The arithmetic of solids
  The set of segments, each of the next is n times bigger than the first one is a simple geometric interpretation of the set $\mathbb{N}$ of natural numbers. In this paper we investigate the opposite situation. We construct an algebraic structure similar to the set $\mathbb{N}$ which describes the set of congruent triangles, each of the next has the sides n times bigger than the first one. Later we do the same with the set of congruent tetrahedrons, and finally with a set of simplices of any dimension. 
Edward Mieczkowski
math.GM