The solution of linear equations

For the creativity of Gauss, there is an organic 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 is the extensive creation of Gauss - "Arithmetic Studies" (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.

From the large number of principal and small results given in the "Arithmetic Studies", it is necessary to note the complete concept of quadratic forms and the first confirmation of the quadratic reciprocity law. At the end of life, Gauss gives a perfect concept of the separation equations of the circle, indicating their associations with the problems of constructing polygons, already proven 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 construction of a 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 two different Gaussian numbers. For example, you can 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

The main axiom of algebra is still connected with the name of Gauss, according to which the number of roots of the 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

An unsuitable meaning for all sciences dealing with such a system as Gaussian's methods of solving systems of equations are capable of obtaining more potential values for the measurement of quantities. 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 now it turned out, the great studies of Karl Gauss did not publish 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, because they accidentally found his diary with these records.

Karl's scientific work was based on the solution of linear 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 scientific figures who wanted to become famous for the theme of solutions of linear equations.

Arithmetical research had a great impact on the forthcoming formation of number theory 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 knowledge from his head, as they say.