Gauss s lifetime achievements, what are Gauss s mathematical achievements?

Gauss's theorem, an application to physical mathematics.

Found outPrime numbersDistribution theorem and least squares,GaussThe formula for calculating the date of Easter was derived, and so on.

At the age of 17, Gauss discovered the distribution theorem of prime numbers and the method of least squares. By processing a sufficient amount of measurement data, a new, probabilistic measurement can be obtained. On these foundations, Gauss then focused on the calculation of surfaces and curves, and successfully obtained a Gaussian bell curve (normal distribution curve).

Its function is named the standard normal distribution.

and is heavily used in probability calculations.

With the help of Gauss's theory of measurement adjustment based on the method of least squares, the trajectory of celestial bodies is measured. He used this method to calculate the orbit of the asteroid Ceres.

Talented. 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 kind of geometry was bound to emerge outside of Euclidean geometry, non-Euclidean geometry. He derived the binomial theorem.

, which was successfully applied to infinite series, and developed the theory of mathematical analysis.

Gauss was born in Braunschweig, graduated from the University of Göttingen, a famous German mathematician, and one of the founders of modern mathematics. He discovered the distribution theorem of prime numbers, normal distribution curves and least squares, and made great achievements in his life, with 110 achievements named after his name "Gauss", enjoying the reputation of "Prince of Mathematics", and Archimedes, Newton, and Euler as the world's four great mathematicians. On February 23, 1855, Gauss died in Göttingen.

Gauss made outstanding contributions to mathematics.

Gauss's main mathematical achievements are as follows:

1. The general form of the binomial theorem was independently discovered; Digging and grinding.

2. The "quadratic reciprocal law" in number theory;

3. The prime number theorem in number theory;

4. The arithmetic geometric mean was discovered;

In the year, he created "Theory and Method of Drawing Regular Seventeen-sided Ruler Gauge" and so on.

Gauss was a famous German mathematician, physicist, astronomer and geodetic judge. In 1792, he entered the Technical University of Braunschweig; In 1795 Gauss entered the University of Göttingen; On February 23, 1855 he traveled and died early in the morning.

Gauss's main mathematical achievements are as follows:

1. The general form of the binomial theorem was independently discovered;

2. The "quadratic reciprocal law" in number theory;

3. The prime number theorem in number theory;

4. The arithmetic geometric mean was discovered;

In the year, he created "Theory and Method of Drawing Regular Seventeen-sided Ruler Gauge" and so on.

Gauss was a famous German mathematician, physicist, astronomer and geodesy. In 1792, he entered the Technical University of Braunschweig; In 1795 Gauss entered the University of Göttingen; He died in the early morning of February 23, 1855.

Gauss started school when he was 7 years old. At the age of 10, he entered the math class, which was the first of its kind and the children had never heard of arithmetic before. The math teacher was Buettner, who also played a role in Gauss's growth.

One day, the teacher assigned a question, 1+2+3··· So add it from 1 all the way up to 100.

Gauss quickly figured out the answer, and at first Gauss's teacher, Buettner, did not believe that Gauss had calculated the correct answer"You must have miscalculated, go back and do the math. Gauss said that the answer is 5050, Gauss is calculated in this way, the difference between years and ages is 1+100=101, 2+99=101... Adding 1 to 100 has 50 sets of such numbers, so 50x101=5050.

Buettner was impressed with him. He went out of his way to buy the best arithmetic books from Hamburg and gave them to Gauss, saying, "You have surpassed me, and I have nothing left to teach you."

Gauss then developed a sincere friendship with Bout's assistant Bartles, who played Blinder, until Bartles' death. They studied together, helped each other, and Gauss began real mathematical research.

Gauss, who was not yet eighteen years old, discovered that a regular n-sided shape could be drawn with a ruler and a compass if and only if n was one of the two underlying forms: k = 0, 1, 2 ......In the 17th century, the French mathematician Fermat thought that the formula was k=0,1,2,3,......Gives prime numbers.

In fact, it is currently only determined that f0, f1, f2, f4 are prime numbers, and f5 is not).

Gauss used algebraic methods to solve geometric problems for more than 2,000 years, and found the method of straightening rulers and compasses in regular seventeen sides. He was so excited that he decided to study mathematics for the rest of his life. It is also said that he expressed the hope that a regular heptangram would be engraved on his tombstone after his death to commemorate the most important mathematical discoveries of his youth.

In 1799 Gauss presented his Ph.D., which proved an important theorem of algebra: any unary algebraic equation has roots. This result is mathematically known as the "fundamental theorem of algebra".

In fact, there are many mathematicians among Gauss who think that they have given proof of this result, but none of them are rigorous, Gauss was the first mathematician to give a rigorous and infallible proof, Gauss thought this theorem was very important, and gave a total of four different proofs in his lifetime. Gauss didn't have the money to print his degree**, but fortunately Duke Ferdinand gave him money to print.

In 1807, Gauss became professor of mathematics and astronomy at the University of Göttingen and director of the observatory. Gauss has a proven track record of excellence in many areas. If differential geometry is the product of his practical application of mathematics, then non-Euclidean geometry is the result of his purely mathematical thinking.

He has also made brilliant achievements in number theory, hypergeometric progression, complex variable function theory, elliptic function theory, statistical mathematics, vector analysis, etc. Gauss's research on number theory has made many contributions. He believes that "mathematics is the king of science, and number theory is the king of mathematics".

His work had a profound impact on future generations. In the 19th century, German algebraic number theory developed by leaps and bounds, which is inseparable from Gauss.

At the age of twenty, Gauss wrote in his diary that he had many mathematical ideas in his mind, which could only be recorded in a small part because of the uncertainty of time. Fortunately, he wrote the results of his research into a book called "Arithmetic Research", and published it at the age of twenty-four, this book was written in Latin, originally had eight chapters, because of lack of money, he had to print seven chapters, this book can be said to be the first systematic work on number theory, Gauss introduced the concept of "congruence" for the first time.