Read works of Liu Hui at 百家争鸣 | |||
Book
Liu Hui No legacy mathematical works rarely, the left are well-was removed to make private copies of. His major works include:
"Nine Chapters note" 10 volumes;
"Important difference", Volume 1, to the Tang Dynasty renamed the "Sea Island Mathematical";
"Nine Chapters on weight difference map" l volume, the latter two are unfortunately lost in the Song Dynasty.
Achievement
Liu Hui in mathematics broadly into two areas:
One ancient Chinese mathematical system clean-up and laid its theoretical basis. This embodied in "s Jiu" in. It really has become a more complete theoretical system:
① The number system theory
With a number of similar and heterogeneous elaborated a common denominator, some points, four operations, and simplify complex fraction algorithms such as; in the Notes prescribing surgery, meaning he was not the departure from the prescription discussed unreasonable root of exist, and the introduction of a new number, created using an infinite decimal fraction approximation method of irrational roots.
② calculus theory in the chips
First give a clear definition to compare rates on, he repeatedly by, pass around, Qi based on the same three basic operations, the establishment of a uniform number and computing the theoretical foundation, he has used the "rate" to define the ancient Chinese mathematics The "equation" that modern mathematics of linear equations of the augmentation matrix.
③ In the Pythagorean theory
One by one, the Pythagorean theorem and the solution demonstrated Gougu Xing basis for calculation, the establishment of a similar Gougu Xing theory, the development of the Pythagorean measurement technique, through the "hook in the capacity horizontal" and "share the content directly," like the typical graphics on the analysis, the formation of a similar theory with Chinese characteristics.
④ In the theoretical area and volume
Complementarity with access to the principle of profit and tonic, "Cyclotomic" the ultimate way to move the Liu Hui principle, and to address a variety of geometric, geometry of the area, volume calculation. Theoretical value of these areas are still shining afterglow.
The second is based on the succession to their creative. This is mainly embodied in the following representative of the creative:
① Cyclotomic and pi
In his "Nine Chapters • Circular field technique" Note, the use of Cyclotomic show the exact area of a circle formula and gives the scientific method of calculating pi. He first started from the cut hexagon inscribed circle, each time doubling the number of edges, count to 192 polygon area, by π = 157/50 = 3.14, then count to the 3072 polygon area, by π = 3927 / 1250 = 3.1416, known as the "emblem rate."
② Liu Hui principle
In the "Nine Chapters • Yang Equestrian" Note, he separated in a solution with infinite cone size, the proposed terms of the volume of Liu Hui on the polyhedral theory.
③ "Mou square cover together," said
In the "Nine Chapters • Operation of Sphere" Note, he pointed out that the ball volume formula V = 9D3/16 (D the ball diameter) is inaccurate, and the concept of "profit-making co-side cover" the well-known geometry. "Mou together side cover" refers to the cube of the two axes perpendicular to each other within the cutting cylinder of consistent cross section.
④ Equation surgery
In the "Nine Chapters • equation technique" note in his understanding of the new method of linear equations, using the ratio method of thinking.
⑤ weight difference technique
In White Writing "Sea Island Mathematical", he made important difference technique, using a heavy table, with cable and tired moments, etc. away altimeter measurement method. He also used "derived by analogy" approach to weight differential operation measured by the two hope to develop a "three-Wang", "looked in all directions." India in the 7th century, Europe in the 15 ~ 16th century began to look the problem of the two measurements.
Contribution and status
Liu Hui's work, not only the development of mathematics in ancient China had a profound impact, but also in world mathematics Officials also established a lofty place in history. In view of Liu Hui's great contribution, so many of his books called "History of Mathematics in China Newton."
Translated by Google