On brillouin zones and related constructions

in this paper we discuss the physical and geometrical content of the various equivalent definitions that have been given so far in the literature of a crystal's brillouin zones. this serves as a motivation to introduce a computationally and conceptually simpler definition. calculation of brillouin zone related properties in two-dimensional lattices is carried out as an illustration of the versatility of this new approach, particularly a count of the number of landsberg subzones in these bravais lattices is given, which could be of interest for theoretical physics and number theory.