Integer lattice

Approximations of regular pentagrams with vertices on a square lattice with coordinates indicated

Rational approximants of irrational values can be mapped to points lying close to lines having gradients corresponding to the values

In mathematics, the n-dimensional integer lattice, denoted ⁠$\mathbb {Z} ^{n}$⁠, is the lattice in the Euclidean space ⁠$\mathbb {R} ^{n}$⁠ whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice (or grid lattice) and the three-dimensional integer lattice is called the cubic lattice. ⁠$\mathbb {Z} ^{n}$⁠ is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice.