Complex sentence: Klein model is strongly analogous to the gnomonic projection of spherical geometry, which maps great circles to straight lines; the formulae relating these two to the hyperboloid model and the sphere, respectively, are very similar.
Split into simpler sentences: Klein model is analogous to the gnomonic projection of spherical geometry, in that geodesics (great circles in spherical geometry) are mapped to straight lines. The formulae relating these two to the hyperboloid model and the sphere, respectively, are very similar.