The Saccheri quadrilateral and the Lambert quadril
The Saccheri quadrilateral and the Lambert quadrilateral were among the first theorems on this topic. One form can be described by four models, while another has three. In one model, the cross-ratio is used to describe distances. They are useful for modeling space, since one type can describe the edges of the universe where no matter exists, and since the theory of relativity states that space is curved where there is matter. In another model, called the hyperspheric model, lines are modeled by great circles. They do not obey the parallel postulate, (*) since in the hyperbolic type there are infinitely many lines intersecting a point A not on a line L, and in the elliptical type all lines intersect. FTP, name these geometries that do not follow the precepts of an ancient Greek geometer.
The Saccheri quadrilateral and the Lambert quadrilateral were among the first theorems on this topic.
{non}-{Euclidean} geometries (accept response of {hyperbolic geometry} before while another has three)