Let R be a convex region symmetrical about the origin with area greater than 4. Show that R must contain a lattice point different from the origin. This is the 2-D case of Minkowski's theorem, right ? How about the n-dimensional version ? The n-dimensional version is : Given a convex region R symmetrical to the origin in the n-dimensional space. How to show that if R has volume greater than 2^n, then R contains a lattice point different from the origin ?