Of course, the zodiac also has questions about mathematics. In ancient China, the twelve earthly branches corresponded to 12 kinds of animals, which was called the Zodiac. Zodiac involves all aspects of people's lives and forms a long-standing zodiac culture. Recently, I read Boyou Zhushan's poems about the zodiac, and many interesting math problems are related to the zodiac. It will be interesting to compile them.

First, the mouse through the wall problem: the mouse is located in the first place of the zodiac. China's most important mathematical work in ancient times, Nine Chapters Arithmetic, contains an interesting question about a mouse going through a wall. Translate this question into modern Chinese, the general idea is as follows: the existing wall is 5 feet thick, and two mice are opposite to each other. On the first day, the rat and the mouse each made a hole of 1 foot. After that, the mouse's daily progress was twice that of the previous day, and the mouse's daily progress was only half that of the previous day. Ask two mice how many days they met. This is the ninth chapter of arithmetic 12. This chapter focuses on the problem of "surplus and deficiency". The residual method is a unique algorithm in ancient China, which occupies an important position in the history of mathematics development and also has an important influence on the development of mathematics in later generations. From the perspective of methodology, the residual method includes modeling method, reduction method, approximation method and approximation method. This problem is to give the model through the surplus and deficiency, and then get the approximate value of the solution through approximation. If you want to use modern mathematical methods, you can use the equation of equal proportion series and then find the approximate value of the root.

Second, the problem of cattle eating grass is the second of the 12 zodiac animals. There are many problems related to cattle in interesting mathematics. For example, the famous mathematicians Archimedes and Newton made up interesting mathematical problems related to cattle. Newton put forward a problem that cows eat grass: there are three pastures, and the grass in the fields grows equally densely and quickly. Their areas are 10/3 mu, 10 mu and 24 mu respectively. The first pasture can raise 12 cows for 4 weeks, and the second pasture can raise 2 1 cow for 9 weeks. If the third pasture is to be raised for 18 weeks, how many cows will be raised in this pasture? There are many solutions to this problem, but Newton especially likes his arithmetic solution. The problem of Archimedes' cow is a long poem composed of 22 pairs of sentences, which was found in a Greek manuscript in 1773.