Topology in Grammar - Euler Characteristic of a Simple Sentence

TSU, 115 - 17.40-18.05

Topology, the modern branch of geometry, studies those properties of geometric figures which are invariant with respect to continuous deformations. One of the first such invariants is Euler Characteristic  e = (number of vertices) – (number of edges) + (number of faces). Euler mentioned that for a pyramid, cub, prism, and, generally, for any polytope which can be deformed to sphere this combination is always 2. This, in particular, implies the famous fact that there exist only 5 regular polytopes, Platonic Solids. We present also application of Euler characteristic in syntactic structure of simple sentence, particularly the topological consequences of one rule of Georgian grammar: Number of members in a simple sentence is one greater than the number of syntagms. This means exactly that the Euler characteristic of a simple sentence equals to 1.