Imaginary Language Hyperbolic Space Language 2011

Imaginary Language Hyperbolic Space Language TANAKA Akio September 5, 2011 [Preparation] 3 dimensional hyperbolic space H3 Spherical surface at infinity Sx Ideal simplex that has vertexes on Sx Σ Internal angles of triangle that is projected to plane z = 0 Internal angles of ideal simplex α, β,γ Internal angles except α, β,γ α1, β1,γ1 Volume of ideal simplex V <Theorem> V (Σ) = Λ(α) +Λ(β)+Λ(γ) [Interpretation] Language model is expressed by V (Σ). Word is expressed by Σ. This paper has been published by Sekinan Resarch Field of Language. All rights reserved. © 2011 by The Sekinan Research Field of Language