- #1
LeoYard
- 16
- 0
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 ?
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 ?