# The solution of linear equations

For the creativity of Gauss organicthe association between theoretical and practical arithmetic, the depth of problems. The works of Gauss had a tremendous impact on the formation of algebra (confirmation of the main axiom of this science), the solution of linear equations of number theory (the internal geometric surface), mathematical physics (the Gauss principle), the theory of electricity and magnetism, geodesy (the development of the method of smaller squares) and almost all sections astronomy.

"Arithmetical research"

The first of its kind extensive creation of Gauss -"Arithmetical Research" (published in 1801), which lasted almost all the years of his life. The next formation is the fundamental sections of arithmetic - the theory of numbers and higher mathematics, which included the solution of linear equations.

Of a large number of principal and smallthe results given in the "Arithmetic Studies", we must note the complete concept of quadratic forms and the first confirmation of the quadratic law of reciprocity. At the end of life, Gauss gives the perfect concept of the separation equations of the circle, indicating their associations with the problems of constructing polygons, proven already in ancient times about the ability to construct by a compass and ruler a regular polygon with the correct number of sides.

Gauss showed all the numbers under which the constructionA true polygon using a compass and ruler can be simple. These are the so-called "five different Gaussian regular numbers": three and five, seventeen and two hundred and fifty-seven, and 65237, and multiplied by a different stage of two of the Gaussian numbers. For example, to build a faithful (3x5x17) with the help of office tools, a gon is allowed, and the correct 7-gon is impossible, since the figure is not Gaussian, it has the usual number.

The main axiom of algebra

With Gauss's name, the main axiom is still connectedalgebra, according to which the number of roots of a polynomial (real and complex) is the same (in the transformation of numerical roots, the complex root will be counted as many times as its step). The first confirmation of the main axiom of Gauss algebra was made in 1799, and later introduced a number of additional proofs.

Processing of observations

Unsuitable meaning for all sciences dealing withsuch a system, as the methods of solving systems of equations developed by Gauss, are able to obtain more potential values of measurement values. Particularly widespread popularity was made by Gauss in 1821. way smaller squares. Scientists have also laid the foundations of the theory of errors.

The meaning of Gauss studies

Almost everything, as it turned out, greatStudies of Karl Gauss were not published during life. They were preserved in the guise of sketches, sketches, which corresponded with his comrades. The Göttingen scientific community was engaged in the study of these works, and it was possible to publish twelve volumes of Gauss's works. More fascinating and popular work "Solving linear equations" was published late, as they accidentally found his diary with these records.

The scientific creativity of Charles was based on the decisionlinear equations. Applied mathematics was fully implemented in the basic part of science, it was given with great difficulty. It was necessary to fight for ideas, there were many scientists who wanted to become famous for the theme of solutions of linear equations.

Arithmetical researchinfluence on the forthcoming formation of the theory of numbers and algebra. The laws of reciprocity still occupy one of the most important places in algebra. This great scientist did not have the literature needed to work on such works as "Arithmetic Studies", "Matrix Solution by the Gauss Method," and "Solving Linear Equations," he took all the knowledge from his head, as they say.