Hyperbolic law of cosines - 1st law
In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry.
Take a hyperbolic plane whose Gaussian curvature is -1/k2 . Then given a hyperbolic triangle ABC with angles α, β, γ, and side lengths BC = a, AC = b, and AB = c, two rules hold the first of which is shown here.Related formulas
|a||side length (dimensionless)|
|b||side length (dimensionless)|
|c||side length (dimensionless)|