The Euler characteristic

The Euler characteristic is a fundamental number that helps describe the shape or structure of a geometric object. In simple terms, it can be thought of as a way to summarize the object's features. For example, for simple shapes, the Euler characteristic is calculated using the formula: \( V - E + F \), where \( V \) is the number of vertices, \( E \) is the number of edges, and \( F \) is the number of faces. It provides insights into the object's topology, helping distinguish between different shapes even if they look similar.