Give me a few little stories about math 5

Gaussian clever counting, ruler gauge to draw 17 sides. "Fermat" conjecture, Chen Jingrun's "1+2".

Gauss's story is very famous.

Every piece of paper has two sides and an edge that closes the curve, is it possible if there is a piece of paper that has one edge and only one face, so that an ant can reach any other point on the paper without going over the edge? In fact, it is possible to twist a piece of paper tape in half and then attach both ends. This is the German mathematician M?

1790-1868) was discovered in 1858, and since then the belt has been named after him as the Mebius belt. With this toy, topology, a branch of mathematics, flourished.

Good luck with your studies!

I can't find a small story with an indispensable meaning. But I don't know if mathematicians can be helped by others.

There are many interesting things in the world, and there are many interesting things in our kingdom of mathematics. For example, in my current workbook for Book 9, there is a question that goes like this: "A passenger car travels 45 kilometers per hour from Dongcheng to Xicheng, and after traveling for an hour, it stops, and then it is exactly 18 kilometers away from the midpoint of the east and west cities, how many kilometers are the distance between the east and west cities?"

When Wang Xing and Xiaoying solved the above problem, the calculation method and result were different. The kilometers calculated by Wang Xing were less than those calculated by Xiaoying, but Mr. Xu said that the results of both were correct. Why is that?

Did you come up with it? You can also calculate the results of the two of them. Actually, we can quickly make a way to solve this problem, that is:

45 km), km), km), but if you look closely, you don't feel right. In fact, here we ignore a very important condition, that is, the word "away" in the condition "at this time is just 18 kilometers away from the midpoint of the East and West Cities", does not say that it has not reached the midpoint, or has exceeded the midpoint. If it is less than 18 kilometers from the midpoint, the column formula is the previous one, and if it is more than 18 kilometers from the midpoint, the column formula should be 45 kilometers), kilometers), kilometers).

So the correct answer should be: 45 km), km), km) and 45km), km), km). Two answers, that is to say, Wang Xing's answer plus Xiaoying's answer is comprehensive.

In daily learning, there are often many math questions with multiple answers, which are easy to be ignored in exercises or exams, which requires us to carefully review the questions, awaken life experience, carefully scrutinize, and fully and correctly understand the meaning of the questions. Otherwise, it is easy to ignore the other answers and make the mistake of generalizing.

Tian Ji horse racing.

Tian Ji used the dismount to the upper horse of the King of Qiwei, the upper horse to the middle horse of the King of Qiwei, and the middle horse to the dismount of the King of Qiwei. The result of the game was a best-of-three game, and Tian Ji won. It's the same horse, but by reversing the order of the race, the result is to turn defeat into victory.

The story of Gauss as a child.

When Gauss was ten years old, his elementary school teacher had an arithmetic problem: "Calculate 1 2 3....＋100＝？This is difficult for a beginner arithmetic student, but Gauss solved the answer in a few seconds, using the symmetry of arithmetic series (difference series) and then putting together pairs of numbers in the same way as the process of finding the sum of ordinary arithmetic series:

1＋100，2＋ 99，3＋98，……49 52, 50 51 And there are 50 sets of such combinations, so the answer can be quickly found as: 101 50 5050

But it looks good, and the Mekong River is odd and even

When Gauss was in elementary school, once after the teacher taught addition, because the teacher wanted to rest, he came up with a problem for the students to calculate, the topic was:

The teacher was thinking to herself, now the children must be counted as the end of class! I was about to excuse myself when I was about to excuse myself to go out, but I was stopped by Gauss!! It turns out that Gauss has already calculated, do you know how he calculated, kid?

There are 100 100 added up, but the equation is repeated twice, so dividing 10100 by 2 gives the answer equal to <5050>

Since then, Gauss's learning process in primary school has already surpassed other students, which has laid the foundation for his future mathematics and made him a math genius!

After finishing speaking, Liu Zhanhao understood, and he said with deep feelings: It seems that mathematics is inseparable everywhere! Mathematics Stories (2) Bajie went to Huaguo Mountain to find Wukong, but the Great Sage was not at home. The little monkeys warmly entertained Bajie and picked the mountains.

After a while of class, Min Zhencai came running from outside the apricot forest in disheveled clothes, and Teacher Kong always advocated that people should be neatly dressed, which could be old but not shabby, and seeing him like this, he stopped the lecture and waited for him to get dressed. After a while, Min was dressed, and the students looked at it, but they laughed one after another. It turned out that he was wearing a black sock on his left foot and a white sock on his right foot, which was very strange, what was going on?

If only the missing one was exactly a pair of the same color, what was even more unfortunate was that there was one black sock and one white sock missing, and the rest would not be a pair. I searched for a long time, but I couldn't find it, so I came in a hurry. After a pause, he let out a long sigh and said:

In short, today is an unlucky day! When Mr. Kong heard this judgment he gave himself, he laughed and said, "As the saying goes, 'the house leaks when it rains overnight, and the broken ship meets the head wind', and when bad luck happens, it is always the most unlucky of all possible situations that are more likely to happen."

This feeling is common among people, and in fact, it is also very correct from a mathematical point of view. Using mathematics, we can prove that there is no single line of misfortune!

Turning around, he wrote "Black 1, Black 2, White 1, White 2" on the blackboard and said, "Let's give each of the four socks a code name for easy analysis." If you take two of these four socks to make a pair, then you have ...... of these optionsWith that, he continued to write:

black 1 black 2; Black 1 White 1; Black 1 White 2; Black 2 White 1; Black 2 White 2; White 1 white 2. "Look, how many possibilities are there? We said in unison

6 kinds. "How many of them happen to be the same color and can be paired together?" "There are only two kinds of black, black, black, 2, white, and white.

Yes, how many kinds are there that are not right? "4 kinds! "Yes, this means that the probability of losing socks is only one-third that the same color does not affect the remaining socks, and the probability that the remaining socks are not good is two-thirds.

In other words, Min lost a pair of socks, which is indeed quite unlucky, but he happened to lose socks of different colors, and the 'more unlucky possibility' that caused the remaining socks to be difficult to match was twice as good as the other possible two-rent raids! And, if the number is higher, let's say Min has five pairs of socks, then this 'more unlucky' probability will be 8 times greater! "Ahh

This time, the students not only spoke in unison, but also exclaimed, but they did not expect that the feeling of "disaster is not a single line" in life is actually mathematical. Later, we came up with a law called the "Law of Bad Luck," which means "If something bad is possible, it will happen, and it's always the worst." We also wanted to call this law "Min's Law", but unfortunately he didn't agree, and everyone had to give up.

There was a crazy artist who, in search of inspiration, tore a very large piece of paper millimeter-thick in half, overlapping it, and then tearing it in half and overlapping it. Suppose he repeated the process like this, tearing it 25 times, how thick would this stack of paper be? Here are four answers, which do you think is closer?

a.As tall as a mountain bAs tall as a tall building cAs tall as a person dAs thick as a book.

AnswerAnswerAnswer: a. Because with each tear, the thickness of the stack doubles.

After tearing 25 times, the thickness of the paper is equivalent to 2 2 2 ......2 (25 2's multiplied), the thickness is about 3355 meters, which is equivalent to the height of a large mountain. Of course, this is only a hypothetical situation, and no one can tear a piece of paper like this.