Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel...

the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed...

geometry hold in hyperbolic geometry as well as in Euclidean geometry. Absolute geometry is inconsistent with elliptic geometry: in elliptic geometry...

elliptic geometries, that have no parallel lines. Absolute geometry is an extension of ordered geometry, and thus, all theorems in ordered geometry hold...

plane intersect in two antipodal points, unlike coplanar lines in Elliptic geometry. In the extrinsic 3-dimensional picture, a great circle is the intersection...

now rarely used sequence elliptic geometry (spherical geometry), parabolic geometry (Euclidean geometry), and hyperbolic geometry. In the former Soviet Union...

solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic geometry...

geometry, the representation of a line rarely conforms to the notion of the "straight curve" as it is visualised in Euclidean geometry. In elliptic geometry...

spatial dimensions and 1 time dimension. In non-Euclidean geometry (elliptic or hyperbolic geometry) the three Euclidean properties mentioned above are not...

not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite...

the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed...

one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also...

section). The intersection of an elliptic cone with a concentric sphere is a spherical conic. In projective geometry, a cylinder is simply a cone whose...

properties of elliptic, Euclidean and hyperbolic geometries contrast as follows: Given a line l and a point P not on the line, Elliptic there exists no...

absolute geometry, while negating it yields hyperbolic geometry. Other consistent axiom sets can yield other geometries, such as projective, elliptic, spherical...

resulting geometries were later developed by Lobachevsky, Riemann and Poincaré into hyperbolic geometry (the acute case) and elliptic geometry (the obtuse...

since antiquity was a non-Euclidean geometry, an elliptic geometry. The development of intrinsic differential geometry in the language of Gauss was spurred...

differential geometry Metric tensor Riemannian manifold Pseudo-Riemannian manifold Levi-Civita connection Non-Euclidean geometry Elliptic geometry Spherical...

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...

algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only introductory algebra and geometry. In this...

arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...

However, the Pythagorean theorem remains true in hyperbolic geometry and elliptic geometry if the condition that the triangle be right is replaced with...

a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry. In the latter case, hyperbolic motions provide...

In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point....

fundamental to various fields of research such as differential geometry and optimal transport. Elliptic differential equations appear in many different contexts...

initiated the study of elliptic geometry when he wrote "On the definition of distance".: 82  This venture into abstraction in geometry was followed by Felix...

developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180° and...

unifying idea in geometry since the method is used to provide metrics in hyperbolic geometry, elliptic geometry, and Euclidean geometry. The field of non-Euclidean...

sphere. Spherical geometry is a form of elliptic geometry, which together with hyperbolic geometry makes up non-Euclidean geometry. The sphere is a smooth...

point in elliptic and hyperbolic geometries are not different from Euclidean ones.[clarification needed] Affine geometry and projective geometry have not...