China's most important mathematical work in ancient times, Nine Chapters Arithmetic, contains an interesting question about a mouse going through a wall. 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, rats and mice made holes of 1 ft each. After that, the daily progress of rats doubled compared with the previous day, and the daily progress of mice was only half that of the previous day. How many days did the two mice meet?
This is the ninth chapter of arithmetic 12. This chapter is devoted to the problem of "surplus and deficiency". The remainder 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.
For example, the famous mathematicians Archimedes and Newton made up interesting mathematical problems related to cattle. Newton put forward a problem of "cows eat grass": there are three pastures, and the grass in the fields grows as densely and as fast. Their areas are 10/3 mu, 10 mu and 24 mu respectively. The first pasture can feed 12 cows for 4 weeks, and the second pasture can feed 2 1 cow for 9 weeks. If the third ranch is to keep 18 weeks, how many cows will this ranch keep? There are many solutions to this problem.
Third, tigers and foxes.
People are familiar with Smith's fables, but tigers are not vegetarians after all. Once he sees through the fox's trick, he will kill the fox without mercy. Then, there is the following interesting math problem: a tiger found a fox 10 meters away from it and immediately jumped at it. The tiger runs 7 steps, and the fox runs 1 1 step, but the frequency of the fox is fast. Tigers can run three steps, and foxes can run four. Can the tiger catch up with the fox? How many meters will the tiger run if it can catch up? The tiger can catch up with the fox when it runs 66 meters.
Fourth, the hungry wolf pounced on the rabbit.
Fibonacci sequence was originally an interesting mathematical problem, which was based on the reproduction of rabbits, and later developed into an important branch of mathematics.
During the European Renaissance, the famous artist Leonardo da Vinci raised an interesting question: As shown in Figure 2, point C is a rabbit hole, and a rabbit is foraging at point O, 60 meters south of the hole. A hungry wolf lingers at point A 100 meters due east of the rabbit.
The rabbit suddenly turned around and met the greedy and cruel eyes of the hungry wolf. He had a premonition of disaster, so he quickly turned and fled to his cave. At that moment, the hungry wolf will run away when he sees the coming delicious food, and will not give up. Immediately follow the rabbit at twice the speed of the rabbit. Excuse me, can this hungry wolf catch rabbits?
The wolf is always staring at the rabbit, so it will constantly change the direction of its movement. The route it runs is not a straight line, but a curve. When the rabbit entered the hole safely, the wolf was almost two meters away from the hole and watched the rabbit escape into the hole. If the hungry wolf doesn't "stare at the rabbit", but looks farther, goes straight to the hole, and then "waits for the rabbit" at the hole, the rabbit can't escape bad luck.