In regards to mutual length contraction, Fig. 2-9 illustrates that the primed and unprimed frames are mutually rotated by a hyperbolic angle (analogous to ordinary angles in Euclidean geometry).In a Cartesian plane, ordinary rotation leaves a circle unchanged. In spacetime, hyperbolic rotation preserves the hyperbolic metric. Because of this rotation, the projection of a primed meter-stick onto the unprimed x-axis is foreshortened, while the projection of an unprimed meter-stick onto the primed x′-axis is likewise foreshortened.
In regards to mutual length contraction, Fig. 2-9 illustrates that the primed and unprimed frames are mutually rotated by a hyperbolic angle (analogous to ordinary angles in Euclidean geometry).In a Cartesian plane, ordinary rotation leaves a circle unchanged. In spacetime, hyperbolic rotation preserves the hyperbolic metric. Because of this rotation, the projection of a primed meter-stick onto the unprimed x-axis is foreshortened, while the projection of an unprimed meter-stick onto the primed x′-ax,is is likewise foreshortened.