Hetu Luoshu expresses a mathematical idea. As long as we analyze it carefully, we will know that number and symmetry are the most direct and basic characteristics of "books", and the mathematical relationship of "sum" or "difference" is its basic connotation. It is completely possible to use mathematical methods to prove or deduce Hetu and Luoshu, and prove that Hetu and Luoshu come from the same source. It can also be found that there is a certain degree of connection between Hetu Luoshu and "Abacus" and "Swastika".
Hetu Luoshu uses black or white dots as the basic elements to form a number of numbers in a certain way. The two pictures are combined differently and arranged into a matrix as a whole, as shown in the figure.
The most famous source of the Hetu Luoshu comes from the "Hechu Tu" in "Yi Zhuan·Xici". "Luo published the book, and the sage followed it", and based on this, it is believed that the Bagua was deduced from these two pictures, thus becoming one of the important topics in the study of Yi. Because all dynasties believed that they were "dragons and horses carried by the body" ", the turtle is listed on the back", so for centuries, it has been cloaked in mystery and is recognized as the eternal mystery of the source of Chinese national culture.
When examining and sorting out the Hetu Luoshu After the historical traces, we will find some knowledge like this:
- Hetu Luoshu, which is recorded in the classics of the Pre-Qin and Western Han Dynasties, "Shangshu·Gu Ming" said "Dayu, "Yiyu, the celestial sphere, and the river map are in the east preface"; "The Analects of Confucius·Zihan" states that "Zi said: If the wind and birds do not come, and the river does not come out of the map, I am already dead!" "; "Guanzi·Xiaochen" said: "In the past, those who received orders were dragons and turtles, rivers came out of pictures, Luo came out of books, and earth came out of yellow. Today, there are no such three auspicious things. " Later, it was also mentioned frequently in the works of Liu Xin, Kong Anguo, Yang Xiong, Ban Gu and others in the Han Dynasty.
As for what the Hetu Luoshu looks like, there is no clear statement in each book.
——Hetu Luoshu was only discovered in the early Song Dynasty. They were first handed down by Chen Tuan, a Taoist from Huashan in the Song Dynasty. The schema he proposed is called "Long Tuyi" and is contained in "Song Wenjian". The article "Preface to the Dragon Picture" talks about the three changes of the dragon picture, that is, the first one becomes the number of the sky and the earth that are not combined, the second one becomes the number of the heaven and the earth that have been combined, the third one becomes the negative figure of the dragon and horse, and finally the river figure Luo is formed. However, Chen Tuan did not mention the name of He Tu and Luo Shu after the Three Changes of Dragon Picture. It was Liu Mu, a Yi scholar in the Northern Song Dynasty, who studied Chen Tuan's work for the first time. He passed down "Long Tu Yi" and wrote "Yi Shu Gou Yin Tu", so He Tu Luo Shu became known to the world. At that time, there was a debate on whether to use "Picture Ten Book Nine" or "Tu Jiu Shu Ten". , was finally located in Figure 10 and Book 9, and continues to this day. Xiang mathematicians in the Song Dynasty believed that Bagua was deduced from the two diagrams of Hetu and Luoshu. As a result, the use of Hetu and Luoshu to explain the origin of Bagua was formed in the history of Yi studies.
——The nine chambers of Mingtang recorded in Luoshu and the early Han Dynasty work "Dadai Liji", and the nine palaces in the late Western Han Dynasty work "Qianzhedu", in 9. The orientation and configuration of the numbers are completely consistent. Mingtang appeared around the end of primitive society. It was a building with ritual and sacrificial functions in ancient Chinese social life and was deeply valued by rulers of all ages.
In short, since then. Judging from the existing relevant historical materials, the origin of Hetu Luoshu is ancient and confusing, and there is no clear and reliable answer.