Data content of mathematical handwritten newspaper

Mathematics is indeed a wonderful masterpiece, just like the creation of a painter or poet-it is the synthesis of ideas; Like the synthesis of colors or words, there should be internal harmony. The following is the information content of Math Manuscript. Welcome to read it.

Interesting mathematics knowledge in junior high school

1. Two boys each ride a bicycle, starting from two places 20 miles apart (1 mile +0.6093 km) and riding in a straight line. At the moment they set off, a fly on the handlebar of one bicycle began to fly straight to another bicycle. As soon as it touched the handlebar of another bicycle, it immediately turned around and flew back. The fly flew back and forth, between the handlebars of two bicycles, until the two bicycles met. If every bicycle runs at a constant speed of 10 miles per hour and flies fly at a constant speed of 15 miles per hour, how many miles will flies fly?

answer

The speed of each bicycle is 10 miles per hour, and the two will meet at the midpoint of the distance of 2o miles after 1 hour. The speed of a fly is 15 miles per hour, so in 1 hour, it always flies 15 miles.

Many people try to solve this problem in a complicated way. They calculate the first distance between the handlebars of two bicycles, then return the distance, and so on, and calculate those shorter and shorter distances. But this will involve the so-called infinite series summation, which is very complicated advanced mathematics. It is said that at a cocktail party, someone told john von neumann (1903 ~ 1957, one of the greatest mathematicians in the 20th century). ) Put forward this question, he thought for a moment, and then gave the correct answer. The questioner seems a little depressed. He explained that most mathematicians always ignore the simple method to solve this problem and adopt the complex method of summation of infinite series.

Von Neumann had a surprised look on his face. "However, I use the method of summation of infinite series," he explained.

2. A fisherman, wearing a big straw hat, sat in a rowboat and fished in the river. The speed of the river is 3 miles per hour, and so is his rowing boat. "I must row a few miles upstream," he said to himself. "The fish here don't want to take the bait!"

Just as he started rowing upstream, a gust of wind blew his straw hat into the water beside the boat. However, our fisherman didn't notice that his straw hat was lost and rowed upstream. He didn't realize this until he rowed the boat five miles away from the straw hat. So he immediately turned around and rowed downstream, and finally caught up with his straw hat drifting in the water.

In calm water, fishermen always row at a speed of 5 miles per hour. When he rowed upstream or downstream, he kept the speed constant. Of course, this is not his speed relative to the river bank. For example, when he paddles upstream at a speed of 5 miles per hour, the river will drag him downstream at a speed of 3 miles per hour, so his speed relative to the river bank is only 2 miles per hour; When he paddles downstream, his paddle speed will interact with the flow rate of the river, making his speed relative to the river bank 8 miles per hour.

If the fisherman lost his straw hat at 2 pm, when did he get it back?

answer

Because the velocity of the river has the same influence on rowing boats and straw hats, we can completely ignore the velocity of the river when solving this interesting problem. Although the river is flowing and the bank remains motionless, we can imagine that the river is completely static and the bank is moving. As far as rowing boats and straw hats are concerned, this assumption is no different from the above situation.

Since the fisherman rowed five miles after leaving the straw hat, he certainly rowed five miles back to the straw hat. Therefore, compared with rivers, he always paddles 10 miles. The fisherman rowed at a speed of 5 miles per hour relative to the river, so he must have rowed 65,438+00 miles in 2 hours. So he found the straw hat that fell into the water at 4 pm.

This situation is similar to the calculation of the speed and distance of objects on the earth's surface. Although the earth rotates in space, this movement has the same effect on all objects on its surface, so for most problems of speed and distance, this movement of the earth can be completely ignored.

3. An airplane flies from city A to city B, and then returns to city A. In the absence of wind, the average ground speed (relative ground speed) of the whole round-trip flight is 100 mph. Suppose there is a persistent strong wind blowing from city A to city B. If the engine speed is exactly the same as usual during the whole round-trip flight, what effect will this wind have on the average ground speed of the round-trip flight?

Mr. White argued, "This wind will not affect the average ground speed at all. In the process of flying from City A to City B, strong winds will accelerate the plane, but in the process of returning, strong winds will slow down the speed of the plane by the same amount. " "That seems reasonable," Mr. Brown agreed, "but if the wind speed is 100 miles per hour. The plane will fly from city A to city B at a speed of 200 miles per hour, but the speed will be zero when it returns! The plane can't fly back at all! " Can you explain this seemingly contradictory phenomenon?

answer

Mr. White said that the wind increases the speed of the plane in one direction by the same amount as it decreases the speed of the plane in the other direction. That's right. But he said that the wind had no effect on the average ground speed of the whole round-trip flight, which was wrong.

Mr. White's mistake is that he didn't consider the time taken by the plane at these two speeds.

It takes much longer to return against the wind than with the wind. In this way, it takes more time to fly when the ground speed is slow, so the average ground speed of round-trip flight is lower than when there is no wind.

The stronger the wind, the more the average ground speed drops. When the wind speed is equal to or exceeds the speed of the plane, the average ground speed of the round-trip flight becomes zero, because the plane cannot fly back.

4. Sunzi Suanjing is one of the top ten famous arithmetical classics in the early Tang Dynasty, and it is an arithmetic textbook. It has three volumes. The first volume describes the system of counting, the rules of multiplication and division, and the middle volume illustrates the method of calculating scores and Kaiping with examples, which are all important materials for understanding the ancient calculation in China. The second book collects some arithmetic problems, and the problem of "chickens and rabbits in the same cage" is one of them. The original question is as follows: let pheasant (chicken) rabbits be locked together, with 35 heads above and 94 feet below.

Male rabbit geometry?

The solution of the original book is; Let the number of heads be a and the number of feet be b, then b/2-a is the number of rabbits and a-(b/2-a) is the number of pheasants. This solution is really great. When solving this problem, the original book probably adopted the method of equation.

Let x be the pheasant number and y be the rabbit number, then there is

x+y=b，2x+4y=a

Get a solution

y=b/2-a，

x=a-(b/2-a)

According to this set of formulas, it is easy to get the answer to the original question: 12 rabbits, 22 pheasants.

Mathematical famous sayings

NO 1。 Learn mathematics as a language, learn the usage of every term, and be familiar with the meaning of every symbol.

NO2。 Look at "Mathematics forms ideas" instead of "Mathematics becomes dead".

Third. Mathematics looks at language, while mathematics looks at patterns (questions).

Fourth place. Don't let go of any seemingly simple examples-they are often not that simple or can lead to many knowledge points.

Fifth place. Just because you can use math formulas doesn't mean you can do math.

Sixth place. If you are not a genius, you don't want to play games if you want to learn math-you think you have done it, but your math level has not improved with your ability to pass the customs-in fact, you can always remember that learning math makes you play the big game of "life" better!

Seventh place. Impetuous people are easy to say: it is useless to learn mathematics, but something useful should be learned; -it's useless! ?

Eighth place. Impetuous people easily ask: how should I learn? -Don't ask, learn.

Ninth place. Impetuous people are easy to ask: Is it better to write on the blackboard in class or not to take notes and follow the teacher's ideas? I'm telling you, everything is fine. Just learn.

There are two kinds of impetuous people: a) people who are ignorant and just wait and see; B) only learn from those who don't insist.

NO 1 1 Please don't be impetuous.

NO 12 talks about novel problem-solving methods, and it is best to keep the conventional problem-solving methods in mind.

Mathematics is more than just solving problems.

One of the best ways to learn to solve problems is to study examples.

NO 15 Don't think that you have solved enough problems at any time.

NO 16 Please read the mathematics textbook and master the standard expressions of mathematics.

17 example, please read it carefully; Please bite the bullet and don't understand examples.

No. 18. Don't expect to remember and master anything the first time-please read it the second time and the third time.

No. 19. Don't stay in the cradle of basic problems, learn to treat basic problems as comprehensive problems made up of parts.

20 th place. Don't think that some words in mathematics have exactly the same meaning just because they look the same as those in natural language.

NO2 1。 The secret of learning mathematics is: solving problems, solving problems, and solving problems again.

The 22nd. Remember: the concepts and objects in mathematics are not unique to mathematics, so don't forget to use mathematics in other disciplines.

The 23rd. Please do the examples in the book yourself.

The 24th. Please find some exercises and use the problem-solving methods learned in books!

The 25th. Please pay attention to the details of the problem-solving mistakes and remind yourself before the exam.

The 26th. Always review the problems solved before, try new solutions and apply the new knowledge you have learned.

The 27th. Don't leave out any exercises in the book-please finish them all and write down your thoughts.

The 28th. When you find that your method is poor in the middle of a problem-solving idea, please don't throw it away immediately, at least after solving the problem with a new and better method, come back and re-analyze the previous idea.

The 29th. Never follow some problem-solving norms that you are not proficient in just because the topic is "small"-good habits are cultivated, not remembered at the moment.

The thirtieth. Every time you learn a math difficulty, try to explain it to others and make them understand-you can make it clear that you really understand it.

NO3 1。 Save all the exercises you work out-that's one of your best accumulations.

Thirty-second. Please love math!