Qu Yuan felt the bones for fortune telling.

During the Northern and Southern Dynasties, there was a character who was a household name in China. China has a figure named after the June Sphere Crater, and his name is one of them.

His position in history and among the people is more important than that of emperors and generals, although at that time, he was only a teaching assistant, county magistrate and court official.

He was Zu Chongzhi who lived at the turn of the Song and Qi Dynasties. A bright light in the corner of his troubled times.

Zu Chongzhi is most famous for his accurate pi to six decimal places.

Pi is the ratio of circumference to diameter. You can draw a circle around a fixed point with a fixed radius, so the circumference of a circle is always connected with the radius, but there is no very accurate answer about how many meters a circle with a radius of 1 m can draw.

Divergent ideas, although the eyeball is spherical, it can roughly measure the position and length of points and lines, but the circumference of the circle is far from visual. Therefore, if you want to calculate the circumference of a circle, you must have an algorithm.

There are so many mathematical concepts, why did our ancestors calculate pi? Originated from architecture. Why did Zu Chongzhi calculate pi? Because his grandfather was a great craftsman in the Liu and Song Dynasties, he was also the Minister of Housing and Urban-Rural Development.

When drawing architectural drawings, it is impossible to measure the circumference of a circle with a rope in every drawing, so a simple formula must be found for conversion. Not long ago, Liu Hui, a mathematician in Zu Chongzhi, calculated the pi of 3. 1428 by cyclotomic technique, but this number is still a bit large. In the practical application of architecture, there will still be a waste of consumables. When building a large building, if the circular building is designed according to this pi, it will often be an unfinished project in the end.

Therefore, Zu Chongzhi, a genius, shared his worries for his father and made efforts to make pi accurate, and finally got the data between 3. 14 15926 and 3. 14 15927, which was quite extravagant, 800 years earlier than the westerners who repeated this work later.

Now I finally know why many ancient buildings in China are reliable and have a good foundation in science.

In application, this value can be used for all measuring instruments related to circles, such as funnels and kettles.

It is easy for us to calculate pi now, but it is a rather laborious process for Zu Chongzhi to calculate pi. Why?

Because China's ancient arithmetic had no big foundation, it was a self-contained algorithm.

Especially in the Northern and Southern Dynasties, there were no modern mathematical concepts such as Arabic numerals, negative numbers and infinity, that is to say, Newton had no giant on his shoulders, and many numerical values were calculated on the basis of existing simple symbols. If this calculation is made by ordinary people, it will be boring.

At that time, people probably didn't even know the basic purpose of their official duties. That is to say, what day is today? A few days later, today is my first day in this world. They may not even know it, and even birthdates needs to rely on special people or institutions to check and record it.

In developed places, the government and large families can have the Gregorian calendar and check the time. But things change and the government is in chaos. That's it. "I don't know when today is, regardless of Wei and Jin Dynasties" happened. Ordinary people ask for a birthday, so they can only turn to the old street fortune-teller (fortune-telling, bone-touching, acupuncture, arithmetic and other schools, here is the arithmetic school)

In ancient times, a large part of charlatans lived by selling time. Many times, they are deliberately vague and turn mathematical calculation into a mysterious theory.

Enough talking. Now let's look at Zu Chongzhi's calculation of pi.

Materials: One is the unit of measurement promulgated by the imperial court (in the past, the unit of measurement was based on the will of the emperor. Take the length as an example, ask several people to take ten steps, take their average value, then give a data, and then publish it in the name of the emperor. Put a ruler in the official office and let everyone take a rope to measure it for their own use. Second, there are square or flat sticks (these sticks are primitive calculations. At that time, there was no abacus, no written formula, and no number to express the concept of decimal. Different numbers can only be expressed by different calculations). Three people have a pen. The fourth is a sheet piling that records the calculation process. Add, subtract, multiply and divide five symbols for reference, and the 99 multiplication table is the main supplement. This is all the materials that Zu Chongzhi can prepare.

With the above, it is really necessary to calculate and record pi accurately to seven decimal places. As long as the mind is broken, the work ahead will be extinguished in an instant like Wei's delay in entering Zhuge Liang's account.

So I said, it is a hard process to calculate this operation. Zu Chongzhi is a calm person, a steady and wise thinker, and a model figure in civil science.

The above is Zu Chongzhi's greatest contribution, but he is a generalist, because his contribution is more than this.

Zu Chongzhi also corrected the calendar, which was even more important than pi at that time.

The Northern and Southern Dynasties were a major breakthrough in China's astronomy. I don't know much about how to treat astronomical phenomena in ancient times, so I can only explain it with my own understanding thinking.

In the Middle Ages, when knowledge had not exploded like this, people were full of imagination about the unknown world. Qu Yuan's Tian Wen represents a series of illusions that the ancients could not find the answer to the world. Such as the role of the queen mother, goddess and princess Xiang, as well as scenes such as driving, tigers playing drums and phoenix coming to the instrument.

The earth and heaven are in front of us. In ancient times, there were not always people who were imaginative like Qu Yuan, but also people who tried to seek true knowledge. As for what the solution looks like, it is a wise man who sees wisdom. However, such people must exist in every era, so as to promote social progress.

The following is my own opinion, briefly explaining the key and context of China people's cognition of nature before the Middle Ages.

First, the sun and the moon.

China did not dispute the origin and function of the sun and the moon, that is, they are the embodiment of gods, and they represent the will of the supreme god to look after the world. The sun and the moon are clumsy and often oppressed by dark clouds and lightning. They may be inferior immortals, animals driven by great gods, or even fireboats towed away by divine beasts. At the same time, they are regular, bring light to the world, and are the embodiment of goodness. But on the whole, their status among the gods is not high. From the incident of two children arguing about Japan, we know that China people take the sun and the moon more seriously than others, which is different from foreign countries.

Second, the stars.

Stars are more important than the sun and the moon, which is the difference of China astronomy, because China thinks that stars are more difficult to understand and mysterious than the sun and the moon, and sometimes there are meteors, comets and nebulae. And the ancients were more interested in it than the sun and the moon.

In conjecture, sometimes it is inevitable to give the stars the brilliance of humanity, such as Cowherd and Weaver Girl, Galaxy Bridge and Seven Fairy Stars.

Of course, the seven planets are the most concerned.

I remember when I was a child, there was a text called "Children Count Stars". When people in ancient times counted the stars, they found that several planets moved with the largest amplitude and were very regular, so they attached great importance to these planets and gave him various meanings: Venus = Taibai, Qi Ming, Chang Gung; Jupiter = old star, too old; Mercury = star; Mars = flashing; Saturn = town star, and so on.

Generally, these planets appear in accordance with the law. If the rules are inaccurate or covered up by something, there will be some predictions, especially when Venus and Mars are abnormal, which is even more surprising. Friends who are interested in astrology know more, so I just make a rough guess.

Third, the world outlook.

The great change of astronomy in the Southern and Northern Dynasties is that the astronomical department's view of the whole universe has changed from "Gaitian theory" to Huntian theory.

According to textual research, the historical origin of the legend of Pangu's creation should be in the Eastern Jin Dynasty at the earliest. Pangu, a god, does not exist in the interpretation of mainstream myths. He is a god grafted halfway, which has a lot to do with the introduction of the concepts of creator such as Buddhism and Zoroastrianism, and this Pangu god has really become the evidence of the spread of Huntian theory.

China used to think it was a "round place", but in the Northern and Southern Dynasties, it was still a "round place", except that there was something underground, filled with elements such as gas and liquid. Therefore, with this explanation, people live in a colorful world full of vitality and energy, and the whole world is like a human body, composed of various elements.

Then why did China at that time slowly accept the idea of Huntian Theory? In addition to the accurate test of solar eclipse and lunar eclipse by the armillary sphere designed by Tiangong, this theory is also slightly accurate in the division and interpretation of calendar time.

China people's time measurement is closely related to the sun and the moon and the Zhouyi.

The gossip map was originally a time projection map. The ancients in China, who lived in the Yellow River valley, first used bamboo poles to calculate the change of the sun shadow. Then, people in this area carved the length of the shadow on the wall in rows at fixed points in the same proportion.

Day after day. Decades later, someone went back to analyze these shadow length records and found that the shadow length caused by the sun was very regular and short.

Further analysis is that when the shadow is long, it will be cold weather, frozen rivers and yellow leaves; When the shadow is short, it will be fierce sunshine, the rushing Yellow River and the shade of birds and animals.

So, people with brains simply push down the wall, make a gossip disk according to the cycle of shadow length, abbreviate the record of length, and finally divide it into eight main lines.

Later, they found that they can also use the law that the shadow of the sun is gossip to guide agricultural production. It can be seen that the four seasons are related to people's life and production.

According to the law, these four seasons can be divided into about 360 days (4×9).

In the four seasons, knowledgeable people continue to seriously put the changing relationship of 24 moons into 360 days around the moon's ups and downs, and call the changing cycle of the moon's ups and downs January for short. The most powerful people announce which period of the moon is the new moon and start farming accurately every month.

By analogy, in order to calculate 360 days in the form of written records, heavenly stems and earthly branches was created in all dynasties. Heavenly stems and earthly branches repeatedly reversed the cycle, and heavenly stems and earthly branches repeated the cycle six times a year.

Based on the reincarnation of heavenly stems and earthly branches, a lot of data can be seen at a glance, which can clarify the relationship between time and time. It is the local priest who is mainly responsible for managing, recording and clarifying the relationship between these numbers and time, and can also be called a wizard in the village.

However, the above algorithm is an ideal algorithm. Due to the influence of gravity, it is impossible for the real earth and the sun to circulate on time in 360 days, so the 360-day period needs to be fine-tuned according to the actual situation.

This work is explained by Huntington's theoretical model: the operation of celestial bodies is also affected by water, gas and other factors, so it will not be on time. Similarly, according to the demonstration and explanation of the armillary sphere, many astronomical phenomena have been verified, and the problem of one year will be explained sooner or later.

Thus, in the Middle Ages, a rigorous celestial computing system was formed, taking into account the planetary movements in the solar system. Although it is not very scientific, there is no big flaw in the calculation. The planetarium algorithm has ruled China for thousands of years.

Zu Chongzhi put forward Da Ming Li on the basis of Huntian theory. He carefully calculated the time difference of direct sunlight at the same point every year, and then combined with big data, proposed a new leap method of 39 1 year, 144 leap month.

After 360 days and several leap months, the sun returned to its original fixed point, and then he defined a tropical year as 365+38+0.

This discovery is an accurate correction of the calendar of China at that time. Although it is not very accurate, it is already a major calendar reform.

Unfortunately, this calendar was not adopted at that time, and it was won by his son Zuxuan.

Zuxuan is also excellent. He inherited his father's career and made great contributions to the history of China and even the world in astronomy and arithmetic. He was the first to put forward the principle of equal product of spheres-"If the potentials are the same, the products cannot be different". This principle was discovered 1 100 years earlier than that of western mathematicians. Now, it is often used in the field of calculus.

Unfortunately, since Nanqi revoked the concept of Ming Zong, imperial academy only specialized in the other three theories. In the south, talents devoted to arithmetic and yin and yang have withered, and talented people have changed careers. Yan Zhitui once said: "Arithmetic is rare in Jiangnan, and only john young and Zuxuan are good at it."

The development process of Chinese science history has once again entered the super slow tunnel lane.

Zu Chongzhi's all-rounder is also reflected in machinery manufacturing.

Zu Chongzhi reformed the South Guide Car. The Southern Compass is a unique invention of China, which is said to have existed in the period of the Yellow Emperor. However, in the historical changes, the inheritance of mentoring was forgotten, and the original technology was not retained. With the help of ancient books, Zu Chongzhi redesigned the loading and unloading, which probably restored the original appearance of the South Guide Car.

Zu Chongzhi combined water hammer with water mill and invented water hammer mill. After this thing was invented by Zu Chongzhi, farmers can use natural water resources to do work repeatedly, grind rice for many times, and thresh rice in a small area, which is very beneficial to agricultural development. Du Yu invented and improved this thing hundreds of years ago.

Zu Chongzhi designed a thousand-mile boat and a wooden ox and a flowing horse. These two can't see the real thing now, and the thousand-mile ship should be driven by a waterwheel. The invention is helpful to the water war in the Southern Dynasties, and can also realize the rapid transportation of grain. Cattle herding Liu Ma is an ancient rail car, and there are no drawings of this invention.

Zu Chongzhi made a ritual vessel. Now there is a similar object, probably a timer, which is also an instrument to remind people to be human, so I will not explore it any more.

Zu Chongzhi has made great achievements in literature, just like seismologist Zhang Heng. Zu Chongzhi's biography is arranged in the biography "Literature".

In fact, as long as Zu Chongzhi has studied Chinese characters, knows the rhythm, and makes up some words casually according to his practical experience, it is better than learning literature on an empty stomach. He is engaged in construction, contact with construction workers, river and lake history; He is engaged in calendars, and he wants to contact farmers, the river of heaven and earth; He is a tool maker, and he has to get in touch with farmland water conservancy and field work; He is engaged in strange research, contact with legendary ghost stories and so on. These life experiences are enough for him to write endless stories, and his literary attainments are estimated to kill a large group of narcissists at that time.

Now, let's sum up why Zu Chongzhi is a generalist.

The first is to promote the political and economic environment.

In feudal society, the agricultural people were more creative than the nomadic people in promoting historical development, and the nomadic people often perished a feudal farming dynasty. Historians believe that this is a retrogression of history, which not only stifled an advanced feudal system, but also killed talents like Zu Chongzhi, making agricultural civilization continue the fault.

For example, the sharp weapon of farming, water diversion device, earthquake measuring device, wind and rain forecast, pen and ink, textile machine, cloth and silk clothes and even the discovery of iron and coal are all masterpieces that can only appear in farming society. Mongolia, the most powerful nomadic people, has only played the role of cultural exchange between China and the West, and its achievements in promoting people's scientific and technological progress and people's livelihood development are almost zero. Coupled with their slaughter, their role in promoting history can be said to be negative.

In the Southern Dynasties where Zu Chongzhi lived, land was a new land that needed to promote agriculture. The brutal cultivation method of slash-and-burn has to be changed, and it is necessary to take advantage of the advantages of planting by mountains and rivers in the south. However, this requires systematic theoretical guidance and some practical inventions, so Zu Chongzhi and others devoted themselves to studying these things.

The second is leadership, and the Southern Dynasties attached importance to education.

This is a cliche. It has been mentioned many times in the article that the top leaders in the early Song and Qi Dynasties attached importance to developing agriculture and expanding their territory to the north, so they needed new weapons and transportation of grain and grass, so they attached importance to education and trained specialized personnel.

Zu Chongzhi is a special talent. Because Zu Chongzhi's father was a court architect, his intelligence as a teenager has long been known to outsiders. When Zu Chongzhi was in his twenties, Emperor Xiaowu of Liu Song sent him to the general survey work at that time. This is a school in Xiao Daocheng, except that Xiao Daocheng is a student and he is a teacher.

Zu Chongzhi became a professor of literature and history, Yin and Yang here, and also studied astronomical calendars and arithmetic buildings in the vast sea of books. At that time, Liu Song and Liu Yu were keen on carpentry, and Zu Chongzhi also made efforts. Xiao Daocheng was very interested in his war equipment, such as wooden cows and horses, thousands of miles of ships and compass cars, and used them on the battlefield.

Therefore, after Xiao Daocheng proclaimed himself emperor, he paid more attention to education and gave special project funds for the expansion of these educational institutions. So, Zu Chongzhi has the identity, the money, the praise of the whole world, and that's all.

With the academic attention and freedom in the Southern Dynasties, talents like Zu Chongzhi were born, which is also a kind of historical luck.