Image for Minkowski's theorem

Minkowski's theorem

Minkowski's theorem in geometry relates to how shapes can be represented in space. It states that any convex shape in a lattice (a regular grid of points) can be expressed as a combination of points from that lattice. Essentially, this means you can build complex structures using simple, repeating units. In number theory, it helps understand solutions to equations and relationships between numbers. Overall, Minkowski's theorem bridges geometry and algebra, showing how spatial objects can be understood through a mathematical framework.