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The benefits of mathematics are too numerous to mention, and scientists at all times and all over the world have also pointed out it. /kloc-J.J. Sylvester, a mathematician in the 0/9th century, pointed out: "Constant exploration and pursuit in the field of mathematics can sublimate human thinking activities to a pure and harmonious realm." Wang Hao, a contemporary mathematical logician, also said that mathematics has pure beauty. J. Abbas Nott said: "Mathematical knowledge makes thinking more energetic and frees thinking from prejudice, credulity and superstition." W.E. Cerraul said, "Just like literature induces people's emotions, mathematics stimulates people's imagination and reasoning ability."

In a word, mathematics can make your thinking pure and harmonious, and it will add vitality to your thinking. It gives you wings of imagination and opens the channel of reasoning for you. Mathematics is used by us in real life. It teaches us something and how to gain benefits. Sometimes mathematics can help us identify deception and even create deception.

Many students may have tried computer fortune telling, or they may believe it. "Computer fortune telling" looks mysterious. As long as you report the year, month, day and sex of your birth, a so-called character and destiny will appear on the screen when you press the button. It is said that this is your "destiny".

In fact, this is just a computer game at best. We can easily use the pigeon hole principle in mathematics to illustrate its absurdity.

Pigeon hole principle, also known as pigeon cage principle or Dirichlet principle, is a special method to prove the existence in mathematics. For the simplest example, if you put three apples in two drawers in any way, there must be two or more apples in one drawer. The same reasoning can be obtained:

500-word composition

Principle 1 If more than n objects are put into n drawers, at least one drawer has more than two objects.

Principle 2 If there are more than mn objects in N drawers, at least one drawer has more than m+ 1 or m+l objects.

If calculated in 70 years, the number of combinations with different sexes according to the date of birth should be 70× 365× 2 = 5 1 100, and we regard it as the number of drawers. The current population of China is 1 1 100 million, and we regard this figure as the number of "things". Because1.1× = 2 1526× 51/kloc-0+21400, according to principle 2, it is more than 21526, although

In ancient China, people knew how to use the pigeon hole principle to expose the fallacy of birth. For example, in Qing Dynasty, Chen Qiyuan wrote in Notes on Leisure Zhai: "I don't believe in the theory of pushing the stars, thinking that one person is born at a time (note: one hour, two hours), and twelve people are born in one day, which is 4,320 people in terms of age. Counting a Jia (note: 60 years), there are only 259,200 people. Today, only one county is counted. During this period, when the princes were born, there must be people born at the same time. What is the difference between the rich and the poor? " Here, a year is calculated as 360 days, and a day is divided into 12 hours, and the number of drawers obtained is 60× 360× 12 = 259200. Composition 300 words

The so-called "computer fortune-telling" is nothing more than storing the manually compiled fortune-telling sentences in their respective cabinets in advance like Chinese medicine cabinets. Who wants to tell fortune, that is, according to the different combinations of birth date, date and gender, according to different codes, mechanically take out the so-called fate sentence from the computer cabinet. It is blasphemy to put the aura of modern science on the dead who were superstitious in ancient times.

Cheating in business is also inseparable from mathematics. Two generations of love give us the best explanation.

The Eid al-Adha Festival is coming, and the atmosphere of the festival is everywhere in the north and south of Tianshan Mountain. In the market town, the traffic is busy and lively. Shops, roadsides, and stalls are full of goods everywhere, with a dazzling array of things. Fruit merchants have moved out the fresh apples, grapes, Sydney, oil and cantaloupe, hoping to sell them at a good price.

At noon that day, Afandi finished half a day's work and rode a donkey to the market. Two generations of love are famous for their intelligence, ability, integrity and integrity. Who doesn't know him? Along the way, he kept greeting his acquaintances and friends. Suddenly, I heard someone calling his name. Two generations of love turned around and saw Ai Shan, the owner of the fruit shop. This man is treacherous and greedy. He not only uses fake and shoddy goods to harm customers, but also specializes in usury to exploit the people. He is a bad guy that everyone hates. Two generations of love have long wanted to teach this guy a lesson, but he didn't have a chance. At this time, Aishan is sitting in front of two baskets of grapes with a balance beam. A basket is purple grapes, the price is 2 yuan 1 kg; A basket is green grapes, the price is 1 yuan 2 Jin. It's just that many people ask and few people buy. Composition 500 words

"Any lift eldest brother, it is not easy to do some business now. You see, I've been here all morning, and I haven't sold a few Jin of grapes. Now there are 60 kilograms of purple grapes and green grapes. I don't know when to sell! " Ai Shan really wanted to ask Avanti to help him come up with an idea to sell grapes, but he was embarrassed to say it.

Afandi heard the implication and thought: This guy just came to the door, so let him pay some money and make everyone angry. He came to the fruit stand and said to Ai Shan, "Oh, Ai Shan, you are so stupid! Purple grapes are sweet, but expensive. Green grapes are cheap, but they taste sour. Why not mix the two kinds of grapes and sell them at the price of 3 kg of 3 yuan, that is, per kg 1 yuan, which is not only easy to sell but also convenient? "

When Ai Shan heard this, he suddenly smiled and quickly gave a thumbs-up and praised: "The two generations of big brothers are really smart, and they really deserve their reputation!" So Ai Shan sold grapes according to the method of two generations of love, and sure enough, more people bought them. Soon, 120 Jin of grapes sold out.

However, after calculating the amount of money sold, Ai Shan couldn't help frowning: if the grapes are sold at the original price, the purple grapes should be sold in 2 yuan× 60 = 1 20 yuan, and the green grapes should be sold in1yuan× (60 ÷ 2) = 30 yuan, which should be able to sell 120 yuan +30 yuan = 65438. He wandered around in front of the grape stall, looking for it everywhere, but he couldn't find the lost 30 yuan money. Finally, I realized that two generations of love had played a trick on me. When he wanted to catch up with the two generations of love and ask him, the two generations of love had gone without a trace on a donkey.