Is there an intuitive explanation for the problem of brick accumulation in mathematical modeling?
Brick piling is caused by the leaning tower of Pisa, Italy. Under normal circumstances, the same bricks, without any adhesive, are stacked up and down in turn. Each layer of bricks (the first layer of bricks is placed on the ground) must be staggered from the next layer of bricks by a certain distance to ensure that the system is in a state of mechanical balance, that is, the maximum length of different numbers of bricks can be obtained under the same premise. For this problem, we only use the general method of linear programming to establish the corresponding mathematical model, and then use mathematical software to find the optimal solution under the given number of bricks. On this basis, it is concluded that there are generally n bricks. The first problem requires that the corresponding mathematical model be obtained and solved in the case of 2, 3 and 4 bricks. In 23n, the constraints under two principle conditions are established according to two principles in theoretical mechanics, one is based on the position of the whole center of gravity, and the other is based on the principle of analyzing the force balance of objects. However, when the constraints under these two principles are simplified (the objective function is the same), they become the same constraints. Solve it with mathematical software LINGO and get 12. When 3n, the second brick extends 14, the third brick extends 12, when 4n, the second brick extends 16, the third brick extends 14 and the fourth brick extends 12. Because the number of bricks has expanded to n, it is somewhat complicated to establish a mathematical model by using the balance principle in mechanics, so the mathematical model is established only by using the position of the center of gravity in theoretical mechanics. Since it is extended to n bricks, it can no longer be solved by mathematical software to draw a conclusion. At the same time, the topic requires that the situation of my sister at this time be obtained according to the result of the first question. In other words, the extension of the I-th brick means that according to the topic, N is. Judging from the general result of the second question, this time can be proved according to the series knowledge in advanced mathematics, and it is concluded that if I have enough bricks, I can extend it indefinitely. It is worth emphasizing that it must be carried out under the assumption at the beginning of the topic in order to achieve it.