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...
18 KB (2,642 words) - 01:10, 21 August 2024
the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed...
44 KB (6,023 words) - 21:22, 27 August 2024
geometry hold in hyperbolic geometry as well as in Euclidean geometry. Absolute geometry is inconsistent with elliptic geometry: in elliptic geometry...
76 KB (10,902 words) - 02:44, 15 June 2024
solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic geometry...
13 KB (910 words) - 14:17, 27 June 2024
elliptic geometries, that have no parallel lines. Absolute geometry is an extension of ordered geometry, and thus, all theorems in ordered geometry hold...
9 KB (1,111 words) - 14:19, 23 May 2024
now rarely used sequence elliptic geometry (spherical geometry), parabolic geometry (Euclidean geometry), and hyperbolic geometry. In the former Soviet Union...
56 KB (7,019 words) - 21:44, 8 August 2024
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...
30 KB (4,299 words) - 13:27, 2 July 2024
spatial dimensions and 1 time dimension. In non-Euclidean geometry (elliptic or hyperbolic geometry) the three Euclidean properties mentioned above are not...
23 KB (2,793 words) - 05:24, 28 August 2024
plane intersect in two antipodal points, unlike coplanar lines in Elliptic geometry. In the extrinsic 3-dimensional picture, a great circle is the intersection...
15 KB (1,955 words) - 02:05, 6 May 2024
the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed...
100 KB (9,886 words) - 03:41, 24 August 2024
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...
39 KB (5,094 words) - 22:52, 6 June 2024
not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite...
19 KB (2,162 words) - 00:01, 23 March 2024
Parallel postulate (category Elementary geometry)
resulting geometries were later developed by Lobachevsky, Riemann and Poincaré into hyperbolic geometry (the acute case) and elliptic geometry (the obtuse...
25 KB (3,227 words) - 00:17, 29 August 2024
Cylinder (redirect from Elliptic cylinder)
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...
21 KB (2,899 words) - 15:08, 18 July 2024
Cone (redirect from Elliptical cone)
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...
16 KB (2,283 words) - 08:00, 27 August 2024
absolute geometry, while negating it yields hyperbolic geometry. Other consistent axiom sets can yield other geometries, such as projective, elliptic, spherical...
14 KB (1,747 words) - 13:00, 25 July 2024
differential geometry Metric tensor Riemannian manifold Pseudo-Riemannian manifold Levi-Civita connection Non-Euclidean geometry Elliptic geometry Spherical...
8 KB (679 words) - 11:05, 12 February 2024
since antiquity was a non-Euclidean geometry, an elliptic geometry. The development of intrinsic differential geometry in the language of Gauss was spurred...
46 KB (5,912 words) - 08:09, 21 August 2024
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...
59 KB (7,080 words) - 06:43, 5 August 2024
Pythagorean theorem (category Euclidean plane geometry)
However, the Pythagorean theorem remains true in hyperbolic geometry and elliptic geometry if the condition that the triangle be right is replaced with...
93 KB (12,572 words) - 10:57, 28 August 2024
arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...
15 KB (1,464 words) - 19:56, 6 May 2024
Plane (mathematics) (category Geometry)
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...
7 KB (1,661 words) - 00:13, 16 August 2024
Rotation (mathematics) (redirect from Rotation (geometry))
point in elliptic and hyperbolic geometries are not different from Euclidean ones.[clarification needed] Affine geometry and projective geometry have not...
24 KB (3,129 words) - 11:23, 3 May 2024
Cayley–Klein metric (redirect from Cayley–Klein geometry)
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...
26 KB (3,691 words) - 20:52, 11 February 2024
Projective polyhedron (redirect from Elliptic tiling)
also referred to as elliptic tessellations or elliptic tilings, referring to the projective plane as (projective) elliptic geometry, by analogy with spherical...
16 KB (2,111 words) - 21:40, 1 November 2022
Clifford parallel (category Non-Euclidean geometry)
In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point....
5 KB (586 words) - 21:56, 24 May 2024
Space (category Geometry)
developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180° and...
35 KB (4,431 words) - 09:29, 30 July 2024
a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry. In the latter case, hyperbolic motions provide...
11 KB (1,517 words) - 23:24, 7 September 2023
Sphere (redirect from Sphere (geometry))
sphere. Spherical geometry is a form of elliptic geometry, which together with hyperbolic geometry makes up non-Euclidean geometry. The sphere is a smooth...
41 KB (5,328 words) - 16:32, 24 August 2024
algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only introductory algebra and geometry. In this...
54 KB (8,301 words) - 16:50, 17 August 2024