I have no money, so it's really difficult to have another one ~ ~ ~ ~ ~ ~

Ha-ha, these were all achievements at that time. The following overview will give you a better understanding of the correct method of calculating pi proposed by Liu Hui in Wei, Jin and Southern and Northern Dynasties

Liu Hui, a famous mathematician in Wei and Jin Dynasties. At the end of Cao Wei's reign, he wrote Nine Arithmetic Notes in Nine Chapters, and put forward the correct method of calculating pi-cyclotomy. "Nine Chapters Arithmetic" says that "the diameter of three weeks is one", that is, the approximate value of pi is 3. Liu Hui thinks this is too inaccurate, and points out that "three-week diameter one" is not pi, but the ratio of circumference to diameter of a regular hexagon inscribed in a circle. Liu Hui found that when the number of sides inscribed with a polygon in a circle increased infinitely, the circumference of the polygon approached the circumference of the circle infinitely, thus creating the circle cutting technique. He said, "If you cut it finely, you will lose less, and if you cut it, you will cut it again, so that you can't cut it, and you will have nothing to lose." Liu Hui successively calculated the side length of regular dodecagon, regular icosahedron and regular 96-sided polygon from the point where the circle is inscribed with regular hexagon, worked out the area of regular 192-sided polygon, and reached the conclusion that pi was 3.14. Later, he calculated the area of a circle inscribed with a regular polygon of 3,72, and got a more accurate pi, which is 3.1416. Liu Hui used the preliminary concept of limit and put forward the secant technique, which was the most advanced in the world at that time.

Zu Chongzhi

Zu Chongzhi (429-5) was an outstanding mathematician in ancient China. The word Wen Yuan. Zhuolu, Hebei (now north of Laishui County, Hebei Province). At the end of the Western Jin Dynasty, the ancestral home moved from the north to the south. He used to be Liu Songnan, the secretariat of Xuzhou (now Zhenjiang, Jiangsu) and the county magistrate of Louxian (now Kunshan, Jiangsu). Xiao Qi, a captain of Changshui, is in charge of the Guards guarding the capital. He once wrote "On Security" and suggested that Qi Mingdi "open up wasteland and cultivate extensively". But his main achievement is in natural science, especially in the accurate calculation of pi. Zu Chongzhi is a famous scientist in the world. His colorful marble statue is embedded in the corridor of the "Exhibition of World Scientists" of Moscow University in the Soviet Union.

Zu Chongzhi's most outstanding contribution

Zu Chongzhi is a great scientist, who has made great contributions to mathematics, astronomical calendar and machinery manufacturing. At the age of 33, he put forward the "Daming Calendar", which was the most advanced calendar at that time, and corrected the error of the "Yuanjia Calendar" prevailing at that time. He rebuilt the compass, invented the thousand-mile boat and the water hammer mill, which promoted the development of productive forces. But his most outstanding contribution is that, for the first time in the world, the value of pi is accurately calculated to the seventh digit after the decimal point, that is, between 3.426 and 3.27. According to "Sui Shu's Records of the Law", "Nine numbers in ancient times, three pi, one pi, and its skill is sparse. Since the disciples of Liu Xin, Zhang Heng, Liu Hui, Wang Fan and Pi Yanzong, they have set their own new rates, but they have not reached a compromise. At the end of the Song Dynasty, South Xuzhou was engaged in the history of Zu Chongzhi, and even more secret method was adopted, with the circle diameter of 1 million as ten feet, and the circumference abundant number (surplus approximation) was three feet, one foot, four inches, one minute, five cents, nine millimeters, two seconds, seven seconds, and seven seconds. Three feet, one foot, four inches, one minute, five percent, nine cents, two seconds and six seconds, and the positive number is between the profit limit and the profit limit. Density, circle diameter 113, circumference 355. Contract rate, circle diameter 7, Tuesday 12. Also set the open difference power, open difference and stand, and take the exact circle as a parameter. The finger should be precise, and the one who counts is the best. The book written is called "Composing", and scholars can't study its profundity, so they ignore it. "

pi

pi is the ratio of the circumference to the diameter of a circle, which is usually expressed by the Greek letter "π". Pi is widely used in astronomy, calendar, machinery and other academic fields, as long as it involves the problem of circle, it should be applied to pi. Pi is an infinite decimal that can never be divided. The accuracy of pi indicates the level of ancient mathematics and science.

Zu Chongzhi calculated the exact value of pi about a thousand years earlier than foreign countries.

Zhang Heng, a scientist in the Eastern Han Dynasty and Liu Hui, a mathematician in the Three Kingdoms period, made great achievements in calculating pi. Zu Chongzhi inherited the predecessors' achievements and calculated pi between 3.1415926 and 3.1415927. He was the first outstanding mathematician in the world to accurately calculate the value of pi to seven digits after the decimal point. It was not until the 15th century that the Arab mathematician Al Cassie surpassed his achievements. However, Al Cassie was nearly a thousand years behind Zu Chongzhi. In Europe, it was not until the 16th century that German Otto and Dutchman Antuoni recalculated this figure, which was more than 1,1 years later than Zu Chongzhi.

Zu Chongzhi collected and read a large number of ancient astronomical and mathematical documents

Before Zu Chongzhi, the ancient astronomical and mathematical documents in China mainly included: Eight volumes of Tian Wen Xing Zhan written by Chu Man Gan De in the Warring States Period and Eight volumes of Astronomy written by Wei Ren Shi Shen. Later generations combined these two works into one book, called Gan Shi Xing Jing, which was the earliest astronomical work in the world. Xia Xiaozheng is a calendar book compiled during the Warring States Period, which basically preserves the summer calendar, that is, February after the winter solstice is the first month, which is more in line with the changes of the four seasons, and is the most progressive calendar in the world at that time. Zhou Piai suan Jing was written before the 1st century BC, and Nine Chapters Arithmetic was written in the Western Han Dynasty. The official book in Historical Records records many astronomical phenomena. In addition, the Zhuan Xu Calendar was written in the Qin Dynasty, the taichu calendar and the Three Calendars were written by Emperor Wu of the Han Dynasty, the Dry Elephant Calendar was written by Liu Hong, and the Lingxian was written by Zhang Heng. These documents on astronomy, calendar and mathematics are very helpful to Zu Chongzhi.

calculation of pi value

in the production practice of ancient Chinese working people, the ratio of circumference to diameter was roughly three to one. Later, with the continuous progress of science and technology, the calculation of pi value is becoming more and more accurate. From Liu Xin in the Western Han Dynasty to Zu Chongzhi in Qi Liang, many people made contributions to the calculation of pi. Liu Xin (? -23), the word Zijun, later renamed Xiu, the word Yingshu. As a captain of Zhongli, he sorted out literary and artistic books and made contributions to the bibliography of classics. Wang Mang established a new regime and was appointed as a national teacher. Later, he committed suicide because of his involvement in the murder of Wang Mang. Familiar with astronomical calendar, author of three calendars. Liu Hui was a mathematician in Wei and Jin Dynasties. Around four years ago, Wei Jingyuan wrote nine chapters of arithmetic and ten volumes, and wrote nine chapters of gravity difference diagram and one volume, creating a method of observation and calculation. His main invention is to find pi by cutting logs, and to calculate the area of a regular 372-sided polygon in a circle, and the pi is 3.1416. He Chengtian (37-447), an astronomer in the Southern Song Dynasty, was born in Donghai. Yuan Jia wrote and edited Song Shu for Zuo Lang, but he died without success. He has a good knowledge of classics and history, and is good at astronomical laws and calendars. He once pointed out in the above table that the calendar used at the beginning of the scene was improper, so he called it Yuan Jiali calendar, which had a great influence on the calendar of later generations.

Jia Sixie

Jia Sixie, an outstanding agronomist in ancient China. Shandong Yidu people. At the end of the Northern Wei Dynasty, he was the satrap of Levin (now northwest of Zibo). He studied predecessors' works on agriculture, collected folk songs and proverbs, visited experienced farmers, made careful observation and comparison in the actual production struggle, and wrote the book Qi Min Yao Shu. This book is a summary of agricultural science in China at that time, from which we can know the development of agricultural science at that time. What is contained in this book is still useful now and can be used for reference. Therefore, this book is a valuable scientific and cultural heritage of our country.

Qi Min Yao Shu

Qi Min Yao Shu is the oldest and most complete agricultural book in China. There are 92 books, divided into 1 volumes and about 11, words, including agronomy, horticulture (cultivation of vegetables and fruit trees), forest, animal husbandry (raising poultry and livestock), fish farming and agricultural products manufacturing (such as brewing and food processing) and other agriculture and handicrafts. Among them, agronomy and horticulture account for an important part. Since the Western Zhou Dynasty, the knowledge and technology that China has acquired in agriculture and handicrafts are summarized in this book. In the cultivation and planting of crops, Qi Min Yao Shu emphasizes that "when the weather is favorable, the amount and location are favorable, and the effort is less and the success is more". The book records the sowing date of main crops, such as millet, millet and millet, and introduces how to select seeds, soak seeds and accelerate germination of rice, as well as the experience of crop rotation and interplanting. The book not only emphasizes the adaptation to local conditions and time, but also attaches great importance to the improvement of soil and farming techniques (tillage, hoeing, etc.), and puts forward that it is necessary to always maintain the appropriate amount of water contained in soil and enhance soil fertility, and to make use of the different nutrients absorbed by crops to carry out crop rotation, intercropping, mixed cropping and interplanting. It should be pointed out that the book puts forward the method of green manure rotation. At that time, the cultivation method of rotation fallow was widely practiced in Europe, and it was not until the 193s that Europeans implemented the green manure rotation system in agriculture. In the aspect of vegetable cultivation, it is considered that land should be highly utilized and manure should be used heavily in production. In the aspect of fruit tree planting, the grafting method is introduced in detail. In livestock breeding, pay attention to feeding and water feeding. The book also introduces in detail more than 2 methods of making wine. The book quotes 156 kinds of related works, which occupies an important position in the history of agriculture in China and the world.

Li Daoyuan

Li Daoyuan (? —527) was born in Zhuoxian County, Fanyang, Northern Wei Dynasty (now Zhuozhou City, Hebei Province). He was the suggestion lieutenant, and later served as Ambassador Guan You. Yongzhou secretariat Xiao Baoyin rebelled and was killed. Be fond of sex and pay attention to geography. Collect a large number of geographical and historical materials, quote local myths and legends, and write a book "Notes on Water Classics".

The Water Classic

The Water Classic, a masterpiece of ancient Chinese geography, was written by Sang Qin in the Han Dynasty. The book describes 137 rivers and waterways in China, systematically takes waterways as the key link, describes their origins and places where they flow, and establishes the method of proving land by water.

Notes on Water Classics

Notes on Water Classics, a masterpiece of ancient Chinese geography, with 4 volumes. Li Daoyuan made a note for Shui Jing. The number of waterways in this book has increased to 125, with 2 times as many annotations as the original book, and more than 4 kinds of bibliographies have been cited, which greatly enriched the content of Shuijing. The Notes on Water Classics systematically describes the origin, ancient and modern changes and water conservancy development of major water systems such as the Yellow River, the Yangtze River and the Huaihe River. Taking the waterway as the key link, it records the natural phenomena such as mountains, plains, hydrology, climate, soil and vegetation in the areas along the river, as well as the establishment, evolution, rise and fall of cities and Guanjin, as well as relevant historical figures, historical events, myths and legends, etc., including almost all historical geography. In the process of copying and circulating, there are many confusions and mistakes in the scriptures and annotations of Shui Jing Zhu. Scholars of Ganjia in Qing Dynasty did a lot of collating work on Notes on Water Classics, such as Quan Zuwang's Notes on Water Classics for the Whole School, Zhao Yiqing's Notes on Water Classics and Dai Zhenxiao's Notes on Water Classics. In modern times, Yang Shoujing and Xiong Huizhen also wrote Notes on Water Classics, which indicated that Li's notes cited the original facts, detailed the migration of the waterway described in Li's notes, and revised the explanations of all the schools, including Quan, Zhao and Dai. It is a good reference book about Shui's Notes.

The description of apes on both sides of the Three Gorges in Shui Jing Zhu

Translated into vernacular: The sound of apes calling came from an empty valley, which was so sad and lasting for a long time. The fisherman sang: The Wuxia Gorge of the Three Gorges in Badong is the longest, and the three cries of an ape make people cry.

Description of the picture

Ancient bone calculation

This is the bone calculation of the Western Han Dynasty unearthed in Qianyang County, Shaanxi Province in 1971, and it is the earliest one ever seen. Calculation and preparation is the earliest calculation tool in China, which appeared as early as the Spring and Autumn Period. At that time, in addition to bone calculation, there were various materials such as wood, iron and copper. When people calculate, they put the calculation chips into horizontal and vertical forms. Horizontal type means ten digits, thousands digits, 1, digits ... Vertical type means one digit, hundreds digits, 1, digits ... and so on, alternating vertically and horizontally, all kinds of numbers can be expressed. If you encounter "zero", don't put the calculation chip, and leave this number blank. The calculation chip on the right side of the figure indicates the number of 1976. Calculation and preparation were used in ancient China for nearly two thousand years, and were gradually replaced by abacus calculation

(1) Overview

Wei, Jin, Southern and Northern Dynasties were famous troubled times in ancient China. In order to summarize the historical experience of managing the rise and fall of chaos, many historians and scholars have devoted their energy to sorting out and studying the data left over from this period since the Tang Dynasty. Among them, Zi Zhi Tong Jian is the first book with great achievements. In this chronological history book, the historical events in the 4 years of Wei, Jin, Southern and Northern Dynasties are not only sorted out in an orderly way, but also Sima Guang expressed his views on some historical events and figures in the form of "Chen Guang Yue". In addition to Zi Zhi Tong Jian, there are other works that investigate or involve this period of history, such as Meng Xi Bi Tan by Shen Kuo in Song Dynasty, Rong Zhai Essay by Hong Mai, Yan Fan Lu by Cheng Dachang, Lu You's Notes on Old Learning Temple, Wang Yinglin's Notes on Learning Difficulties, Ye Shi's Notes on Learning, Li Zhi's Collection of Books and Continuation by Ming Dynasty. Wang Fuzhi, a beginner in the late Ming and Qing Dynasties, systematically analyzed and criticized the success or failure of the rulers in this historical period. Ganjia School in Qing Dynasty is the peak of traditional historiography research. Many entries in Qian Daxin's Textual Research on the Twenty-two History, Zhao Yi's Notes on the Twenty-two History and Wang Mingsheng's Discussion on the Seventeen History involve the study of the history of Wei, Jin, Southern and Northern Dynasties. Before the 2th century, scholars in previous dynasties had made a lot of achievements in the study of the history of Wei, Jin, Southern and Northern Dynasties, but generally speaking, they were all confined to the circular view of history, and the basic way was just to write, test and evaluate history. China's new historiography began to sprout at the turn of the 19th-2th century. A group of scholars, influenced by various views on evolutionary history and development history from the west, pay attention to getting rid of the shackles of old historical research and gradually step into a new world. Throughout the 2th century, China historians are no longer willing to sort out the national heritage, but try to find the motivation, connection and understanding with some regularity hidden behind the historical appearance by analyzing historical materials. Therefore, the study of China's history of Wei, Jin, Southern and Northern Dynasties has turned a new page. The research on the history of Wei, Jin, Southern and Northern Dynasties in China in the 2th century can be divided into two periods in 1949. The previous period can be divided into two stages: 191-1929 and 193-1949. The latter period can be divided into three stages: 1949-1966, 1966-1978 and 1978-2.

in the early 3 years of the 2th century, the research on the history of Wei, Jin, Southern and Northern Dynasties in China was characterized by the transition from old historiography to new historiography. According to rough statistics, from 191 to 1919, there were less than 9 papers on the history of Wei, Jin, Southern and Northern Dynasties, and only more than 1 kinds of works were published, and the ideas and methods of most of the works were quite old, which basically broke away from the traditional historiography. Of course, there are also some articles in this period that are masterpieces of pioneering research using the new historical concept. Liang Qichao wrote in 192 that China's autocratic politics had been continuously strengthened from the Warring States Period to the Qing Dynasty, "there was a noble class in the middle" and "it was a social phenomenon in China for thousands of years". However, after analysis, he thinks that "the Six Dynasties era, on the whole, was aristocratic, not aristocratic politics. Its evolution in authoritarian politics, there is no damage "(1). This view is still enlightening today. In addition, Tang Yongtong's Zhu Daosheng and Nie? Xue (Sinology Quarterly, No.12, 1925), Rong Zhaozu's Thoughts on He Yan Wang Bi (Journal of Language History, Sun Yat-sen University, No.12, 1927), Lu Xun's demeanor in Wei and Jin Dynasties and the relationship between chapters and medicine and wine (Beixin Semimonthly, No.11, 1927), and Liang Peizhen's Politics in China during the Southern and Northern Dynasties The Great Migration of the Han Nationality in the Jin Hui Emperor's Era (No.7 of Chengda Historical Journal in 1929) and the Times Background at the Time of the Han and Wei Dynasties (No.11 of Central University Semimonthly in 1929), etc., respectively, investigated the society of Wei, Jin, Southern and Northern Dynasties from the perspectives of religious culture, politics, population mobility and the change of scholar style, giving people a refreshing feeling.

in the 193s and 194s, Wei and Jin Dynasties in China.