## Archive of posts with tag “algebraic number theory”

### Rotational symmetry of plane lattices as a simple example of algebraic number theory

For a plane lattice, there is only a finite number of different rotational symmetries that are compatible with the discrete translational symmetry. For example, the 5-fold rotational symmetry is not one of them. Why is that? It turns out that whether an $m$-fold symmetry is compatible with translational symmetry is the same as whether $\varphi(m)\le2$.

- Categories: math
- Tags: complex, condensed matter physics, algebraic number theory, lattice, mathematical physics