Proof of Euler's Formula for Polyhedron | Used since childhood, but ever tried to prove?

Euler's Formula for Polyhedron states that for any convex polyhedron (a solid with flat faces and straight edges), the number of faces (F), vertices (V), and edges (E) are related by the equation F + V - E = 2. This formula reveals a fundamental relationship between these three elements, demonstrating that the sum of the faces and vertices minus the edges always equals 2, regardless of the specific shape or size of the polyhedron. Euler's Formula provides valuable insights into the topological properties of polyhedron and has applications in various fields of mathematics and engineering.

What is Graph?
In graph theory, a graph is a mathematical structure that consists of a set of vertices (also known as nodes) and a set of edges (also known as connections) that connect pairs of vertices. Graphs are used to represent and study relationships or connections between objects. They are composed of nodes that represent entities and edges that represent the connections or interactions between those entities. Graph theory provides a powerful framework for analyzing and solving problems related to networks, relationships, and various real-world applications, ranging from social networks to computer networks and optimization problems.

What is Planer and Non-planer graph?
A planar graph is a graph that can be drawn on a plane without any of its edges crossing each other. It can be represented in a two-dimensional space without any intersections. On the other hand, a non-planar graph is a graph that cannot be drawn on a plane without edge crossings. Non-planar graphs require a higher-dimensional representation or additional edge crossings to be visualized. Determining whether a graph is planar or non-planar is an important problem in graph theory with various theorems and algorithms to address it.

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