In fact, there are many formulas called Euler formula. But in geometry, Euler's formula refers to the relationship between the number of vertices V, the number of faces F and the number of edges E of a simple polyhedron: V+F-E=2. The geometric bodies we have learned, such as prisms and pyramids, are all simple polyhedrons. There are many ways to prove Euler's formula. Prove 1: gradually reduce the number of edges of polyhedron, analyze V+F-E, and take simple tetrahedron ABCD as an example to prove. Remove a face to make it a plane figure. After deformation, the number of vertices v, edges v and remaining faces F 1 of tetrahedron remain unchanged. Therefore, in order to study the relationship between V, E and F, we only need to remove one surface and turn it into a plane figure, and prove that V+F 1-E= 1. (1) If one edge is removed and one face is reduced, V+F 1-E remains unchanged. Remove all faces in turn and become a "tree". (2) Every time an edge is removed from the remaining tree, a vertex is reduced, and V+F 1-E remains unchanged until only one edge remains. In the above process, V+F 1-E remains unchanged, and V+F 1-E= 1, so a removed surface is added, and V+F-E=2. For any simple polyhedron, this method has only one line segment left. Therefore, this formula is correct for any simple polyhedron. Prove 2: Calculate the internal angles of the faces of the polyhedron, and set the number of vertices V, faces F and edges E of the polyhedron. Cut off a face, make it into a plane figure (expansion diagram), and find the sum of all internal angles σ α (1). In the original drawing, find the sum of internal angles with each surface. There are f faces, the number of sides of each face is n 1, n2, …, nF, and the sum of the internal angles of each face is: σ α = [(n1-2)1800+(N2-2)1800+… Let a cutting surface be an N-polygon, and the sum of its internal angles is (n-2 n-2) 1800, then among all V vertices, there are N vertices on the side and V-n vertices in the middle. The sum of the internal angles of the V-n vertices in the middle is (V-N) 3600, and the sum of the internal angles of the N vertices on the side is (N-2 n-2) 1800. So the sum of the internal angles of a polyhedron: σ α = (v-n) 3600+(n-2)1800+(n-2)1800 = (v-2) 3600. (2) Defined by (65438).