A mathematical story that contains mathematical ideas .

Math Stories - Vignettes on the way to learn from the scriptures.

The four Tang monks and apprentices went to the west to learn scriptures, and they were tired and hungry that day. Wukong said: "What about going to ** to find food?" Bajie volunteered and said, "Master, I'll go fast!" The master said, "Bajie, go and go back quickly, don't be greedy." ”

Bajie walked and saw a peach tree full of peaches, and he was very happy. He couldn't wait to count the peaches on the tree, a total of 17 peaches. Bajie thought:

How can the four of the 17 peaches not be divided? There are four masters, four Sha brothers, four monkey brothers, four me, and four fours are 4x4=16 (pieces). But there are 17 peaches in total?

17-16=1 (one) One person, four, what if there is one left? At this time, Zhu Bajie's eyes turned, and the problem of gluttony was committed again. I thought:

I'll eat the extra one first, and I'll take the remaining 16 back and divide them. At this time, Bajie was already drooling, and swallowed the peach in one bite. But I never thought that the peach was changed by Sun Wukong.

Sun Wukong said in Zhu Bajie's stomach: "Idiot, you are not stupid to dare to steal food from the master, see if I don't clean you up." Sun Wukong jumped a few times in Zhu Bajie's stomach, and the painful Bajie only shouted:

Brother Monkey spares his life, I will no longer be greedy. "Since then, I have never been greedy when I fasted.

Heart-shaped lines The love story of mathematician Descartes. Descartes was born in France in 1596, when the Black Death broke out on the European continent, he wandered to Sweden, met the 18-year-old princess Christine of a small principality of Sweden, and later became her math teacher, and they fell in love with each other every day. Descartes fell seriously ill shortly after returning to France, and he wrote letters to the princess every day, but Christine never received Descartes' letter because she was intercepted by the king.

Descartes died of exhaustion after sending Christine a thirteenth letter with a short formula: r=a(1-sin). The king could not understand it, and felt that there was not always a love talk between the two of them, so he gave the letter to Christine, who had been sullen, and when the princess saw it, she immediately understood the lover's intentions, and she immediately began to draw the figure of the equation, and when she saw the figure, she was very happy, and she knew that the lover was still in love with her, and the figure of the equation was in the shape of a heart.

This is also known as the "heart-shaped line".

After the death of the king, Christine ascended the throne and immediately sent people around Europe to look for her sweetheart, but the deceased man was one step ahead of her, leaving her alone in the world.

It is said that this world-famous alternative love letter is still preserved in the memorial of Descartes in Europe.

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.

One day in 1796, a young man began to work on math problems left by his mentor.

The first two questions were completed smoothly. There is only the third question left: it is required to draw a regular 17-sided shape using only a ruler and a gauge.

The young man racked his brains, but nothing was done.

Difficulties stir up fighting spirit. He finally got the job done.

The tutor was stunned to see the student's assignment. He said excitedly, "You know what? You've solved a math puzzle that's been left over 2,000 years ago! ”

It turned out that the tutor handed the note to the student because of a mistake.

Whenever he recalled, the young man always said, "If someone had told me that this was a mathematical problem that was more than 2,000 years old, I might never have the confidence to solve it." ”

This young man was Gauss, the prince of mathematics.

Gaussian with regular heptans.

One day in 796, at the University of Göttingen, Germany, a 19-year-old young man with a great talent for mathematics finished dinner and began to do the daily routine of three math problems assigned to him by his tutor. The first two questions were successfully completed in two hours. The third inscription is written on another small piece of paper:

It is required to draw a regular 17-sided shape using only a compass and a ruler without a scale. He felt very struggling. Time passed minute by minute, and there was no progress on the third question.

The young man racked his brains, but he found that all the math he had learned did not seem to help solve the problem. The difficulty aroused his fighting spirit: I must make it!

He picked up the compass and the ruler, and as he pondered, he drew on the paper, trying to find answers with some unconventional ideas. When the window showed light, the young man breathed a sigh of relief, and he had finally completed the puzzle. When meeting the mentor, the youth felt some guilt and self-blame.

He said to his mentor, "I did the third question you assigned to me all night, and I failed to live up to your cultivation ...... meThe tutor took the student's homework and was immediately stunned. He said to the young man in a trembling voice:

Did you make it yourself? The young man looked at the mentor with some confusion and said, "I did it."

However, I spent the whole night. The instructor asked him to sit down, took out the compass and ruler, spread the paper on the desk, and asked him to make another regular 17-sided shape in front of him. The youth quickly made a regular 17-sided shape.

The mentor excitedly said to him, "Do you know? You've solved a math mystery that's more than 2,000 years old!

Archimedes didn't solve it, Newton didn't solve it, you solved it in one night. You are a true genius! It turned out that the mentor had always wanted to solve this puzzle.

On that day, it was because of a mistake that he handed the note with the question written on it to the student. Whenever the young man recalls this scene, he always says: "If someone had told me that this was a math that was more than 2,000 years old, I would probably never have the confidence to solve it."

This young man was Gauss, the prince of mathematics. There are some things that we tend to be able to do better when we don't know how hard it really is! From this point of view, the real difficulty is not the difficulty itself, but our fear of it.