The Euler characteristic is a topological invariant that provides a way to classify surfaces and shapes. It is calculated using the formula \chi = V - E + F , where V is the number of vertices, E is the number of edges, and F is the number of faces in a polyhedron. For example, a cube has an Euler characteristic of 2. This concept is named after the mathematician Leonhard Euler, who introduced it in the 18th century. The Euler characteristic helps in understanding the properties of different geometric structures, such as toruses and spheres, and is fundamental in the field of topology.