Hyperbolic orthogonality

In geometry, given a pair of conjugate hyperbolas, two conjugate diameters are hyperbolically orthogonal. This relationship of diameters was described by Apollonius of Perga and has been modernized using analytic geometry. Hyperbolically orthogonal lines appear in special relativity as temporal and spatial directions that show the relativity of simultaneity.

Keeping time and space axes hyperbolically orthogonal, as in Minkowski space, gives a constant result when measurements are taken of the speed of light.

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