Question

What is meant by Euler's theorem?

Answer 1

Answer:

Euler’s formula, either of two important mathematical theorems of Leonhard Euler. The first formula, used in trigonometry and also called the Euler identity, says eix = cos x + isin x, where e is the base of the natural logarithm and i is the square root of −1 (see irrational number). When x is equal to π or 2π, the formula yields two elegant expressions relating π, e, and i: eiπ = −1 and e2iπ = 1, respectively. The second, also called the Euler polyhedra formula, is a topological invariance (see topology) relating the number of faces, vertices, and edges of any polyhedron. It is written F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges. A cube, for example, has 6 faces, 8 vertices, and 12 edges and satisfies this formula.

Explanation:

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Answer 2

Question:

What is meant by Euler's theorem?

Answer:

Euler's theorem states that in any polyhedron, we have

V+F-E=2

V = Number of vertices in the polyhedron

F = Number of faces in the polyhedron E = Number of edges in the polyhedron

More to know:

Polyhedron:

A polyhedron is a solid made up of polygonal regions called its faces.