The middle columns relate to functions within the same hyperbolic 2-space, only radii are the fundamental vectors of intersecting 2-spaces in hyperbolic Lorentz geometry (and thus as shown are invariant). Trigonometric relations in extended 2- and 3-space are referred to as 'circular' to avoid confusion with 'spherical trigonometry', however, 'spherical' is used in the context of 3-space in contrast to hyperbolic vector space. Hypotenuse is meant to be synonymous with radius.