Jintan joke

Gauss 1777~ 1855 was born in Brunswick, north-central Germany. His grandfather is a farmer, his father is a mason, his mother is a mason's daughter, and he has a very clever brother, Uncle Gauss. He takes good care of Gauss and occasionally gives him some guidance, while his father can be said to be a "lout" who thinks that only strength can make money, and learning this kind of work is useless to the poor.

Gauss showed great talent very early, and at the age of three, he could point out the mistakes in his father's book. At the age of seven, I entered a primary school and took classes in a dilapidated classroom. Teachers are not good to students and often think that teaching in the backcountry is a talent. When Gauss was ten years old, his teacher took the famous "from one to one hundred" exam and finally discovered Gauss's talent. Knowing that his ability was not enough to teach Gauss, he bought a deep math book from Hamburg and showed it to Gauss. At the same time, Gauss is familiar with bartels, a teaching assistant who is almost ten years older than him. bartels's ability is much higher than that of the teacher. Later, he became a university professor, giving Professor Gauss more and deeper mathematics.

Teachers and teaching assistants went to visit Gauss's father and asked him to let Gauss receive higher education. But Gauss's father thought that his son should be a plasterer like him, and there was no money for Gauss to continue his studies. The final conclusion is-find a rich and powerful person to be his backer, although I don't know where to find it. After this visit, Gauss got rid of weaving every night and discussed mathematics with Bater every day, but soon there was nothing to teach Gauss in Bater.

1788, Gauss entered higher education institutions despite his father's opposition. After reading Gauss's homework, the math teacher told him not to take any more math classes, and his Latin soon surpassed the whole class.

179 1 year, Gauss finally found a patron-the Duke of Brunswick, and promised to help him as much as possible. Gauss's father had no reason to object. The following year, Gauss entered Brunswick College. This year, Gauss was fifteen years old. There, Gauss began to study advanced mathematics. Independent discovery of the general form of binomial theorem, quadratic reciprocity law in number theory, prime number theorem and arithmetic geometric average.

1795 gauss enters gottingen (g? Ttingen) university, because he is very talented in language and mathematics, so there was a time when he was worried about whether to specialize in classical Chinese or mathematics in the future. At the age of 1796 and 17, Gauss got an extremely important result in the history of mathematics. It was the theory and method of drawing regular heptagon ruler that made him embark on the road of mathematics.

Mathematicians in the Greek era already knew how to make a positive polygon of 2m×3n×5p with a ruler, where m is a positive integer and n and p can only be 0 or 1. However, for two thousand years, no one knew the regular drawing of regular heptagon, nonagon and decagon. Gauss proved that:

If and only if n is one of the following two forms, you can draw a regular n polygon with a ruler:

1、n = 2k，k = 2，3，…

2, n = 2k × (product of several different Fermat prime numbers), k = 0, 1, 2, …

Fermat prime number is a prime number in the form of Fk = 22k. For example, F0 = 3, F 1 = 5, F2 = 17, F3 = 257 and F4 = 65537 are all prime numbers. Gauss has used algebra to solve geometric problems for more than 2000 years. He also regarded it as a masterpiece of his life and told him to carve the regular heptagon on his tombstone. But later, his tombstone was not engraved with a heptagon, but with a 17 star, because the sculptor in charge of carving thought that a heptagon was too similar to a circle, so people would be confused.

1799, Gauss submitted his doctoral thesis and proved an important theorem of algebra:

Any polynomial has (complex) roots. This result is called "Basic Theorem of Algebra".

In fact, many mathematicians think that the proof of this result was given before Gauss, but none of them is rigorous. Gauss pointed out the shortcomings of previous proofs one by one, and then put forward his own opinions. He gave four different proofs in his life.

180 1 year. At the age of 24, Gauss published "Problem Arithmetic AE" written in Latin. There were eight chapters originally, but he had to print seven chapters because of lack of money.

This book is all about number theory except the basic theorem of algebra in Chapter 7. It can be said that it is the first systematic work on number theory, and Gauss introduced the concept of "congruence" for the first time. "Quadratic reciprocity theorem" is also among them.

At the age of 24, Gauss gave up the study of pure mathematics and studied astronomy for several years.

At that time, the astronomical community was worried about the huge gap between Mars and Jupiter, and thought that there should be planets between Mars and Jupiter that had not been discovered. 180 1 year, Italian astronomer Piazi discovered a new star between Mars and Jupiter. It was named Cere. Now we know that it is one of the asteroid belts of Mars and Jupiter, but at that time, there was endless debate in the astronomical circles. Some people say it's a planet, others say it's a comet. We must continue to observe to judge, but Piazi can only observe its 9-degree orbit, and then it will disappear behind the sun. So it is impossible to know its orbit, and it is impossible to determine whether it is a planet or a comet.

Gauss became interested in this problem at this moment, and he decided to solve this elusive star trajectory problem. Gauss himself created a method to calculate the orbits of planets with only three observations. He can predict the position of the planets very accurately. Sure enough, Ceres appeared in the place predicted by Gauss. This method-although it was not announced at that time-was the "least square method".

1802, he accurately predicted the position of the asteroid II Pallas Athena. At this time, his reputation spread far and wide, and honor rolled in. Russian Academy of Sciences in St. Petersburg elected him as an academician. Olbers, the astronomer who discovered pallas, asked him to be the director of the G? ttingen Observatory. He didn't agree immediately and didn't go to Gottingen until 1807.

1809, he wrote two volumes on the motion of celestial bodies. The first volume contains differential equations, circular spine parts and elliptical orbits. The second volume shows how to estimate the orbits of planets. Most of Gauss's contributions to astronomy were before 18 17, but he kept observing until he was seventy years old. Although doing the work of the observatory, he took time out to do other research. In order to solve the differential force path of celestial motion by integral, he considered infinite series and studied its convergence. 18 12 years, he studied hypergeometric series, and wrote his research results into a monograph and presented them to the Royal Academy of Sciences in G? ttingen.

From 1820 to 1830, Gauss began to do geodesy in order to draw a map of Hanover Principality (where Gauss lived). He wrote a book about geodesy, and because of the need of geodesy, he invented the heliograph. In order to study the earth's surface, he began to study the geometric properties of some surfaces.

1827, he published "Problems General Circa Supericies Curva", which covered some "differential geometry" in university studies.

During the period from 1830 to 1840, Gauss and Withelm Weber, a young physicist 27 years younger than him, were engaged in magnetic research. Their cooperation is ideal: Weber did experiments and Gauss studied theories. Weber aroused Gauss's interest in physical problems, while Gauss used mathematical tools to deal with physical problems, which influenced Weber's thinking and working methods.

1833, Gauss pulled an 8,000-foot-long wire from his observatory, passed through the roofs of many people, and arrived at Weber's laboratory. Using Volt battery as power supply, he built the world's first telegraph.

1835, Gauss set up a geomagnetic observatory at the Observatory and organized the "Magnetism Association" to publish the research results, which promoted the research and measurement of geomagnetism in many parts of the world.

Gauss got an accurate geomagnetic theory. In order to obtain the proof of experimental data, his book General Theory of Geomagnetism was not published until 1839.

1840, he and Weber drew the world's first map of the earth's magnetic field, and determined the positions of the earth's magnetic south pole and magnetic north pole. 184 1 year, American scientists confirmed Gauss's theory and found the exact positions of the magnetic south pole and the magnetic north pole.

Gauss's attitude towards his work is to strive for perfection, and he is very strict with his own research results. He himself once said, "I would rather publish less, but I publish mature results." Many contemporary mathematicians asked him not to be too serious, and to write and publish the results, which is very helpful for the development of mathematics. One of the famous examples is about the development of non-Euclidean geometry. There are three founders of non-Euclidean geometry, namely Gauss, Lobachevski (1793 ~ 1856) and Bolyai (Boei, 1802 ~ 1860). Among them, Bolyai's father is a classmate of Gauss University. He tried to prove the parallel axiom. Although his father opposed him to continue this seemingly hopeless research, Bolyai Jr. was addicted to parallel axioms. Finally, non-Euclidean geometry is developed, and the research results are published in 1832 ~ 1833. Old Bolyai sent his son's grades to his old classmate Gauss, but he didn't expect Gauss to write back:

Praising it means praising myself. I can't praise him, because praising him means praising myself.

As early as several decades ago, Gauss had obtained the same result, but he was afraid that this result would not be accepted by the world and was not published.

The famous American mathematician Bell (E.T.Bell) once criticized Gauss in his book Mathematicians:

Only after Gauss's death did people know that he had foreseen some mathematics in the19th century, and had predicted that they would appear before 1800. If he can reveal what he knows, it is likely that mathematics will be half a century or even earlier than it is now. Abel and jacoby can start from where Gauss stayed, instead of spending their best efforts on discovering what Gauss knew at birth. Those creators of non-Euclidean geometry can apply their genius to other aspects.

1On the morning of February 23rd, 855, Gauss died peacefully in his sleep. ......

1 bus length190m, and truck length is 240m. The two cars are traveling at a speed of 20 meters per second and 23 meters per second respectively. How many seconds does it take to meet from front to back on the double-track railway?

Answer: 10 second.

2 calculation1234+2341+3412+4123 =?

Answer:111/kloc-0.

The first item in arithmetic progression is 5.6, and the sixth item is 20.6. Find its fourth project.

Answer: 14.6

The sum of 4 is 0.1+0.3+0.5+0.7+...+0.87+0.89 =?

Answer: 22.5

5 Solve the following congruence equations:

(1)5X≡3 (module 13) (2)30x≡33 (module 39) (3)35x≡ 140 (module 47) (4) 3x+4x ≡.

Answer: (1) x ≡11(mod13) (2) x ≡ 5 (mod 39) (3) x ≡ 4 (mod 47) (4) x.

Can the number 220652532 1 be divisible by 7113?

Answer: Yes.

7 There are 100 coins, with 1 minute, 2 points and 5 points, with a total value of 2 yuan. It is known that the total value of 2 cents is more than 1 cent 13 cent. How many coins are there in each of these three types?

Answer: 5 1 `One cent, 32 cents, 17 cents.

8 Find a rule to fill in the numbers:

0, 3, 8, 15, 24, 35, _ _ _, 63 Answer: 48.

How many parts can a 9 100 straight line divide a plane into at most?

Answer: 505 1

10 A B Two people went to the ocean, each with 12 days of food, and they explored for _ _ _ days at most.

Answer: 8 days

The number of all natural numbers in the range of 1 100 that can be divisible by 2, 3, 5 or 7.

Answer: 78

12 1/2 + 1/2+3 + 1/2+3+4 + ......+ 1/2+3+4+....+ 10=?

Answer: 343/330

13 Choose at most a few numbers from 1, 2, 3, ... 2003, 2004, so that the difference between any two numbers is not equal to 9?

Answer: 1005

14 Find all the divisors of 360. Answer: 24.

15 parking lot, with 24 cars, four wheels for cars and three wheels for motorcycles, a total of 86 wheels. There are _ _ _ _ kinds of three-wheeled motorcycles. Answer: 10 vehicle.

16 has eight divisors, and the smallest natural number is _ _ _ _. Answer: 24.

17 Find the sum of all two digits except four and one; 12 10