Question

a polyhedron is made by placing a square pyramid exactly on one face of a cube. verify euler formula for this solid​

Answer 1

Answer:

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Answer 2

A polyhedron is made by placing a square pyramid exactly on one face of a cube. verify euler formula for this solid​

Step-by-step explanation:

This theorem involves Euler's polyhedral formula (sometimes called Euler's formula). Today we would state this result as: The number of vertices V, faces F, and edges E in a convex 3-dimensional polyhedron, satisfy V + F - E = 2.

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

The Most Beautiful Equation. Euler's Identity is written simply as: e^(iπ) + 1 = 0, it comprises the five most important mathematical constants, and it is an equation that has been compared to a Shakespearean sonnet. The physicist Richard Feynman called it “the most remarkable formula in mathematics”.

Three-dimensional geometry is a very rich field; this is just a little taste of it. Our main protagonist will be

a kind of solid object known as a polyhedron (plural: polyhedra). Its characteristics are:

• it is made up of polygons glued together along their edges

• it separates R

3

into itself, the space inside, and the space outside

• the polygons it is made of are called faces.

• the edges of the faces are called the edges of the polyhedron

• the vertices of the faces are called the vertices of the polyhedron.

The most familiar example of a polyhedron is a cube. Its faces are squares, and it has 6 of them. It also has

12 edges and 8 vertices.

Another familiar example is a pyramid. A pyramid has a bottom face, which can be any polygon (you are

probably most familiar with pyramids that have square bottoms), and the rest of its faces meet in one point

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