Li Daoyuan (about 466-527), who lived in the Northern Wei Dynasty, was born in an official family in Zhuoxian County, Hebei Province. He loved sightseeing when he was a teenager. Later, when he became an official, he traveled all over the country. Every time he visited places of interest, he also carefully surveyed the topography of the water surface and learned about coastal geography, landforms, soil, climate, people's production and life, and regional changes. He found that the ancient geography book "Water Mirror" lacked accurate records of the ins and outs of large and small rivers. However, due to the changes of the times and the rise and fall of cities, some rivers changed their routes and names, but they were not supplemented and explained in the book. Li Daoyuan then personally annotated the water mirror.

In order to write notes about water mirrors, he read more than 400 books, consulted all the maps, studied a large number of cultural relics, and personally went to the field to check the records in the books. Water mirror has 65,438+037 rivers and 65,438+100,000 words. After Li Daoyuan's annotation, the number of river maps increased to 1252, with * * * 300,000 words, 20 times more than the original. The book describes the origin and flow direction of rivers, the physical geography and economic geography of each basin, as well as volcanoes, hot springs and water conservancy projects. This book is beautiful and vivid, and it can also be said to be a literary work. Because of its great value in the history of China's scientific and cultural development, many scholars in the past dynasties specially studied it and formed "Sydney".

The eloquent Li Daoyuan attacked Yongning Hou first, and the case was reduced to Bo. Li Biao, the assistant commander of the suggestion, wrote a decree in Daoyuan, and cited it as a book to help the suggestion. Biaoyou is played as a servant, and Daoyuan is relieved of his official position. Jingmingzhong is a Jizhou town with a long history. The secretariat is very strong and obedient to the queen's father. The west is Guanzhong, and it has not yet reached the state. Daoyuan acted for three years. The government is harsh, officials are afraid, and traitors flee to other places. After trying to defend Luyang County, Daoyuan issued a statement advocating persuasion. Zhao said: "Luyang was originally a barbarian, and there was no college student. Listen to it now, so as to be a good man and keep Wen Weng. " Daoyuan is in the county seat, and the mountain is quite famous. I dare not be a coach. Yan Changzhong, as the secretariat of East Jingzhou, was a powerful politician, as in Jizhou. The barbarian told me that he had invited Kouzuli, the former secretariat. And sent Daoyuan back to Beijing with 70 garrison soldiers, and the two were relieved of their duties.

After that, He Nanyin. Ming Di changed the towns of Woye, Huai Shuo, Bo Gu, Wuchuan, Fuming, Rouxuan, Huang Huai and Yuyi into states, and its county, county and garrison were named as ancient cities. Zhao Daoyuan holds the festival and serves as assistant minister of Huangmen. Chiyi and Li Chong, the viceroy, should set up a position and cut their future. Towns will rebel, but they will return in vain.

At the beginning of Xiaochang, Liang sent generals to attack Yangzhou, and Yuan Mu rebelled in Pengcheng. Zhao Daoyuan kept the festival, served as a servant, took photos of Taiwan officials, saved the armies, and shot Li Ping's story according to the servant. Liang Jun went to Yang Guo, but failed. There are many gains from the recovery of Daoyuan.

After the suggestion, lieutenant. Tao Element is called Meng Yan, and Quan Hao is afraid of it. But it can't be corrected, and its reputation is even worse. Alice and Ruyue have a good relationship and often sleep together. And the election of state officials is mostly because of reading. I often sleep in seclusion and return to my home. Daoyuan came to see me secretly, took my thoughts and sent me to prison. Queen Yue Qiling, please read your mind and forgive me. Daoyuan did his best because he was satisfied with it.

At that time, the secretariat of Yongzhou was slightly exposed, and the assistant minister and Chengyang Wang was jealous of Daoyuan, and was sent as a close friend ambassador on the grounds of satirizing the court. Bao was worried about Daoyuan's self-interest and sent a physician to surround Daoyuan at the Yinpan Post Station. The pavilion is on the mountain and often eats wells under the mountain. Now we are surrounded. Without water, we can't cross the well more than ten feet. The water bent as hard as it could, and the thief climbed over the wall and went in. Daoyuan and his brother Daoque were both killed. Knife scolds thieves, sharp death. Baoyu sent his father and son to Chang 'an East. Things were peaceful, and the funeral was also given to Shangshu of the official department, the secretariat of Jizhou and the Duke of Anding County.

Daoyuan was eager to learn and read strange books, and wrote 40 volumes of Water Mirror, with 0/3 articles in this journal/kloc. It is also a "seven hires", and all articles are in the world. However, brothers don't get along and are too jealous.

Zu Chongzhi, also known as Fan Yang (now Laiyuan, Hebei Province) was born in Kuaixian County. Born in 429 A.D. in Jiankang (now Nanjing, Jiangsu), he was an official family. Although he was originally from the north, several generations of ancestors were officials in Jiangnan and were familiar with the calendar. My grandfather is in charge of civil engineering construction, and my father is also knowledgeable. He had the opportunity to receive scientific knowledge from his family since he was a child. When he was young, he entered Hualin University, which specializes in academic research. Zu Chongzhi once worked as a state official, joined the army, served as a county magistrate, from the highest official to a captain in Changshui, and enjoyed four salaries. He died in 500 AD.

Zu Chongzhi was a great mathematician and astronomer in ancient China. His life's works are varied. Unfortunately, all the books on mathematics have been lost. In all kinds of book catalogues at home and abroad, we can see that the titles of his mathematical works are "Composition" 6 volumes, "Notes on Nine Chapters of Arithmetic Meaning" 9 volumes and "Notes on Heavy Difference" 1 volume respectively. In astronomical calendar, he compiled Da Ming Calendar and wrote a refutation for Da Ming Calendar. In the annotation of ancient books, Zu Chongzhi has such works as The Book of Changes, Lao Zi Yi, Zhuangzi Yi, The Analects of Confucius and The Interpretation of Filial Piety, but they are all lost. In terms of literary works, he wrote 10 volume "Telling Different Stories", and fragments of this work can be seen in books such as "Taiping Magnolia".

Zu Chongzhi was interested in astronomy and mathematics since he was a child. He collected almost all kinds of documents, records and materials from ancient times to his life for research, and personally made accurate measurements and careful calculations. As he himself said, "measure your feet, bow detector, do your best, make a decision before you move." He made a serious study of the work of scientists such as Liu Xin, Zhang Heng, Zheng Xuan, Kan Yi, Wang Fan and Liu Hui, refuted their mistakes one by one, and obtained many valuable results. A well-known example is the value of garden rate, which is accurate to 7 digits.

The calculation of garden rate π shows the mathematical level of a country and a nation. In ancient China, like any other countries and regions with earlier cultural development in the world, the earliest rate of people using gardening was 3. This value with great error has been used until the Han Dynasty. After entering the Han Dynasty, the improvement of garden rate attracted the attention of many scientists, who all did some work. The most important is Liu Hui, a mathematician in Wei and Jin Dynasties. He used "gardening" to calculate the gardening rate as 3. 14.

Regarding Zu Chongzhi's work on the rate of garden completion, its historical materials can only be found in the records of Sui Shu's Law, and Zu Chongzhi also gives two approximate fractional values of the rate of garden completion:

Security rate: π=355/ 1 13, with 6 digits after the decimal point accurate,

Approximation rate: π=22/7, accurate to 2 decimal places.

In Europe, the calculated value after 1 100 years is 355/13, which is called "Anthonis rate". 19 12 years, Japanese mathematician Masao Sanshi proposed that π=355/ 1 13 was called "ancestral rate".

It is a great pity that there is no historical record about how Zu Chongzhi calculated such an accurate result. But judging from the situation at that time, Zu Chongzhi still used Liu Hui's Horticulture. If so, Zu Chongzhi needs to calculate the area of the regular 12288 polygon and the regular 24576 polygon in the garden. You need to add, subtract, multiply, divide, square root and other operations for more than 130 times, and each operation must be accurate to 9 digits. It is conceivable that in those days, it took great care and superhuman perseverance to calculate by listing. The calculation of sphere volume is another great achievement of Zu Chongzhi and his son (Rihuan) in mathematics. Grandfather got the formula of sphere volume according to Liu Hui's correct method in "Nine Chapters Arithmetic Note".

Sphere volume =4/3πγ3.

Grandfather summed up the so-called "Zu's principle" in the process of deducing the formula of sphere volume. In the west, this principle is called "cavalieri's principle", but its discoverer, Italian mathematician cavalieri (1598 ~ 1647), was many years later than his grandfather.

Zu Chongzhi's achievements in astronomical calendar are mostly contained in his Da Ming Calendar and his Refutation for Da Ming Calendar. Through precise observation and measurement, Zu Chongzhi found many mistakes in the Yuan Kerry Calendar compiled by the famous astronomer He Chengtian, so he set out to compile the Daming Calendar, which was compiled in 462 AD at the age of 33. Zu Chongzhi made many creative contributions to the compilation of calendars. Daming Calendar is the best calendar in this era, but it was opposed by court courtiers. It was not until 10 year after Zu Chongzhi's death that Daming Calendar was officially promulgated due to the insistence of his son (Rihuan) and the textual research on the actual astronomical phenomena.

About 1800 years ago, in the Eastern Han Dynasty (AD 1 17), a large astronomical instrument driven by water was successfully manufactured in Luoyang, Kyoto, Eastern Han Dynasty. Twenty years later (A.D. 138), another instrument installed in Luoyang, Kyoto, "Houfeng Seismograph", accurately reported earthquakes thousands of miles away in the west. This marks the beginning of a new era of human recording and studying earthquakes with instruments.