Mathematical story

Meteorologist Lorenz put forward an article entitled "Can butterflies flap their wings to cause tornadoes in taxonomic groups?" ? This paper discusses that if the initial condition of a system is a little worse, its result will be very unstable. He called this phenomenon "the butterfly effect". Just like we roll the dice twice, no matter how deliberately we roll, the physical phenomena and points thrown twice are not necessarily the same. Why did Lorenz write this paper?

This story happened in the winter of 196 1 2008. He operated the meteorological computer in the office as usual. Usually, he only needs to input meteorological data such as temperature, humidity and air pressure, and the computer will calculate the possible meteorological data at the next moment according to the built-in three differential equations, thus simulating the meteorological change map.

On this day, Lorenz wanted to know more about the subsequent changes of a record. He re-entered the meteorological data at a certain moment into the computer, so that the computer could calculate more subsequent results. At that time, the speed of computer processing data was not fast enough, so he had time to have a cup of coffee and chat with his friends for a while before the results came out. An hour later, the result came out, but he was dumbfounded. Compared with the original information, the original data is similar, and the later data is more different, just like two different pieces of information. The problem is not the computer, but the data he entered is 0.0005438+027. These subtle differences make a world of difference. So it is impossible to accurately predict the weather for a long time.

References:

Cao Cao's Gourd (Volume II) —— Yuan Zhe Science Education Foundation

2. The mathematical genius of animals

Honeycomb is a strictly hexagonal cylinder, with a flat hexagonal opening at one end and a closed hexagonal diamond bottom at the other end, which is composed 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.

Red-crowned cranes always move in groups, forming a "human" shape. 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! Is it a coincidence or some "tacit understanding" of nature?

The spider's "gossip" net is a complex and beautiful octagonal geometric pattern, and it is difficult for people to draw a symmetrical pattern similar to a spider's net even with the compass of a ruler.

In winter, when a cat sleeps, it always hugs its body into a ball. There is also mathematics in it, because the shape of the ball minimizes the surface area of the body, so it emits the least heat.

The real "genius" of mathematics is coral. Coral writes a "calendar" on its body, and "draws" 365 stripes on its wall every year, apparently one a day. Strangely, paleontologists found that corals 350 million years ago "painted" 400 watercolors every year. Astronomers tell us that at that time, the earth only had 2 1.9 hours a day, not 365 days a year, but 400 days. (Life Times)

About 1500 years ago, European mathematicians did not know how to use "0". They use Roman numerals. Roman numerals are symbols representing numbers, which are combined to represent different numbers according to certain rules. When using this number, the number "0" is not needed.

At that time, a scholar of the Roman Empire discovered the symbol "0" from Indian notation. He found it very convenient to use "0" for mathematical operation, and he was very happy. He also introduced the Indian method of "0" to everyone. After a while, it was known by the pope at that time. At that time, it was the Middle Ages in Europe. The power of the church was very strong, and the power of the pope far exceeded that of the emperor. The Pope was very angry. He rebuked that the sacred number was created by God, and there was no such monster as "0" in the number created by God. Anyone who wants to introduce now is blasphemous! So the Pope ordered the scholar to be arrested and tortured, and his ten fingers were tightly clamped with a clamp, so that his hand was disabled and he could no longer write with a pen. In this way, "0" was banned by the ignorant and cruel Pope.

However, although the use of "0" is forbidden, Roman mathematicians still use "0" secretly in mathematical research regardless of the ban, and still make a lot of mathematical contributions with "0". Later, "0" was finally widely used in Europe, but Roman numerals were gradually eliminated.

Children, do you know the story of Gauss, a mathematical genius, when he was a child?

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

1+2+3+ .....+97+98+99+ 100 = ?

The teacher is thinking, now the children must start class! I used this as an excuse to go out, but Gauss stopped me! ! It turns out that Gauss has worked it out. Little friend, do you know how he did it?

Gauss told everyone how he worked it out: add 1 to 100, and add 100 to 1, adding two lines, that is:

1+2+3+4+ .....+96+97+98+99+ 100

100+99+98+97+96+ .....+4+3+2+ 1

= 10 1+ 10 1+ 10 1+ .....+ 10 1+ 10 1+ 10 1+ 10 1

* * * There are one hundred sums 10 1, but the formula is repeated twice, so the answer is equal to < 5050 & gt.

Since then, the learning process of Gauss Elementary School has already surpassed other students, which laid the foundation for his future mathematics and made him a mathematical genius!

In daily life, mathematics is everywhere, such as: buying and selling vegetables, calculating how much …

The following is a short story, a story between numbers.

One day, when the digital cards were having lunch together, the youngest one spoke.

Brother 0 said, "Let's take some photos together. What do you think? "

0' s brothers and sisters said in unison, "Good."

Brother 8 said, "Brother 0' s idea is really good. I will be a good person once. Shall I provide camera and film for Brother 8? "

Old 4 said, "Brother 8, it's good, but it's a little too much trouble. Better use my digital camera. That's settled. "

So, they got busy. Finally, they took pictures for them and immediately sent the digital camera to the print shop. The computer sister tried to ask them for money, but who paid for it? They stared at each other one after another. This is what the computer sister said, "A ***5 yuan, a * * * eleven brothers and sisters, how much does one person pay on average?"

Among the eleven of them, Lao Liu is the cleverest, and this time he is the first to work out the result. Do you know how it is worked out?

Tang Priest and his disciples picked peaches.

One day, the Tang Priest told his disciples Wukong, Bajie and Friar Sand to go to Huaguoshan to pick peaches. Before long, the three disciples returned happily after picking peaches. Tang Priest and his disciples asked: How many peaches did each of you pick?

Bajie said with a silly smile, Master, let me test you. Each of us took the same amount of money. There are less than 65,438+000 peaches in my basket. If we count three peaches, there are 1 peach left in the end. Do the math. How many did each of us choose?

Friar Sand said mysteriously, Master, I will test you, too. If there are four peaches in my basket, there is 1 left in the end. Do the math. How many did each of us choose?

Wukong smiled and said, Master, I'll test you, too. If there are five peaches in my basket, there will be 1 in the end. Do the math. How many shall we each choose?

Tang Priest quickly said the number of peaches he had picked. Do you know how many peaches they each picked?