Euler's Formula for Polyhedra

For any convex polyhedron, Euler discovered in 1750 that V − E + F = 2, where V is the number of vertices, E is edges, and F is faces. A cube: 8 − 12 + 6 = 2. A tetrahedron: 4 − 6 + 4 = 2. This seemingly simple formula was proved to be a topological invariant — the Euler characteristic. For a torus (donut shape) it becomes V − E + F = 0. Topology was born from this formula, and an entire branch of mathematics descended from one observation about counting corners and edges.