Conversely the ct and x axes can be constructed for varying coordinates but constant ζ. The definition tanh ⁡ ⁡ ζ ζ = sinh ⁡ ⁡ ζ ζ cosh ⁡ ⁡ ζ ζ , provides the link between a constant value of rapidity, and the slope of the ct axis in spacetime. A consequence these two hyperbolic formulae is an identity that matches the Lorentz factor cosh ⁡ ⁡ ζ ζ = 1 1 − − tanh 2 ⁡ ⁡ ζ ζ .