Geometry of Numbers

"In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space. The geometry of numbers was originated by Hermann Minkowski. The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity. The geometry of numbers deals with the use of geometric notions, especially convexity and lattice, to solve problems in number theory."