The field Geometry of Numbers was christened by Minkowski when he proved his fundamental theorems on shortest vectors and successive minima. P. G. L. Dirichlet. Approximating the SVP to within a factor. A lattice L is a discrete additive subgroup of R n . It is the set of all integral linear combinations of an underlying generating set of linearly independent vectors from R n .
Many problems concerning lattices are both fascinating and challenging.
Given an n dimensional lattice, find the shortest non zero lattice vector in the lattice. Although the medial axis is a natural geometric object, its careful mathematical study has been lacking in the pure mathematics communities. G.L. Dirichlet, Uber die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen , J. of Reine Angew. In this section we discuss the conditions to be satisfied by the nuclei of a Voronoi tessellation in order to establish the mean value relations in Section 4. 2.2. J. Reine und Angew.