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.
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Saturday, 14 September 2019
Imaginary Language Hyperbolic Space Language
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