Historical contribution Gaussian distribution 18-year-old Gaussian discovered the prime number distribution theorem and the least square method. After processing enough measurement data, new probability measurement results can be obtained. On this basis, Gaussian then focuses on the calculation of surfaces and curves, and successfully obtains Gaussian bell curve (normal distribution curve). Its function is named standard normal distribution (or Gaussian distribution), which is widely used in probability calculation. When Gauss 19 years old, a regular 17 polygon was constructed with only a ruler and compasses, and there was no scale (neither Archimedes nor Newton drew it). It also provides the first important supplement to Euclidean geometry which has been circulated for 2000 years since ancient Greece. Gauss, triangle congruence theorem, summarizes the application of complex number in calculating ceres trajectory, and strictly proves that every n-order algebraic equation must have n complex number solutions. In his first masterpiece, Number Theory, he proved the law of quadratic reciprocity, which became an important basis for the continued development of number theory. The first chapter of this book deduces the concept of triangle congruence theorem. Gauss, the theory of celestial motion, calculated the trajectory of celestial bodies with the help of his measurement adjustment theory based on the least square method. So we found the trajectory of ceres. Ceres was discovered by Italian astronomer Piazi in 180 1 year, but he delayed his observation due to illness and lost the trajectory of this asteroid. Piazi was named after the goddess of harvest (Ceres) in Greek mythology, that is, Planetoiden Ceres, and announced the previously observed position, hoping that astronomers all over the world would look for it together. It only took 24-year-old Gauss a few weeks to learn about it. Through the previous three observation data, he obtained the elliptical orbit of Ceres by his own least square method, and calculated the trajectory of Ceres. Although Gauss received his Ph.D. two years ago for proving the basic theorem of algebra, and published his classic book Arithmetic Research in the same year, it was the orbit of Ceres that made him famous in the earthquake science community. Austrian astronomer Heinrich Olbers successfully discovered this asteroid in the orbit calculated by Gauss. Since then, Gauss has become famous all over the world. Gauss wrote this method in his book "Oria Motus Corporate Coelestium in ibus Conexis Solem Ambientium". Mathematical achievements Gauss invented the principle of least squares. Gauss's research on number theory was summarized in Arithmetic Research (180 1), which laid the foundation of modern number theory. It is not only an epoch-making work in number theory, but also one of the rare classic works in the history of mathematics. Gauss's important contribution to algebra is to prove the basic theorem of algebra, and his existence proof opens up a new way of mathematical research. Gauss got the principle of non-Euclidean geometry around 18 16. He also deeply studied the complex variable function, established some basic concepts and discovered the famous Cauchy integral theorem. He also discovered the double periodicity of elliptic functions, but these works were not published before his death. 1828, Gauss published "General Theory of Surfaces", which comprehensively and systematically expounded the differential geometry of spatial surfaces and put forward the theory of intrinsic surfaces. Gaussian surface theory was later developed by Riemann. Gauss published 155 papers in his life. He is very strict with his studies and only publishes what he thinks is mature. His works include the concept of geomagnetism and the law of universal gravitation. Repulsion is inversely proportional to the square of distance. In order to know the date of Easter in any year, Gauss deduced the calculation formula of the revival holiday period. Geodetic survey of Hanover Principality 18 18 to 1826 was dominated by Gauss. Through the adjustment method of measurement based on least square method and the method of solving linear equations, the measurement accuracy is obviously improved. Out of interest in practical application, he invented the solar reflector, which can reflect the light beam to a place about 450 kilometers away. Gauss later improved the original design more than once, and successfully trial-produced the mirror sextant widely used in geodesy. Gauss personally participated in the field investigation. He observes during the day and calculates at night. In five or six years, he calculated the geodetic data more than 6,543,800 times. When the field observation of triangulation led by Gauss was on the right track, Gauss shifted his main energy to the calculation of observation results and wrote nearly 20 papers of great significance to modern geodesy. In this paper, the projection formula of ellipse to sphere is derived and proved in detail. This theory still has application value today. Geodetic survey of Hanover Principality was not finished until 1848. This huge project in the history of geodesy can't be completed without Gauss's careful consideration in theory, striving for reasonable and accurate observation and meticulous data processing. It can be said that under the conditions at that time, it was a great achievement to establish such a large-scale geodetic control network and accurately determine the geodetic coordinates of 2578 triangular points. In order to solve the problems in geodesy by using the conformal projection theory of ellipse on the sphere, Gauss also engaged in the research of surface and projection theory during this period, and became an important theoretical basis of differential geometry. He independently proposed that the parallel postulate of Euclidean geometry could not be proved to be' physical' inevitability, at least it could not be proved by human reason. But his non-Euclidean geometry theory has not been published. Perhaps he was worried that his contemporaries could not understand this extraordinary theory. Relativity proves that space is actually a non-Euclidean space. Nearly 100 years later, Gauss's thought was accepted by physics. In the geodesy of Hanover Principality, Gauss tried to verify the correctness of non-Euclidean geometry by measuring the sum of the internal angles of the triangle formed by Brocken of Hartz-Fort sayles-Turing Wald-Brocken of Gottingen, but failed. Janos, the son of Gauss's friend Bao Ye, proved the existence of non-Euclidean geometry in 1823, and Gauss praised his exploration spirit. 1840, Lobachevsky wrote the article "Geometry Research of Parallel Line Theory" in German. After this paper was published, it attracted the attention of Gauss. He attached great importance to this argument and actively suggested that G? ttingen University hire Lobachevsky as an academician of communication. In order to read his works directly, from this year on, 63-year-old Gauss began to learn Russian and finally mastered this foreign language. Finally, Gauss became the most important figure among the ancestors of sum differential geometry (Gauss, Janos, Lobachevsky). Out of interest in practical application, Gauss invented the solar reflector. The sunlight reflector can reflect the light beam to a place about 450 kilometers away. Gauss later improved the original design more than once, successfully trial-produced the mirror sextant, and later it was widely used in geodesy. Magnetometer 65438+In 1930s, Gauss invented the magnetometer, quit his job at the Observatory and turned to physical research. He cooperated with Weber (1804- 189 1) in the field of electromagnetism. He is 27 years older than Webb and cooperates as a teacher and friend. 1833, he sent a telegram to Weber through a magnetic compass. This is not only the first telephone and telegraph system between Weber Lab and the Observatory, but also the first in the world. Although the line is only 8 kilometers long. 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, which were confirmed by American scientists the following year.