Category II: 1+3=4

Category III: 1+5=6

(2) Solution: Let the height of the mountain peak be 100x meters.

5-0.6× 100x=- 1

-0.6× 100x=- 1-5

-0.6× 100x=-6

x= 10× 100

x= 1000

Attendant: The height of the peak is about 1000 meters.

1) What is the class group in your mind?

Classmate relationship: very harmonious, play games together after class and learn to help each other.

Teacher-student relationship: We are friends after class and can care about each other.

Learning atmosphere: excellent students in the class had better learn the plenary session, poor students should try their best to learn, and poor students can ask excellent students after class.

Class cadre team: manage yourself first and set an example for others. Take an active part in activities. There are bad phenomena in the class to stop!

The will of mathematicians

The will of Arab mathematician Hua Razmi, when his wife was pregnant with their first child. "If my dear wife gives birth to a son for me, my son will inherit two thirds of the inheritance and my wife will get one third; If it is a girl, my wife will inherit two-thirds of the inheritance and my daughter will get one-third. " .

Unfortunately, the mathematician died before the child was born. What happened after that made everyone more troubled. His wife gave birth to twins, and the problem happened in his will.

How to follow the mathematician's will and divide the inheritance among wife, son and daughter?

Not a bathhouse.

Amy Nord, a German mathematician, got a doctorate, but she is not qualified to teach because she needs to write another paper before the professor will discuss whether to grant her the qualification as a lecturer.

Hilbert, a famous mathematician at that time, appreciated Amy's talent very much. He ran around asking for permission to be the first female lecturer at the University of G? ttingen, but there was still controversy at the professor meeting.

A professor said excitedly, "How can a woman be a lecturer?" If she is allowed to be a lecturer, she will become a professor in the future and even enter the university Council. Can women be allowed to enter the highest academic institutions of universities? "

Another professor said, "How do our soldiers feel when they come back from the battlefield and find themselves prostrating themselves at the feet of women?"

Hilbert stood up and firmly refuted: "gentlemen, the gender of the candidate should never be an argument against her becoming a lecturer." After all, the university Council is not a bathing hall! "

Can only be single for life.

When alexander humboldt, an outstanding German naturalist, visited Lobachevsky, the founder of Russian non-Euclidean geometry in Kazan, he asked the mathematician, "Why do you only study mathematics? It is said that you have a deep understanding of mineralogy and are proficient in botany. "

What, you only study math? It is said that you have a deep understanding of mineralogy and are also proficient in botany. "

"Yes, I like botany very much," Lobachevsky replied. "When I get married in the future, I will definitely build a greenhouse ..."

"Then get married quickly."

"But contrary to my wish, my interest in botany and mineralogy has made me a bachelor all my life."

The Butterfly Effect

Meteorologist Lorenz put forward an article entitled "Can butterflies flap their wings to cause tornadoes in taxonomic groups?" ? This paper discusses that if the initial condition of a system is a little worse, its result will be very unstable. He called this phenomenon "the butterfly effect". Just like we roll the dice twice, no matter how deliberately we roll, the physical phenomena and points thrown twice are not necessarily the same. Why did Lorenz write this paper?

This story happened in the winter of 196 1 2008. He operated the meteorological computer in the office as usual. Usually, he only needs to input meteorological data such as temperature, humidity and air pressure, and the computer will calculate the possible meteorological data at the next moment according to the built-in three differential equations, thus simulating the meteorological change map.

On this day, Lorenz wanted to know more about the subsequent changes of a record. He re-entered the meteorological data at a certain moment into the computer, so that the computer could calculate more subsequent results. At that time, the speed of computer processing data was not fast enough, so he had time to have a cup of coffee and chat with his friends for a while before the results came out. An hour later, the result came out, but he was dumbfounded. Compared with the original information, the original data is similar, and the later data is more different, just like two different pieces of information. The problem is not the computer, but the data he entered is 0.0005438+027. These subtle differences make a world of difference. So it is impossible to accurately predict the weather for a long time.

Han Xin ordered the soldiers.

Han Xin ordered soldiers, also known as Chinese remainder theorem. According to legend, Emperor Gaozu Liu Bang asked General Han Xin how many soldiers he commanded, and Han Xin replied that every three men 1 or more, five men 2 or more, seven men 4 or more, and 13 men 6 or more. Liu bang was at a loss and didn't know its number.

Let's consider the following questions first: Suppose the number of soldiers is less than 10,000, and there are only three people left for every five, 13, 17, so how many soldiers are there?

First find the least common multiple of 5,9, 13 and 17 (note: because 5,9, 13 and 17 are pairwise coprime integers, the least common multiple is the product of these numbers), and then add 3 to get 9948 (person).

There is a similar question in China's ancient mathematical work Sun Tzu's Art of War: "There are things today, I don't know their numbers, three or three numbers, two, five or five numbers, three or seven numbers, two, ask about the geometry of things? 」

Answer: "Twenty-three"

Technically, it says: "The number of three and three leaves two, take one hundred and forty, the number of five and five leaves three, take sixty-three, the number of seven and seven leaves two, take thirty, get two hundred and thirty-three, and then subtract two hundred and ten. Where the number of three is one, the number of seventy-five is one, the number of twenty-one is one, and the number of seventy-seven is one and fifteen, that's all. 」

The exact age of the author and works of Sunzi Suanjing can't be verified. However, according to textual research, the age of the book will not be after the Jin Dynasty. According to this research, the solution of the above problem was found earlier in China than in the west, so the generalization of this problem and its solution are called China's remainder theorem. China's remainder theorem plays a very important role in modern abstract algebra.