Gaussian distribution 18-year-old gauss 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. Gauss calculated the trajectory of Ceres through the previous three observation data. 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". In order to know the date of Easter in any year, Gauss deduced the formula for calculating the date of Easter. 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. The telegraph designed by Gauss and Weber studied several fields, but only published his mature theory. He often reminds his colleagues that their conclusions have long been proved by himself.
Ming, just because the basic theory is not complete and not published. Critics say he is too pushy. In fact, Gauss is just a crazy typewriter, recording all his results. After his death, he found 20 such notes, which proved that Gauss's statement was true. It is generally believed that even these 20 notes are not all Gaussian notes. Libraries in Lower Saxony and the University of G? ttingen have digitized all Gauss's works and put them on the Internet. Gauss's portrait has been printed on 1989 to 200 1 circulating 10 Deutsche Mark banknotes. Classic works 1799: Satz der algebra based on Dokot Abete Uberden 180 1 year: arithmetic research. 1809: Theory of Celestial Motion (Orion Motus corporate theory in the part of ibus conics solem ambientium)1827: General research on surfaces (general problems about curved surfaces) 1843- 1844: Advanced geodetic theory (I
Leonhard euler leonhard euler1April 5, 707 ~1September 783 18 was a Swiss mathematician and physicist. He is called one of the two greatest mathematicians in history (the other is C.F.Gauss). Euler was the first person to use the word "function" to describe expressions with various parameters, such as y = F(x) (the definition of function was given by Leibniz in 1694). He was one of the pioneers who applied calculus to physics.
Euler's mathematical career began in the year when Newton died. For a genius like Euler, it is impossible to choose a more favorable era. Analytic geometry (1637) has been used for 90 years, calculus for about 50 years, and Newton's law of gravity, the key of physical astronomy, has been used in mathematics for 40 years. In each of these fields, a large number of isolated problems have been solved, and obvious attempts have been made to unify them everywhere. However, the whole mathematics, pure mathematics and applied mathematics have not been systematically studied as later. In particular, the powerful analytical methods of De Kratos, Newton and Leibniz have not been fully utilized as later, especially in mechanics and geometry. Algebra and trigonometry at that time had been systematized and developed at a lower level. Especially the latter, has been basically improved. In the field of Fermat's Diophantine analysis and general integer properties, there can be no such thing.