Euler theorem is named after Swiss mathematician leonhard euler, and this theorem is considered as one of the most beautiful theorems in mathematics. Euler theorem is actually a generalization of Fermat's theorem. There are also euler theorem in plane geometry and euler theorem of polyhedron (in a convex polyhedron, the number of vertices-number of edges+number of faces =2). In western economics, euler theorem is also known as the net theorem of output distribution, which means that under the condition of perfect competition, all products are just enough to be distributed to all factors, assuming that the long-term medium-scale income remains unchanged. There is also an Euler formula.

Euler formula

Description of formula: In the formula, e is the base of natural logarithm and I is the imaginary unit.

e^(ix)=cosx+isinx

E is the base of natural logarithm, and I is the imaginary unit.

It extends the definition domain of trigonometric function to complex number, and establishes the relationship between trigonometric function and exponential function, which occupies a very important position in the theory of complex variable function.

Replace x in the formula with -x to get:

E (-ix) = cosx-isinx, and then we add and subtract the two formulas to get:

sinx=[e^(ix)-e^(-ix)]/(2i),cosx=[e^(ix)+e^(-ix)]/2.

These two are also called Euler formulas.

The formula created by God

Let x in e (ix) = cosx+isinx be π, and then:

e^(iπ)+ 1=0.

This equation, also known as Euler formula, is the most fascinating formula in mathematics. It connects several most important numbers in mathematics: two transcendental numbers: the base e and π of natural logarithm, two units: imaginary number unit I and natural number unit 1, and the common 0 in mathematics. Mathematicians evaluate it as a "formula created by God", which we can only look at but can't understand.