In ancient China, there was a rudimentary mathematics from the time of the "knotted rope chronicle". In ancient oracle bone inscriptions and gold inscriptions, there are symbols for counting. If there is a notation of "1", "11", etc., these marks can be confirmed from the excavated faience pottery.
The carry system in ancient China was mainly decimal places. Both the carry system and the length are directly related to the physiological structure of the ancients, such as human fingers and toes are ten. Ancient China's understanding of "geometry" was also very early, such as the stone tools, bone tools, pottery, dwellings, tombs, etc., which they used had certain geometric shapes.
The initial understanding of numbers and shapes in the late period of ancient Chinese primitive society, and when they made utensils of various shapes and certain proportions, the germ of elementary mathematics appeared.
In the Xia, Shang and Zhou dynasties, China's counting method was from one to ten thousand in a decimal way. If used.
The combination of one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand, ten thousand, and ten thousand is used to record the natural number within 100,000. During this period, the mathematical system of the Shang Dynasty was more advanced and scientific than that of the contemporaries of ancient Babylon and ancient Egypt.
Around the time of the Western Zhou Dynasty, a very important calculation method appeared—calculation. Calculations are made with calculations. The arithmetic chip is a round bamboo stick with a diameter of about 02 cm, about 14 cm long, with 271 sticks as a "grip". During this period, there were also four simple operations, which should be said to be a very remarkable thing in the history of mathematics, and it was a pioneering achievement.
The progress of mathematics in the Spring and Autumn Period and the Warring States Period was mainly reflected in the improvement of the four operations and the progress of calculation tools. For example, in the unearthed tomb of Chu in the Warring States period, there is a bamboo tube, which is filled with brushes, copper sharpening, balances, weights, and calculation chips.
In short, there were both tools, symbols, and some mantras in mathematics at that time, and if you compare these achievements with other regions, it is obvious that they were in an advanced position.
By the Qin and Han dynasties, there had been significant progress in the mathematical sciences in China, which was reflected in the emergence of many mathematical monographs. During this period, there were the earliest astronomical and mathematical monographs in China, such as "Zhou Ji Sutra of Arithmetic" and "Nine Chapters of Arithmetic".
In the Sutra of the Zhou Dynasty, there is a dialogue between Zhou Gong, who is revered as an ancient sage, and a mathematician named Shang Gao, in which the Pythagorean theorem, also known as the Pythagorean theorem, is mentioned. This theorem is that "the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right angles", and this theorem is also known as the "Shang Gao theorem" in China.
The following is a brief introduction to the part of the quotient high theorem, and part of the dialogue between Zhou Gong and Shang Gao:
Zhou Gong: "I heard that you are very proficient in the art of numbers. Can you tell us more about how the ancients measured the degrees of the celestial sphere?There is no ladder that can climb to the sky, and the earth cannot be measured with a ruler. Where does this data come from?”
Shang Gao: "The art of numbers begins with the circle and the square, the circle comes from the square, and the square comes from the rectangle, and the rectangle comes from the fact that 9 9=81."
If you cut the diagonal of the rectangle so that the width is equal to 3 units long and the length is equal to 4 units, then the length of the diagonal is 5 units. The square used by the ancient Dayu to govern the world was developed from these numbers. ”
Zhou Gong sighed and said: "The art of mathematics is really amazing!I would like to ask again how to use the right triangle ruler”
Shang Gao: "By making the right-angled triangular ruler lie flat on the ground, you can use a rope to design straight and square works." By standing the right-angled triangular ruler upright, you can measure the height. An inverted right-angle triangular ruler can be used to measure depth, while a flat position can be used to measure distance. Let it rotate and you can draw a circle;Combine several to get squares and rectangles. ”
Zhou Gong: "This is amazing!."”
The greatness of the Sutra lies not only in the elaboration of mathematical knowledge, but more importantly, in the dominance of astrology and divination, when they discuss the phenomena of heaven and earth, they are not superstitious at all!The mathematical treatise also talks about the shadow of the sun, the difference in length of the shadow at different latitudes, the measurement of the diameter of the sun with a speculum, and so on, as well as a table of the length of the shadow for each solar term of the year.