A Visual Model of the Lorentz Triangular Moduli Space

摘要

We present a schematic construction of the triangularly-shaped space in the Lorentz plane, i.e., the moduli space of all Lorentzian triangles up to similarity. This space turns out to be homeomorphic to a band where the different types of triangles may be located according to the length and the causal character of their sides. In particular, several kinds of equilateral and isosceles triangles are identified.