"Among any 367 people, there must be the same person in Amanome."

"Choose 6 pairs of gloves from any 5 pairs of gloves, of which at least 2 pairs are just a pair of gloves."

"From 1, 2, ..., 10, and there are at least two parity differences. "

Here, the pigeon hole principle is used, and the contents of the pigeon hole principle can be expressed in vivid language as follows:

"put m things into n empty drawers at will (m >；; N), then there must be at least two things in a drawer. "

In the first conclusion above, because there are at most 366 days in a year, at least two of the 367 people were born on the same day in the same month. This is equivalent to putting 367 things into 366 drawers, and at least two things are in the same drawer. In the second conclusion, imagine that five gloves are numbered separately, that is, two gloves with the same numbers are 1, 2, ..., 5, and these two gloves are just a pair. Take six gloves at random. They have at most five numbers, so at least two of them have the same number. This is equivalent to putting six things in five drawers, and at least two things are in the same drawer. ?

Using the above principle, it is easy to prove: "In any seven integers, the difference between at least two numbers of three is a multiple of three." Because there are only three possible remainders when any integer is divisible by 3: 0, 1 and 2, at least three of the seven integers are divisible by 3 to get the same remainders, that is, the difference between them is a multiple of 3.

If there are infinitely many objects discussed in the problem, there is another way to express the pigeon hole principle:

"Put an infinite number of things into N empty drawers at will (N is a natural number), then there must be an infinite number of things in one drawer."

The pigeon hole principle is simple and easy to accept, and plays an important role in mathematical problems. Many proofs of existence can be solved with it. ?

2. ups and downs

Suppose you have 65438+ ten thousand yuan:

The first case: after the daily limit on the first day, it is 1 10000 yuan, and after the daily limit on the second day, it is 99000 yuan.

The second case: 90,000 yuan after the first day's limit, and 99,000 yuan after the next day's limit.

3, covering positions or fixed investment phenomenon

Suppose the net value of a fund is 10 yuan, and you buy 10000 yuan. The following month, the net fund value fell to 5 yuan, and you bought 6,543,800 yuan.

Excuse me: What is your post cost? A.7.5 yuan B.6.67 yuan

Correct answer: the cost of holding a position is 6.67 yuan.

This is the charm of the fund's fixed investment, which can greatly reduce your position cost.

4. The beehive is a strictly hexagonal cylinder, with a flat hexagonal opening at one end and a closed hexagonal diamond bottom at the other end, which consists of three identical diamonds. The rhombic obtuse angle of the chassis is 109 degrees 28 minutes, and all acute angles are 70 degrees 32 minutes, which is both firm and material-saving. The honeycomb wall thickness is 0.073 mm, and the error is very small.

5. Red-crowned cranes always move in groups and form a herringbone. The angle of the herringbone is 1 10 degrees. More accurate calculation also shows that half the angle of the herringbone-that is, the angle between each side and the direction of the crane group is 54 degrees, 44 minutes and 8 seconds! And the angle of diamond crystal is exactly 54 degrees, 44 minutes and 8 seconds! ?

6. In winter, cats always hold their bodies in a ball shape when they sleep. There is also mathematics in this, because the ball shape minimizes the surface area of the body, so it emits the least heat.

7. Capital preservation portfolio

The following two investment products:

Suppose you have 1 10,000 yuan, you invest 800,000 yuan in asset A and 200,000 yuan in asset B.

In this way, you have made a portfolio with guaranteed capital: the worst return is zero, and the best return is 12%.

8. A gambling game: the organizer puts four balls of different colors, five balls of red, yellow, blue and white, and puts them all into a box, from which the participants randomly draw 10 balls. If the four-color combination is 5500, you can get a Leica camera; If it is 54 10, I will give you a Chinese cigarette; But there are two combinations that you want to give him money in turn: one is 3322 and the other is 432 1.

As a result, people who play games catch it there, which is often 3322 or 432 1. This is a math problem that is easy to calculate. Liang Changhong, president of xidian university, is a mathematician. He organized hundreds of students to take tests at school and do calculations on the computer. The results are the same: 3322 and 432 1 account for the highest proportion, close to 30%; And 5500, only one in ten thousand.

9. Rate of return phenomenon: 65,438+10,000 yuan to buy a stock, up 100% is 200,000; But if it falls by another 50%, it will return to 654.38+10,000 yuan. You know, it is much easier to fall by 50% than to rise by 100%.

10, the myth of zero sum and infinity: "0" is also the number I am interested in. I think "0" is what China people call "nothing" in philosophy. Everything is born and nothing is born, so nothing is the source. No, of course, it is the source, because each of us was born with nothing. We were nothing until we were conceived by our mother.

China people have worked hard on the word "nothing". Laozi advocates inaction without desire. "Learning is getting worse and worse, and Tao is getting worse and worse, leading to inaction. Doing nothing and doing nothing. "

Why do you want to do nothing? Because out of nothing, nothing is everything. Therefore, the ancients in China said that there is nothing; Nothing, nothing is not forever; Because nothing can exist, it is nothing, and nothing denies nothing, and nothing itself does not deny nothing. Why can't anything be anything? Because with the help of infinity, nothing can be combined with infinity, and it is possible to produce "existence".

There are various paradoxes between 0 and infinity, between being and nothing. The most basic problem in mathematical paradox is that if you admit that there is, then 0 is also a way of existence. If 0 becomes a certain way, it will be very encouraging.

Extended data:

Mathematics (Mathematics or maths, from the Greek word "Má thē ma"; Often abbreviated as "mathematics"), it is a discipline that studies concepts such as quantity, structure, change, space and information, and belongs to a formal science from a certain point of view. Mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

In the development of human history and social life, mathematics also plays an irreplaceable role, and it is also an indispensable basic tool for studying and studying modern science and technology.

References:

Baidu encyclopedia-mathematics