According to legend, during the time of the Fuxi clan in ancient times, a dragon and horse emerged from the Yellow River in Mengjin County, northeast of Luoyang, carrying a "river map" on its back and dedicated it to Fuxi. Fuxi developed Bagua based on this, which later became the source of "Book of Changes". It is also said that during the reign of Emperor Yu, a magical turtle emerged from the Luo River in Luoning County, west Luoyang, carrying "Luo Shu" on its back and dedicated it to Emperor Yu. Dayu succeeded in controlling the floods based on this, and then divided the world into Kyushu. Based on this, a nine-chapter law was formulated to govern society, which was handed down and included in the Book of Documents, named "Hong Fan". "Yi Xici" says: "The river produces pictures, Luo produces books, and the sages follow them." This refers to these two things. On the river map, the black dots and white dots arranged in a numerical array contain endless mysteries; on the Luo Shu, the sum of the three numbers on the three vertical, horizontal and diagonal lines is equal to 15, which is very strange. Scholars at home and abroad have conducted long-term exploration and research on this, and believe that this is the crystallization of the spiritual thinking of Chinese ancestors and the first milestone of ancient Chinese civilization. The two books "Book of Changes" and "Hong Fan" have an important position in the history of Chinese cultural development and have had a profound impact in the fields of philosophy, politics, military science, ethics, aesthetics, and literature. As the origin of Chinese history and culture, the Hetu Luoshu plays an indispensable role. The Hetu Luoshu is the source of Chinese culture and the Yin-Yang and Five Elements magic numbers. It was first recorded in "Shang Shu", followed by "Yi Zhuan", and was recorded by hundreds of schools of thought. Tai Chi, Bagua, Zhouyi, Liujia, Nine Stars, Feng Shui, etc. can all be traced back to this point. The Xingyi Tomb unearthed in Xishuipo, Puyang, Henan in 1987 is about 6,500 years old. The images of green dragons and white tigers painted with shells in the tomb are lifelike, almost the same as in modern times. The river map has four images and 28 places. The shape and meaning of its arrangement are consistent with the stars on the top and geography on the bottom, and it is known that when buried, it will be excavated. A jade piece from the belly of a turtle from Hanshan, Anhui, unearthed in the same year, is an image of Luoshu, dating back about 5,000 years. It can be seen that at that time people were proficient in the physics of heaven and earth, as well as the numbers of Hetu and Luoshu. According to expert research, the star chart in the Xingyi Tomb dates back to 25,000 years ago. This shows that Shao Yong and other sages believed that "Hetu and Luoshu are ancient star maps", and their words are true. 1. Symbols of the River Diagram The River Diagram uses ten black and white dots to represent yin and yang, the five elements, and the four images. The diagram is a square. As follows: North: One white dot inside and six black dots outside, indicating the Xuanwu astrology and the five elements of water. East: Three white dots inside and eight black dots outside, indicating the astrology of the green dragon and the five elements of wood. South: Two black dots inside and seven white dots outside, representing the Suzaku astrology and the five elements of fire. West: four black dots inside and nine white dots outside, indicating the white tiger astrology and the five elements of gold. Center: Five white dots are inside and ten black dots are outside, representing the singularity of space and time, and the five elements are earth. (Among them, the white dots in odd numbers are yang, and the black dots in even numbers are yin. Among the four images, each image controls seven constellations, with a total of 28 constellations.) The above is the "River Map". Among them, the four images, according to the orientation of the ancient people's seat facing north and south, are: Suzaku in the front, Xuanwu in the back, Qinglong on the left, and white tiger on the right. This is the source of Feng Shui pictograms. 2. The number of the river map 1. The number of heaven and earth: There are 10 numbers in the river map, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Among them, 1, 3, 5, 7, and 9 are Yang, and 2, 4, 6, 8, and 10 are Yin. The sum of yang numbers is 25, the sum of yin numbers is 30, and the sum of yin and yang is 55. Therefore, the ancients said: "The number of heaven and earth is fifty-five", that is, the number of heaven and earth is 55, "the ghosts and gods move through changes". That is to say, the number of all things is derived from the number of heaven and earth. 2. The number of living things: the sky produces water, and the earth produces sixty percent of it; the two of the earth produce fire, and the sky produces seventy percent of it; the three of heaven produces wood, and the earth produces eighty percent of it; the four of the earth produces gold, and the sky produces ninety percent of it; the five of heaven produces earth, and the earth of ten Make it happen. So one is the birth number of water, two is the birth number of fire, three is the birth number of wood, four is the birth number of gold, and five is the birth number of earth. Six is ??the number of water, seven is the number of fire, eight is the number of wood, nine is the number of gold, and ten is the number of earth. All things have a number, and they can only be born when they are born; all things have a number, and they can be completed only when they can be achieved. Therefore, all things exist in numbers. 3. The number of the five elements: The number of the five elements is the number of the five elements, which is water one, fire two, wood three, metal four, and earth five, also called the number of Xiaoyan. One, three, and five are Yang numbers, and their sum is nine, so nine is the number of Yang pole.
Two and four are yin numbers, and their sum is six, so six is ??the extreme number of yin. The numbers of yin and yang are combined into the number 15, so when it is converted into Luo Shu, the number 15 is both vertical and horizontal, which is the number of yin and yang and the five elements. 4. The number of Dayan: The number of Dayan 50 is the number 10 of the five elements multiplied by earth; it is also the number used for the number of heaven and earth. The number of heaven and earth is 55. Subtract the number 5 of Xiaoyan to get the number of Dayan 50. Xiaoyan is the number of heaven and earth, and Dayan is the number of heaven and earth. The so-called "the Dayan number 50 is used for 49" is a divination method that uses the Dayan number to predict: one is the body and forty-nine is the use, so the use is forty and nine. 5. The number of intersections of heavenly stems: The number of tens in the river diagram is the number of ten heavenly stems. The number of friendships is: one or six of the same sect, two or seven of the same way, three or eight as friends, four or nine as friends, five or ten of the same virtue. It is the number by which all things survive. Therefore, Jia and Ji are combined into one and six *** sects, Yi and Geng are combined into two and seven comrades, Bing and Xin are combined into three and eight are friends, Ding and Ren are combined into four and nine are friends, and Wu and Gui are combined into five and ten together. After the ten heavenly stems merge together, they become the five elements of the heavenly stems. The body of the five elements of the river map is transformed into the function of the five elements of the heavenly stems. 6. The number of Liujia receiving sounds: the number of heaven and earth 55 plus the number of five elements 5, combined into 60 Jiazi the number of receiving sounds of five elements. The yin and yang and the five elements of the ten heavenly stems intersect with all things. They seek each other with the same energy, and each produce 12 sounds in the same voice. Silent and silent sounds are not included. According to the river map, the five elements of the north, east, south, west, and middle form the image *** 60 Nayin . It is the number of sounds from the five elements of heaven and earth. Analyzing Hetu Luoshu Intuitively inspecting Hetu Luoshu, it is not difficult to find that these two pictures have two obvious characteristics: numericality and structural symmetry: First, numericality. The concept of number is directly and vividly contained in books. "○" means 1; "● ●" means 2; ...and so on. Hetu contains 1~10***10 natural numbers, and Luoshu contains 1~9***9 natural numbers. Among them, the numbers composed of black dots are even numbers, and the numbers composed of white dots are odd numbers, expressing the concept of odd and even numbers. Therefore, digitality is one of the basic contents of Hetuluoshu. Second, symmetry. The structural distribution of the two pictures is symmetrical, which is reflected in two aspects: first, the structural shape of each number composed of black dots or white dots is symmetrical; second, the overall structural distribution is symmetrical. The river map is divided into five groups with two numbers as a group, with [5, 10] in the middle, and the remaining four groups [7, 2], [9, 4], [6, 1], [8, 3] in order Evenly distributed around. In Luo Shu, the number 5 is in the center, and the other eight numbers are evenly distributed in the eight directions. Further analysis shows that Hetu Luoshu also contains rich mathematical relationships, which are discussed separately below. The mathematical relationships included in the river diagram are: 1. Equality and sum relationships. Except for the middle group of numbers (5, 10), the sum of the four numbers vertically or horizontally is equal to the sum of the odd numbers. Vertical numbers: 7, 2; 1, 6 7 1=2 6 Horizontal numbers: 8, 3; 4, 9 8 4=3 9 and draw the inference: In the river diagram, except for the middle group of numbers [5, 10] Furthermore, the sum of odd numbers is equal to the sum of even numbers, which sums to 20. 2. Arithmetic relationship. The difference between the two numbers on the four sides or in the middle is equal. Upper (7-2); lower (6-1); left (8-3); right (9-4); middle (10-5), the difference is 5. Mathematical relations contained in Luo Shu: 1. Equality and sum relations. It is very obvious that the sum of the three numbers on each vertical, horizontal and diagonal line is equal, and the sum is 15. 2. Arithmetic relationship. Upon closer inspection, Luoshu implies arithmetic and logical relationships. ① Among the three numbers on the four sides of Luo Shu, the difference between two adjacent numbers is 5, and the numbers are not repeated. Upper side [4, 9, 2] 9-4=5 Lower side [8, 1, 6] 6-1=5 Left side [4, 3, 8] 8-3=5 Right side [2, 7, 6] 7-2 =5 Obviously this feature is the same as that of Hetu, which reflects that Luoshu and Hetu have a certain internal connection. ② Through the three numbers on the vertical, horizontal or diagonal lines of the number 5, the absolute value of the difference between the number 5 and the other two numbers is equal.
Vertical |5-9|=|5-1| or 9-5=5-1 Horizontal |5-3|=|5-7| or 5-3=7-5 Right diagonal |5-2|= |5-8| or 5-2=8-5 left diagonal |5-4|=|5-6| or 5-4=6-5 Based on the above analysis, we can clearly find that mathematical relationships and symmetry Nature is the basic characteristic of Hetu Luoshu. Hetu Luoshu contains the basic arithmetic and logical relationship of "sum or difference" between natural numbers. Although there are differences between the two, the mathematical relationships they express are similar*** Where they are similar, there is an inherent inevitable connection. Regarding the content related to Hetu Luoshu: The relationship between Hetu Luoshu and the "Book of Changes" will not be discussed here. What I want to talk about is some relevant content that people don’t pay attention to. 1. Luo Shu implies a swastika. A slight change in the Luo Shu can advance the swastika: ④⑨② ③⑤⑦ ? ⑧①⑥ In the structural state of the swastika, the mathematical relationship implicit in the Luo Shu, which is not easy to see at a glance, is reflected very clearly. For example, the difference between the two numbers is There are four groups of numbers 5; on the two curved arms of the swastika, the sum of each number is equal, both are 25, and so on. In other words, the swastika is a unique mathematical analysis of the Luo Shu, and it reflects the intrinsic mathematical connection between the Luo Shu and the Hetu. As long as the outer sides of the curved arms are straightened, the structural form of the Luo Shu will be in line with the Hetu. The picture is consistent. When there are Luoshu and swastikas, it is okay to omit the Hetu, because the mathematical relationships in the Hetu are basically reflected. In view of the above analysis, rather than saying that the swastika symbolizes the radiant rays of the sun, it is better to say that the swastika is the transformed form of Luo Shu. On the one hand, we cannot see the swastika from the light anyway; on the other hand, the ancients It makes sense to admire the swastika because of the worship of Luo Shu. 2. The Hetu Luoshu contains the mathematical principles of the abacus. First of all, from the perspective of mathematical principles, the mathematical characteristics of the Hetu Luoshu are consistent with the main rules of the abacus: First, the difference between the two numbers on the four sides of the Hetu is 5, which is one Basic natural numbers greater than 5 can be expressed as the number 5 plus a natural number less than 5, which corresponds to the five-liter rule in the abacus bead code that converts 5 lower beads into one upper bead; secondly, Luo Shu's vertical and horizontal The sum of the three numbers in the horizontal and diagonal directions is 15, which is consistent with the value of 7 beads in each gear of the abacus. Secondly, from the perspective of historical discoveries, although the idea of ??"operating with beads" has a long history, the earliest recorded mature abacus is the grand picture "Along the River During the Qingming Festival" that reflected people's lives in the early Song Dynasty (960-1127 AD). The left end of this picture There is a large abacus with fifteen grids (files) and seven black dots (beads). Although there were legends about Hetu Luoshu in the pre-Qin period, it was not known to the world until the early Song Dynasty. There is an amazing coincidence in the historical time between the discovery of Hetu Luoshu and the creation of abacus. To sum up the above reasons, we can make a conjecture that the physical form of the abacus originated from beads, and the mathematical principles of the abacus come from Hetu Luoshu. Finally, it needs to be pointed out that only by starting from the content of the thing itself and the interconnected things can we find the correct answer. The essence of Hetu Luoshu is mathematics, a mathematical achievement created by primitive ancients. These correct ideas will not fall from the sky. The ancients said: "Luoshu is the source of numbers" is worthy of its name.
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