What are the problems in mathematics?
In the history of mathematics, there is a problem of planting 20 trees, which has been famous all over the world for centuries, constantly nourishing and enlightening human wisdom. With the century of human civilization, it has been decorated in the flowers of high-end arts and crafts. Its beauty is enduring, increasing day by day, progressing and developing, and becoming more fragrant and beautiful in the process of human civilization. The problem of planting 20 trees stems from planting trees and is sublimated in the mathematical map. The wisdom, cleverness and beauty of atlas structure are widely used in all aspects of society. The problem of planting 20 trees is simply: there are 20 trees, if there are 4 trees in each row, how to plant (group) to make more rows? As early as16th century, ancient Greece, ancient Rome, ancient Egypt, etc. Sixteen rows have been arranged, and beautiful maps have been widely used in elegant decorative buildings and gorgeous arts and crafts (Figure 1). /kloc-In the 8th century, the German mathematician Gauss guessed that the problem of planting 20 trees should reach the 18th line, but he never published the 18th line map. It was not until19th century that this conjecture was completed by Sam Lloyd, an American master of entertainment mathematics, and an exquisite eighteen-line atlas was drawn. In the 1970s, two math enthusiasts skillfully used electronic computers to surpass the eighteen-line record kept by mathematician Sam Lloyd, and successfully drew an exquisite and beautiful twenty-line atlas, creating a new record of planting twenty trees in the new century and keeping it up to now (Figure 3). In the 2 1 century, the problem of planting 20 trees was put forward by mathematicians again: can there be new progress if 20 trees are planted continuously? Mathematics is waiting for it. With the development of high-tech, it is predicted that in the future, the intelligence and understanding of human beings will break through the current world record of 20 rows, so that the problem of planting 20 trees will be updated and more beautiful, and the new century will be dressed up. (Excerpted from Chongqing Deng China Education Online: Three Difficult Problems in Mathematics) The problems of 20 trees can be arranged in 23 rows to analyze the achievements of predecessors and computers. I think the problem of planting 20 trees can break through 20 rows because the two problems of predecessors and computers have not been solved well. First, the problem of as few peripheral points as possible; The second is the movement of the center point, that is, to solve the single problem of axial symmetry and central symmetry. Through research, I solved the above two problems: the number of peripheral points decreased from 12 to 4. Sixteen to twenty-three lines of various maps have been successfully drawn, from simple axial symmetry and central symmetry to complex graphics with movable central points. The following (Figure 4) and (Figure 5) are twenty-two and twenty-three lines of maps respectively. These two pictures are representative, and the other 18-22 rows of different pictures can be obtained with a little change, and the other pictures are omitted. The problem of planting 20 trees has been updated. Regarding the problem of planting 20 trees, I drew 23 lines of maps, which made new progress in planting 20 trees. The reason why I was able to study and explore this mathematical puzzle that has been circulating for hundreds of years is because of my passion for mathematics. The reason why I was able to draw a 23-line map is only because I stood on the shoulders of giants. Will there be a new breakthrough in planting 20 trees? How many rows can 20 trees be planted in the end? According to my calculation, the problem of planting 20 trees should be ranked in 24 rows. I believe that with the progress of science and technology, the development of human civilization. There must be a wise man who can break the current record of 23 lines, make the problem of planting 20 trees more beautiful, and promote the development of atlas.