Euler proved the polyhedron theorem named after him:
For all convex polyhedra holds:
where e is the number of vertices, f the number of faces and k the number of edges.
This is also the name of the Eulerian straight line. For all triangles it is true that the intersection of the heights - https://domyhomework.club/ , the intersection of the median perpendiculars and the intersection of the bisectors of the sides lie on one (namely this) straight line.
In 1744, Euler's textbook on the calculus of variations appeared, which dealt with problems of calculating extreme values - do my math homework for mу (maximum and minimum). In 1748 he published the first analytical geometry of conic sections in textbook form, in which developments of series for sin x,cos xundex are also found.
Euler wrote more than 900 treatises, more than half of them during his blindness. Thanks to the great reputation he enjoyed, many terms and symbols that he introduced or adopted in his works found their way into mathematics through him and are still used by us today. These include, for example:
- a, b, c for the sides and α,β,γ for the angles of a triangle.
- the sign π for the number of a circle
- sin, cos and tan as distance ratios
- the number e as the limit of (1+1n)n, the basis of the natural logarithms
- the sign Δx for the difference quotient
- the symbol ∑ for the sum
- the symbol i for - 1---√
- the symbol f (x) for functions for which he also gave a definition
Carl Friedrich Gauss wrote about Euler - geometry homework help : "Of no other mathematician of recent or older times can one boast such almost incomprehensible rapidity in the most difficult work with such inexhaustible fertility of new ideas and aids. He worked on all parts of mathematics, and most of them received a completely new shape under his hands.