Shen Kuo s story of the number altar, how to calculate the constant is 28?

One night in the Northern Song Dynasty, the owner of a small hotel was building a wine jar with his buddies. Because business has been very good recently, there are naturally more wine circles. The boss was happy in his heart, and at the same time he was thinking about how to make a bigger fortune.

The jars are stacked beautifully, neatly layered on top of each other. The banner at the entrance of the hotel fluttered in the wind, so that people had to stop and linger, and couldn't help but want to enter the store to drink a few cups. When the hotel owner was proud, he wanted to count how many wine jars there were.

However, counting the jars was not easy, the boss went around from the front to the back, and from the back to the front, and the sweat that had just been wiped out came out again, and the guys laughed.

The next day. This pile of wine jars really attracted a lot of customers, and the boss looked at the wine jar and was very happy. At this time, a well-dressed young scholar walked over, facing the wine jar, thoughtful.

The boss thought to himself: I spent a lot of effort yesterday to count these wine jars, this young man is extraordinary, I want to test him.

Young man, do you know how many of them there are? "The boss asked half-jokingly.

It's easy, just tell me how many rows there are on the top layer of this pile, how many are in each row, and how many are there. I don't have to count at all, I know the number of the jars right away. "The young man was obviously quite sure when he said this.

Oh! "The boss thought to himself: This young man is really good at big words, so he might as well tell him his conditions and see how capable he is. So the boss said briskly:

The top layer has four rows of 8 jars, and the second level has five rows of 9 ......"

Well, there are seven floors in total"The young man interrupted the boss and gave the answer without thinking"There are a total of 567 wine jars. Is that right? "

The boss was so shocked that he forgot to close his open mouth. So fast! The boss immediately invited the young man into the hotel, served tea, toasted, and entertained him very thoughtfully. The boss really admired this young man from the bottom of his heart, and asked for a name, and a method of asking for advice.

This young man's name is Shen Kuo. The privileged family living conditions gave him the opportunity to study, and his curiosity and willingness to study made him a very talented person. Boss Shen Kuo said:

The way I count this jar is actually very simple, because there are 77 in the middle layer, a total of seven layers, just multiply by 7 and add the constant 28 at the end. "

Shen Kuo has been interested in calculation since he was a child and has read many mathematical classics. Later, he wrote a mathematical treatise, "Gap Product", which specialized in the summation of higher-order difference series. Shen Kuo's method of counting is to use the method of summing high-order difference series, which is much more convenient than simply counting.

In addition to the middle layer, the results of subtraction of other layers and the middle layer are 45, 32, 17, -19, -40, -63, which obviously cannot be moved more to make up for less, and 63 plus 40 plus 19 minus 17 minus 32 minus 45 is equal to 28, indicating that 28 is added less, so 28 should be added

The constant 28 is the sum of the difference between the number of jars in each layer and the number of jars in the middle layer (77)!

The younger brother has a bad temper, and the mantra is: Charge him three seven twenty-one! I think he's too tough, but I don't want to hurt the peace.

The baby is in kindergarten middle class, Chinese New Year's Eve, relatives and friends sent a lot of candy, the younger brother promised her: you count the sugar, as long as you count correctly, no matter three seven twenty-one, ten yuan a piece! She counted all afternoon:

Okay, then you peel them out one by one and put them in a bowl, give them to your uncle, and take 210 yuan for the New Year's money. He began to peel again. It was almost finished when Zhao Benshan came out.

Holding the bowl and going straight to the younger brother: "Uncle, look, 21", the younger brother took it and counted it, lowered his head and gave the child 1500 yuan!

There was a burglary on a certain street. The thieves were very cunning and left no clues at the scene, while the money in the safe was missing. How could a thief know the password?

Conan found a small note at the scene, which said 1008, 1260, 1386, 1134 The four numbers, but the password can only be 3 digits, what does it have to do with these four numbers? Suddenly, Conan had a flash of inspiration in his mind, he did a quick calculation, and then pressed 3 numbers on the safe, and the safe opened. Do you know what the password is?

How did you get it?

Answer: 1+8=1+2+6=1+1+3+4=9 1+3+8+6=18

The ancient Greek scholar Archimedes died at the hands of Roman enemies attacking Sicily (before his death he was still in the Lord: "Do not break my circle"). Later, in his honor, the figure of the ball cut into the cylinder was engraved on his tombstone, to commemorate his discovery that the volume and surface area of the ball were two-thirds of the volume and surface area of the inscribed cylinder.

After the German mathematician Gauss discovered the ruler and gauge of the regular seventeen-sided shape, he gave up his original intention to study literature and devoted himself to mathematics, and even made many significant contributions to mathematics. Even in his will, he suggested that a tombstone with a regular seventeen-sided prism as the base be built for him.

The story of the mathematician as a child – Gauss.

Si is a second-grade student, one day his math teacher has already dealt with most of the matter, although the class is over, still wants to complete it, so he plans to give the student a math problem to practice, his problem is: 1+2+3+4+5+6+7+8+9+10=? , Because the addition has just been taught, so the teacher thinks that this problem, the student must have to calculate it for a long time, it is possible to calculate it, and you can use this time to deal with unfinished things, but in a blink of an eye, Gauss has stopped the pen, sitting there idlely, the teacher saw a very angry reprimand Gauss, but Gauss said that he had calculated the answer, that is, 55, the teacher listened to a jump, and asked Gauss how to calculate it, Gauss replied, I just found that the sum of 1 and 10 is The sum of 9 is also the sum of 8 and 7 and the sum of 6 is still 11, and 11 + 11 + 11 + 11 + 11 + 11 = 55, that's how I calculated.

When Gauss grew up, he became a great mathematician. When Gauss was young, he was able to turn difficult problems into simple, of course, qualification is a big factor, but he knows how to observe, seek rules, and simplify difficulties, which is worthy of our learning and imitation.

Once upon a time there was an old man whose three sons gathered around his bed as he was dying.

He said to his sons, "I have seventeen horses for you, three for them." When dividing the horses, the boss has the most effort, getting one-half of the total; the second, one-third of the total; The third child is the youngest, and you, you will take one-ninth of the total. ”

After barely saying these few words, the old man died. When the three brothers executed their will, they agreed that the horses were the beloved of their father during his lifetime, and that they should never be divided into several pieces. But how is it good to have a will be fully complied with?

Coincidentally, at this time, their old lady came on horseback, and after hearing the reason, he raised his eyebrows and said, "I'll divide it." ”

Guess what, how does the old lady divide the horses?

Because it is hoped that each person will get a whole number of horses, according to the will, when dividing horses, the number of horses should be a common multiple of the three denominators. The least common multiple of the denominator is 18, so it is best to divide the total number of horses in a multiple of 18. The old man left 17 horses for his sons, and the old lady temporarily lent one of the horses he brought to make up the number, and a total of 18 horses participated in the distribution.

When it was ready, the old lady began to read and execute the will

…When dividing the horses, the boss has the most effort, getting one-half of the total; At this point, the old lady counted out 9 horses and asked the boss to lead them:

the second, one-third of the total; Reading this, the old lady counted 6 horses and asked the second child to lead them:

The third child is the youngest, and you, you will take one-ninth of the total. After reading the last sentence, the old lady counted out 2 horses and asked the third to lead them:

The sum of the horses that the three juniors got was exactly 17 left by their father:

Of the 18 horses on the field, there is now the last one left, which is of course the one that the old lady brought and borrowed temporarily, and it is still returned to its original owner.

There is a well 7 meters deep, and a snail climbs up from the bottom of the well.

Climb 3 meters during the day and drop 2 meters at night.

Q: How many days can a snail crawl out of a well?

Discover oil.

Once, Shen Kuo read the sentence "Gaonu County has water and is combustible" in the book, and thought it was very strange, how could "water" burn? He decided to go on a field trip. During the expedition, Shen Kuo found a brown liquid, which the locals called "stone paint" and "stone grease", and used it to cook on fires, light lamps and keep warm.

Shen Kuo figured out the nature and purpose of this liquid, and gave it a new name, called petroleum. And mobilize the people to promote the use of trees, so as to reduce the felling of trees. Shen Kuo wrote in his book "Notes on Dream Creek":

There are oil ...... in the territory of Yan and YanIt is quite like pure lacquer, burning like hemp, but the smoke is very thick, and the curtain is very black and ......This thing will be great in the world, and it will be done from the rest. Cover oil at most, and be born in the earth endlessly, not as pine as sometimes exhausted. Shen Kuo discovered oil and predicted that "this thing will be popular in the world in the future", which is very rare.

The term "oil" invented by Shen Kuo has been used to this day.

Shen Kuo (1031-1095), a native of Qiantang (present-day Hangzhou, Zhejiang), was a famous scientist in the Northern Song Dynasty, and he was also an outstanding politician and military strategist.

In astronomy, during his tenure in Si Tianjian, Shen Kuo carried out a lot of work to improve the accuracy of instruments, and reformed astronomical instruments such as armillary spheres, floating leaks, and scenery tables, and wrote "Armillary Sphere Discussion", "Floating Leakage Discussion" and "Scene Table Discussion"; personally observed the celestial phenomena and drew more than 200 maps to determine the position of the North Star; In a few years, he insisted on observing the operation of the shadow and the leaky pot, thus proposing the time difference phenomenon caused by the uneven movement of the sun. In his later years, he proposed a new pure lunar calendar, the Twelve Qi Calendar, which was simple and straightforward and easy to guide farming.

In physics, Shen Kuo discovered the existence of geomagnetic declination more than 400 years earlier than Europe.

In his later years, Shen Kuo settled in Mengxi Garden in Runzhou (now Zhenjiang, Jiangsu) and devoted himself to writing, recording his life experiences and scientific research in "Mengxi Writings". The book contains more than 200 scientific items, including mathematics, astronomy, meteorology, geology, geography, maps, physics, chemistry, metallurgy, water conservancy, architecture, biology, agriculture and medicine, and many other fields, which is a valuable heritage in the history of science and technology in the world.

In order to commemorate Shen Kuo's exploits, people named asteroid 2027 "Shen Kuo asteroid".