Euler formula

Euler formula has different meanings in different disciplines. In complex variable function, e (ix) = (cosx+isinx) is called Euler formula, e is the base of natural logarithm, and I is imaginary unit.

In topology, on any regular spherical graph, if R is used to record the number of regions, V is used to record the number of vertices, and E is used to record the number of boundaries, then R+V-E=2. This was first proved by euler theorem and Descartes in 1640, and later independently proved by Euler in 1752. We call it euler theorem, and some people abroad call it Descartes.

Knowledge expansion:

A formula connecting complex exponential function and trigonometric function, where e is the base of natural logarithm and I is imaginary unit. It extends the definition of exponential function to complex number and establishes the relationship between trigonometric function and exponential function. It not only appears in mathematical analysis, but also occupies a very important position in the theory of complex variable functions, and is also called "overpass in mathematics".

Let G be a connected plane graph with N-order M-edges and R-faces, then n-m+r=2. This formula is called Euler formula. It can be proved by induction, which is similar to that in topology and is omitted here. Although it is very similar to Euler's formula in topology, graph theory generally falls into the research category of discrete mathematics in modern times, so it is listed separately here.

In the natural world where we live, there are both material things and spiritual things. Matter is represented by real numbers. When some specific values in a physical object are deflected and partially or completely transformed into an energy field, mass energy is deflected, and then a variable with mutual induction between energy and mass is generated, that is, a complex number: z = a+b * i.

0, 1 is expressed as logical truth and falsehood, which is widely used in computer science of silicon-based systems and images of Yijing Bagua.