When Gauss was a child, how did Gauss calculate when he was a child, how did he calculate it?

The idea of the equation is that x=1+2+3+......98+99+100, written in reverse order, x=100+99+98+......3+2+1, 2x=101+101+101+......101 + 1101 + 101, (100 imaginary circles).

101*100, x=101*100 2=101*50=5050, Gauss applied the commutative law of addition when he was a child, divided into 50 groups, ie.

101+101+……101 + 101 (50 silver rocks) 5050, memory method, analogous trapezoidal area formula, (upper bottom + lower bottom) * high 2, that is, = (1 + 100) * 100 2 = 5050

Carl Friedrich Gauss (1777-1855) was a German mathematician, astronomer and physicist.

Gauss entered the University of Goettingen in 1795 and received his doctorate at the University of Helmstedt in 1799. In 1807 he was appointed professor of mathematics and astronomy and director of the observatory at the University of Goettingen. His involvement in astronomy began with the study of asteroids, and in 1801 he created the calculation method for determining the orbit of asteroids through three observations, and successfully calculated the orbits of the asteroids Ceres and Homo sapiens. Since then, almost all asteroid orbits have been extrapolated using this method.

Gauss also created the method of finding latitude by using the height of the sun's near meridian, and the multi-star contour method for determining the clock and latitude at the same time, and established the method of arbitrary constant change in the form of Gaussian and the theory of long-term difference. He also introduced a set of auxiliary quantities into the calculation of the ephemeris, which greatly simplified the calculation of the Cartesian coordinates of the heliocentric equator. His invention of mathematical methods such as least squares has great significance for subjects such as astronomy.

In addition, he has made important contributions to geodesy, the theory of the shape of the earth, and geomagnetism.

Gauss (1777-1855) was born in Brunswick, in what is now north-central Germany. His grandfather was a farmer, his father was a plasterer, his mother was the daughter of a stonemason, and he had a very intelligent younger brother, Gauss, an uncle, who took good care of little Gauss and occasionally gave him some guidance, while his father could be said to be a "big old man", thinking that only strength could make money, and that learning this kind of Rausch was useless to the poor.

Gauss showed talent early on, and at the age of three he was able to point out mistakes in his father's books. At the age of seven, he entered primary school, where he taught in a dilapidated classroom, where the teacher was not kind to the students, and often thought that he had never met a talent to teach in a poor rural area. When Gauss was ten years old, his teacher took the famous "From One Plus to One Hundred" exam, and finally discovered Gauss's talent, and he knew that his ability was not enough to teach Gauss, so he bought a deeper math book from Hamburg and read it to Gauss.

At the same time, Gauss became acquainted with Bartels, a teaching assistant who was almost ten years his senior, and Bartels was much more capable than his teacher, and later became a university professor, where he taught Gauss more and deeper mathematics.

The teacher and the teaching assistant went to visit Gauss's father and asked him to let Gauss receive a higher education, but Gauss's father thought that his son should be like him, a plasterer, and there was no money for Gauss to continue his education, and finally concluded that he would find a rich and powerful person to be Gauss's patron, although they did not know where to find it. After this visit, Gauss was relieved of his work of weaving every night and discussed mathematics with Bartels every day, but before long, Bartels had nothing left to teach Gauss.

In 1788, Gauss entered the École Norman, despite his father's objections. The math teacher read Gauss's homework and told him not to have to take math class, and his Latin soon overtook the class.

I remember hearing a story: Gauss is a second-grade student, one day his math teacher has already dealt with most of the matter, although the class is over, he still wants to complete it, so he plans to give the students 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, the teacher thinks that this problem, the student must be able to calculate it for a long time, and it is possible to use this time to deal with unfinished things, but in the blink of an eye, Gauss has stopped writing and sat there idlely, the teacher saw it and reprimanded Gauss angrily, but Gauss said that he had calculated the answer, which was 55, and the teacher jumped when he heard it, and asked Gauss how to calculate it, Gauss replied, I just found the sum of 1 and 10 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.

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The fact that Gauss was able to correct his father's debt accounts at the age of 3 has become an anecdote that has survived to this day. He once said that he learned to calculate on the Mai Xian Ong pile. Being able to make complex calculations in his head was a gift from God that he had given him a lifetime.

When Gauss was 9 years old, Gauss spent a very short time calculating the task assigned by his elementary school teacher: summing natural numbers from 1 to 100. The method he used was:

The sum of 50 pairs of numbers constructed into a sum of 101 is (1+100, 2+99, 3+98......).At the same time, the result is obtained: 5050. However, according to more elaborate mathematical history books, Gauss's solution is not as simple as adding 1 to 100, but 81297+81495+...

100899 (tolerance 198, number of terms 100).

By the time Gauss was 12 years old, he had already begun to doubt the fundamental proofs in elemental geometry. When he was 16 years old, a completely different geometry would inevitably arise outside of Euclidean geometry. He derived the general form of the binomial theorem, successfully applied it to infinite series, and developed the theory of mathematical analysis.

Gauss's teacher Bruettner and his assistant Martin Bartels recognized Gauss's extraordinary talent for mathematics at an early age, and Herzog Carl Wilhelm Ferdinand von Braunschweig was impressed by the gifted child. So they sponsored Gauss's studies and life from the age of 14. This also allowed Gauss to study at the Carolinum Academy (the predecessor of today's Braunschweig College) in 1792-1795 AD.

At the age of 18, Gauss transferred to the University of Göttingen. At the age of 19, he was the first to succeed in constructing a regular 17-angle shape with a ruler.

Gauss (1777-1855), a famous German scientist, was born into a poor family. Gauss learned to do arithmetic on his own before he could speak, and one night when he was three years old, he watched his father calculate wages and corrected his mistakes in calculations.

When he grew up, he became one of the most prominent astronomers and mathematicians of our time. He made some contributions to the electromagnetism of physics, and one of the units of electromagnetism is now named after him. Mathematicians called him the "Prince of Mathematics".

At the age of eight, he entered a rural primary school. The math teacher was a man from the city, and he thought it was useless to teach a few young people to read in a poor rural area. And he is a little biased:

The children of the poor are born stupid, and it is not necessary to teach these stupid children to read, and if there is an opportunity, they should be punished to add some fun to this boring life.

It was a day of low mood for math teachers. When the students saw the teacher's depressed face, they cringed in their hearts, knowing that the teacher would arrest these students and punish them today.

You will count for me today the sum from 1 plus 2 plus 3 all the way up to 100. Whoever can't figure it out will be punished for not being able to go home for lunch. After the teacher said this, he picked up a ** without saying a word, sat on a chair and read it.

The children in the classroom picked up the slate and began to calculate: "1 plus 2 equals 3, 3 plus 3 equals 6, 6 plus 4 equals 10 .......""Some children add a number and then erase the results on the slate, and then add more, the number gets bigger and bigger, which is very difficult to calculate. Some of the children's faces were red, and some of them were sweating from their palms and foreheads.

In less than half an hour, little Gauss picked up his slate and stepped forward. "Teacher, is the answer so? ”

The teacher didn't raise his head, waved his fat hand, and said, "Go, go back and count again!" Wrong. He didn't think he would have an answer so soon.

But Gauss stood still and stretched out the slate in front of the teacher: "Teacher! I guess the answer is right. ”

The math teacher wanted to roar, but when he saw that the number was neatly written on the slate: 5050, he was amazed, because he had calculated it himself, and the number he got was also 5050, how could this 8-year-old kid get this value so quickly?

Gauss explained a method he had discovered, which was used by the ancient Greeks and Chinese to calculate series 1+2+3+....+n. Gauss's discovery made the teacher feel ashamed that he had not been right to look at everything and despise children from poor families. He also began to teach seriously, and often bought some math books from the city to study and lend them to Gauss.

With his encouragement, Gauss later made some important research in mathematics.