagined that when the sun shadow of the benchmark is reduced by six feet, the benchmark will move 60 thousand miles to the south, and the benchmark will be directly below the sun. According to Pythagorean theorem and similarity principle, the distance between the surveyor and the sun can be calculated as 10 Wan Li. According to records, Thales, the first natural philosopher in ancient Greece, also used the shadow of the sun to measure the height of the pyramids. His method is to calculate the height of the pyramid from the shadow length of a vertical rod and the shadow length of the pyramid measured at the same time. Thales is called "the father of measurement" in the west. Thales' work is roughly in the same period as Chen Zi's, but Chen Zi's method is much higher than Thales'. Thales only used similar triangles's knowledge, but Chen Zi can skillfully use Pythagorean theorem besides similar triangles's nature.