1. Mathematical allusions, graphics, interesting calculations, basic knowledge learned and extracurricular knowledge for grades 1 to 5
◆The story of pi 1. Zu Chongzhi, seventh place, first in the world , maintained for a thousand years; "The accuracy of the pi calculated by a country in history can be used as a sign to measure the level of mathematical development of the country at that time." 2.1427, *** Mathematician Al Qasi, 16th; 1596 , Dutch mathematician Rudolf, 35th; in 1990, the computer had 480 million digits; on December 6, 2002, the University of Tokyo, 1,241.1 billion digits.
◆"0" There is no 0 in Roman numerals; in the fifth century, "0" was introduced to Rome from the East. At that time, the Pope was very conservative and believed that Roman numerals could be used to record any number and it was sufficient, so he banned it. With "0", a Roman scholar's manual introduced some uses of 0 and 0. After the Pope discovered it, he tortured it. ◆Using "rules" and "rectitudes" to rule the world In a stone chamber statue in an ancient building in Jiaxiang County, Shandong Province, there are two images of our ancient ancestors in ancient deifications, one is Fuxi and the other is Nuwa.
The object in Fuxi's hand is a ruler, which is similar to a compass; the object in Nuwa's hand is called a moment, which is in the shape of a right-angled ruler. The Drawer Principle in Ancient China In ancient Chinese literature, there are many examples of successful application of the Drawer Principle to analyze problems.
For example, in "Liangxi Manzhi" written by Fei Gun in the Song Dynasty, the drawer principle was used to refute the fallacy of superstitious activities such as "fortune telling". Fei Gong pointed out: The year, month, day and hour of a person's birth (horoscopes) are used as the basis for fortune telling, and the "horoscopes" are used as "drawers". There are only 12*360*60=259200 different drawers.
Considering that all people in the world are "objects", there must be thousands of people who enter the same drawer, so the conclusion is that there are many people born at the same time. But since the "eight characters" are the same, "why are there any differences between the rich and the poor?" Qian Daxin's "Collected Works of Qian Yan Tang", Ruan Kuisheng's "The Guest Talk after Tea", and Chen Qiyuan's "Notes of Yongxianzhai" are all in the Qing Dynasty. Similar text.
However, it is regrettable that although Chinese scholars have long used the drawer principle to analyze specific problems, no general text about the drawer principle has been found in ancient documents. Abstracting it into a universal principle, this principle had to be named after the Western scholar Dirichlet hundreds of years later. Application of the Drawer Principle In 1947, Hungarian mathematicians introduced this principle into the mathematics competition for middle school students. There was a question in the Hungarian National Mathematics Competition that year: "Prove that among any six people, you can definitely find three people who know each other. Or three people who don’t know each other.”
This question may seem bizarre at first glance. But if you understand the drawer principle, it is very simple to prove this problem.
We use A, B, C, D, E, F to represent six people. Find one of them at random, such as A, and put the other five people into "Knowing A" and "Don't know A" "Go into the two "drawers". According to the drawer principle, there are at least three people in one drawer. Let's assume that there are three people in the drawer of "Meet A", they are B, C, and D.
If B, C, and D do not know each other, then we have found three people who do not know each other; if two of B, C, and D know each other, for example, B and C knows each other, then A, B, and C are three people who know each other. In either case, the conclusion of this question is valid.
Due to the novel form of this test question and the clever solution, it soon spread widely around the world, making many people aware of this principle. In fact, the drawer principle is not only useful in mathematics, but also plays a role in real life, such as admissions, employment arrangements, resource allocation, professional title evaluation, etc. It is not difficult to see the role of the drawer principle.
Rabbits in the same cage Have you ever heard of the "chicken and rabbit in the same cage" problem before? This question is one of the famous interesting questions in ancient my country. About 1,500 years ago, this interesting question was recorded in "Sun Zi Suan Jing".
The book narrates this: "Today there are chickens and rabbits in the same cage. There are thirty-five heads on top and ninety-four legs on the bottom. How many are the chickens and rabbits? The meaning of these four sentences is: There are several chickens and rabbits in the same cage. Counting from the top, there are 35 heads; counting from the bottom, there are 94 legs. How many chickens and rabbits are there in the cage? Do you want to know? How does Sun Zi Suan Jing answer this question? The solution is as follows: If half of the legs of each chicken and each rabbit are cut off, each chicken will become a "one-horned chicken" and each rabbit will become a "one-horned chicken". It becomes a "two-legged rabbit"
In this way, (1) the total number of chicken and rabbit feet changes from 94 to 47; (2) if there is a rabbit in the cage, then The total number of legs is 1 more than the total number of heads. Therefore, the difference between the total number of legs, 47, and the total number of heads, 35, is the number of rabbits, that is, 47-35=12 (rabbits). Obviously, the number of chickens is 35-12=23. This idea is novel and unique, and its "foot-cutting method" has also amazed mathematicians at home and abroad.
This way of thinking. Begging for return.
The reduction method means that when solving a problem, we do not directly analyze the problem first, but deform and transform the conditions or problems in the problem until it is finally classified as a solved problem.
Puchoko’s interesting questions Puchoko was a famous mathematician in the former Soviet Union. In 1951, he wrote the book "Primary School Mathematics Teaching Methods".
There is the following interesting question in this book. The store sold 1,026 meters of cloth in three days.
What was sold on the second day was twice as much as the first day; what was sold on the third day was three times as much as the second day. How much rice cloth was sold in each of the three days? This question can be thought of like this: Consider the number of meters of cloth sold on the first day as 1 share.
You can draw the following line segment graph: The first day is 1 portion; the second day is 2 times the first day; the third day is 3 times the second day, that is, the first day 2*3 times. A comprehensive formula can be used to calculate the number of meters of cloth sold on the first day: 1026÷(l+2+6)=1026÷9=114 (meters) and 114*2=228 (meters) 228*3=684 (meters) So the cloth sold in the three days are: 114 meters, 228 meters, and 684 meters.
Please use this method to solve a question. Four people donated money for disaster relief.
B’s donation is twice that of A, C’s donation is three times that of B, and D’s donation is four times that of C. They donated 132 yuan.
How much do each of the four people please donate? In Guigu, there was a general named Han Xin in the Han Dynasty of our country. Every time he calls the troops, he only requires his subordinates to report the number by pressing 1~3, 1~5, 1~7, and then report the remainder of each team's count, so that he will know how many people have arrived.
His ingenious algorithm is called Guigu calculation, also known as partition calculation, or Han Xin's strategy, which is also called by foreigners.
2. What are the simplest computer common sense
The function of each key on the keyboard is F1 to help F2 to change the name F3 to search F4 to address F5 to refresh F6 to switch F10 to the menu CTRL+A to select all CTRL+ C Copy CTRL + Menu CTRL+ESC Start Menu Press CTRL while dragging an item Copy the selected item Press CTRL+SHIFT while dragging an item Create a shortcut Press SHIFT when inserting a disc into a CD-ROM drive Prevent the disc from automatically playing Ctrl+1 ,2,3. Switch to 1, 2, and 3 from the left. Tags Ctrl+A Select all the contents of the current page Ctrl+C Copy the currently selected contents Ctrl+D Open the "Add Favorites" panel (add the current page to favorites) Ctrl+E Open or close the "Search" sidebar ( Various search engines are optional) Ctrl+F Open the "Find" panel Ctrl+G Open or close the "Simple Collection" panel Ctrl+H Open the "History" sidebar Ctrl+I Open the "Favorites" sidebar/other : Restore all vertically tiled or horizontally tiled or cascaded windows Ctrl+K Close all tabs except the current and locked tabs Ctrl+L Open the "Open" panel (Iter addresses or other files can be opened on the current page.) Ctrl+N creates a new blank window (can be changed, Maxthon Options → Label → New) Ctrl+O opens the "Open" panel (iter address or other files can be opened on the current page.) Ctrl+P opens the "Print" panel (can Print web pages, pictures, etc.