Mathematics
The Voronoi Diagram and Its Uses in Spatial Analysis
Quick fact
The Voronoi diagram's dual graph is the Delaunay triangulation, which avoids skinny triangles and is used in mesh generation for everything from weather simulations to computer graphics.
Why this is interesting
Imagine dropping nails on a board and stretching a rubber sheet around them—each nail would claim its own territory. How do we define exactly that territory for any set of points?