Euler formula proves that 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 plus V minus E equals 2, which is euler theorem? It was first proved by Descartes in 1640, and later independently proved by Euler in 1752. We call it euler theorem, and some people abroad call it Descartes theorem.

The strict proof of the first Euler formula given by Cauchy 20 is roughly as follows: If a face is removed from a polyhedron, the remaining faces will become a plane network of points and curves by pulling the edges of the removed faces away from each other, without losing generality, and it can be assumed that the deformed edges will continue to be straight lines.

The Significance of Euler Formula

Mathematical laws and formulas describe the unique laws between the number of vertices, faces and edges in a simple polyhedron. In the process of discovering and proving the theorem, it is conceptually assumed that its surface is rubber film, which can be stretched at will. In this way, the bottom surface is cut off and becomes a plane figure.

With the introduction of topology, the shape, length, distance and area of each face have changed from three-dimensional diagram to open diagram, while the number of vertices, faces and edges remain unchanged. This theorem introduces us into a new field of geometry. Topology, we use a kind of material that can be deformed at will, but it can't be torn or adhered. Topology is to study the invariant properties of graphics in this deformation process.

In Euler's formula, fp is equal to V plus F minus E, which is called Euler characteristic. Euler theorem told us that the simple polyhedron fp is equal to 2, and besides the simple polyhedron, there are non-simple polyhedrons, such as the polyhedron obtained by digging a hole in a cuboid and connecting the corresponding vertices at the bottom.