Euler Characteristic

The Euler Characteristic is a number that describes the shape or structure of a geometric object, particularly in topology, which studies properties that remain unchanged under continuous transformations. It is calculated using the formula \( V - E + F \), where \( V \) is the number of vertices (corners), \( E \) is the number of edges (sides), and \( F \) is the number of faces (flat surfaces). For example, a simple cube has an Euler Characteristic of 2. This characteristic helps classify surfaces, indicating their complexity, such as whether they are connected or have holes.