# Solving linear equations

creative Gauss peculiar organic association between the theoretical and practical arithmetic, the depth of the problems.Proceedings Gauss had a tremendous impact on the formation of the algebra (confirmation of the main axioms of this science), the solution of linear equations of the theory of numbers (internal geometric surface), mathematical physics (principle of Gauss), the theory of electricity and magnetism, geodesy (a method for least squares) and nearly all sectionsastronomy.

«Arithmetic Research»

first of its kind in the vast creation of Gauss - "Arithmetic research" (published in 1801), which lasted almost all the years of his life.The next formation - the principal sections of arithmetic - number theory and advanced mathematics, which included the solution of linear equations.

Of the large number of small and principal outcome listed in "Arithmetic Research", it should be noted the full concept of quadratic forms, and the first proof of the quadratic reciprocity law.At the end of his life Gauss results in a perfect concept of equations division of the circle, indicating their association with the objectives of the polygon, proved already in ancient times, the ability of construction by ruler and compass true polygon with the correct number of sides.

Gauss showed all the numbers in which the construction of a true polygon using a ruler and compass can be simple.This so-called "five different Gaussian normal numbers", three and five, seventeen, and two hundred fifty-seven and 65,237, and even multiplied in different stages of two Gaussian integers.For example, to build with the help of the faithful office equipment (3h5h17) - gon is allowed and the correct 7-gon is impossible, since figure is not Gaussian, it has the usual number.

Home algebra axiom

's name is still linked to the main Gaussian algebra axiom, according to which the number of roots of (real and complex) is the same (when converting numerical root root complex will be counted as many times as its stage).First confirmation of the main axioms of algebra, Gauss did in 1799, and later made a proposal more certain amount of evidence.

Recycling observations

Improper meaning for all sciences dealing with such a system, as the methods for solving systems of equations, developed by Gauss, capable of getting more potential value of the measurement values.Especially widespread popularity was made by Gauss in 1821.method of least squares.Scientists laid back and base of the theory of errors.

sense, the study of Gauss

Almost everything turned out as it is now, the great study of Carl Gauss did not publish during his lifetime.They are preserved in the form of sketches, essays, which were copied by his comrades.The study data was engaged in works of Gottingen scientific community, which turned out to publish twelve volumes of the works of Gauss.More fun and popular work "Solution of linear equations" published late as accidentally found his diary with these records.

Scientific creativity of Charles is based on solving linear equations.Applied Mathematics has been fully implemented in the base part of the science, it was given with great difficulty.For ideas to be fought, there were many academics who wanted to celebrate the theme of the solutions of linear equations.

Arithmetic study had a great impact on the forthcoming formation of number theory and algebra.Reciprocity laws and still occupy an important place in algebra.This great scientist was not literature, necessary to work on such productions as "Arithmetic research", "decision matrix by Gauss" and "Solution of linear equations", he took all the knowledge that is called out of my head.