First, the mathematical achievements in the era of Huangdi Neijing
It is generally believed that Huangdi Neijing was a work in the Spring and Autumn Period and the Warring States Period, and it was written in the Han Dynasty. Its content is not made by one person at a time. At the same time, the mathematical work of the same period was Zhoupian. The book was written in the Han Dynasty. Some people think that it was written in the Zhou Dynasty in the Western Han Dynasty, and some scholars think that it was written in BC 1000. In any case, we can think that it is a contemporary work of Huangdi Neijing. Zhou Kuai suan Jing is actually not a mathematical work, but an astronomical work. This is a book focusing on astronomy. Among them, the important mathematical topics are Pythagorean theorem, proportional measurement and four operations of fractions.
What can really be called a mathematical monograph is Nine Chapters of Arithmetic, which was written in the middle of the Eastern Han Dynasty. It is the first monograph summarizing China's knowledge of ancient mathematics. It involves a wide range of mathematical knowledge, which is much more advanced than western mathematics at that time. It was because of the rich mathematical knowledge at that time that the immortal Huangdi Neijing was born.
Second, the units and methods of measurement in Huangdi Neijing
To carry out mathematical calculation, we must first have the basic concept of number and quantify specific things. Different transactions should have different units of measurement when quantifying, and their calculation methods are also different.
1. Numbers
Huangdi Neijing adopts decimal system. For example, one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand, ten thousand and so on. The book "Nine Needles of Lingshu" says: "First, it is used in heaven; Second, use the law to land; Third, use laws to time; Fifth, use the law to speak; Sixth, use the law to make stars; Eighth, use wind protection; Ninth, use the law to come to the field. " "Su Wen. "On the Differentiation of Yin and Yang" said: "Yin and Yang are counted by ten, pushed by a hundred, pushed by thousands and pushed by ten thousand".
2. Length
In Huangdi Neijing, the length is generally expressed by inch, ruler and ruler. The length is in decimal system, with one foot equal to ten feet and one foot equal to ten inches. For example, "Lingshu Pulse Degree" said: "The pulse is self-sufficient to seven feet and five inches." Length has different names in different situations, such as depth, width, diameter (diameter) and perimeter (perimeter). For example, "Lingshu Gastrointestine" says: "The stomach bends and stretches, two feet six inches long, one foot five inches long and five inches in diameter".
3. Weight
The unit of weight in Huangdi Neijing is Jin and two. One kilogram is equal to sixteen taels. For example, "Lingshushou Medicine is Rigid and Soft" says: "A catty of dried ginger and a catty of Sichuan pepper"; "Soul fulcrum. Stomach and Stomach says: "The tongue weighs twelve liang".
4. Volume
Unit of volume in Huangdi Neijing is fighting, ascending and merging. The volume is in decimal. For example, "Ling Shu Ren Ping is absolutely ancient" said: "Wide intestines ... the valley of nine liters is one of three in one and eight in one".
5. Timing
The timing method adopted in Huangdi Neijing is the method of carving pots and dripping. At the end of Shang dynasty, the number of drops in a day (24 hours) must be 100 minutes. For example, "Star of Lingshuweiqi" said: "One day and one night, underwater for 100 minutes." The only difference is that the timing standard of Fifty Camps of Lingshu is set at 200 minutes per day, which shows that the age of this article is earlier than the last year of Shang Dynasty. Huangdi Neijing also adopts the twelve-hour system. For example, "Farewell to the Spirit of Shu Jing" said: "Six methods build December, and Yin and Yang merge into twelve Chen". The twelve-hour system was already used in the Western Zhou Dynasty. In the Han Dynasty, it was named Midnight, Crow, Pingdan, Sunrise, Food Time, Horn, Japan-China, Sundial, Sunset, Dusk and Man's Decision. It is also expressed by the twelve earthly branches, and it is the child time from 23: 00 to 1 at midnight, the ugly time from 1 to 3: 00, and the Yin Shi time from 3: 00 to 5: 00, which are recursive in turn.
6. Count the days, months and years
Huangdi Neijing has twelve months and 365 days in a year. Such as "Lingshu". "Bad Guest" said: "There are 365 days". The theory of luck in Huangdi Neijing also uses another calendar. There are 360 days in a year, five days for waiting, three days for one breath, six qi for one breath, and four seasons for one year.
7. Angle
The concept of angle is often used to study astrology. For example, "Fifty Camps of Lingshu" said: "Twenty-eight nights a day, thirty-six nights, a week of popularity, 1,800 points." 28*36= 1008 。 It is equivalent to dividing 180 degrees into 1008 parts.
Third, the mathematical methods commonly used in Huangdi Neijing
1. Four operations
Four operations are common mathematical methods in Huangdi Neijing, in which a large number of multiplication formulas are recorded. For example, "Lingshu Pulse Degree" says: "The Du pulse and Ren pulse are four feet five inches, two hundred and forty-eight feet and two hundred and fifty-one feet respectively. Everything is sixteen feet, and two feet are one. "
2. The concept of score
There are some records about scores in Huangdi Neijing. For example, "Ling Shu Ren Ping is absolutely ancient" said: "Wide intestines ... the valley of nine liters is one of three in one and eight in one".
multiply
In Huangdi Neijing, there are several records about multiplication. For example, in "The Theory of Nine Needles of Lingshu", it is said: "Nine is nine, and nine is eighty-one, to count Ling Huang." This is the calculation method of temperament. At that time, there were three quartic methods for similar calculations. For example, "Guanyuan" said: "Where there are five sounds, the first sound is three, and the fourth sound is nine."
4. Ten-point ratio method
Now we usually use the percentage method. But in Huangdi Neijing, the ten-point comparison method is used. For example, in Su Wen. "On the Five Permanent Political Powers" said: "Big poison cures diseases, and six is divided by ten; Often poison cures diseases, nine times out of ten; Small poison cures all diseases, ten in and eight out; Non-toxic treatment, nine times out of ten. "
5. Statistics
In Huangdi Neijing, the cure rate of doctors is also counted by the ten-point method. Such as "Lingshu". "Bad House Disease" said: "The work is complete ... the work is complete ... and the work is complete."
Arrangement and combination
Arrangement and combination are used many times in Huangdi Neijing. For example, the arrangement of twenty-five sounds on the guqin, the name of five sounds is the arrangement and combination; Disyllabic therapy in Lingshu five tones and five flavors is also produced by permutation and combination. The permutation and combination method is widely used in the theory of five movements and six qi. For example, the arrangement of the trunk and branch of the year number, the five-tone healthy movement. It can be said that the theory of five movements and six qi is a huge arrangement and combination closely related to astronomy, geography and people.
7. The concept of fuzzy mathematics
Recently, some people think that Yin and Yang in Huangdi Neijing are the original expressions of modern fuzzy mathematics. For example, "Su Wen. "On the Differentiation of Yin and Yang" said: "Yin and Yang are counted by ten, pushed by a hundred, pushed by thousands and pushed by ten thousand".
Fourth, the practical significance of mathematics in Huangdi Neijing
1. Explain that ancient Chinese medicine did not use mathematical methods, and then refute the pseudo-scientific theory of Chinese medicine.
2. Encourage Chinese medicine to use mathematical methods in clinical, scientific research and teaching, especially modern mathematical methods (including advanced mathematics and statistics).
3. In order to improve the self-confidence of TCM.