 | In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight... 11 KB (1,531 words) - 06:36, 16 November 2023 |
 | Euclidean geometry, each hyperbolic triangle has an incircle. In hyperbolic geometry, if all three of its vertices lie on a horocycle or hypercycle, then... 56 KB (6,945 words) - 18:48, 26 January 2024 |
Hypercycle may refer to: Hypercycle (chemistry), a kind of reaction network prominent in a theory of the self-organization of matter Hypercycle (geometry)... 293 bytes (71 words) - 05:58, 7 February 2022 |
 | Horocycle (category Hyperbolic geometry) the possible closures for its orbits. Horosphere Hypercycle (geometry) Sossinsky, A.B. (2012). Geometries. Providence, R.I.: American Mathematical Society... 10 KB (1,291 words) - 06:28, 8 November 2023 |
 | Descartes' theorem (category Euclidean plane geometry) also holds for mutually tangent configurations in hyperbolic geometry including hypercycles and horocycles, if k j {\displaystyle k_{j}} is taken to be... 50 KB (6,350 words) - 00:25, 24 April 2024 |
in hyperbolic geometry (they form a hypercycle.) Advocates of the position that Euclidean geometry is the one and only "true" geometry received a setback... 76 KB (10,902 words) - 01:42, 12 May 2024 |
surface. It can be used for surface fitting and for defining offset surfaces. Distance between sets Hypercycle (geometry) Moment of inertia Signed distance... 2 KB (295 words) - 06:39, 16 November 2023 |
 | (x,y\cosh(r))} and radius y sinh ( r ) {\displaystyle y\sinh(r)} A hypercycle (a curve equidistant from a straight line, its axis) is modeled by either:... 21 KB (3,560 words) - 20:56, 18 May 2023 |
Order-7-3 triangular honeycomb (category Honeycombs (geometry)) infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 25 KB (1,299 words) - 00:14, 28 January 2024 |
 | Horosphere (category Hyperbolic geometry) the surface would be an (N − 1)-dimensional hypercycle. Roberto Bonola (1906), Non-Euclidean Geometry, translated by H.S. Carslaw, Dover, 1955; p. 63... 3 KB (381 words) - 17:01, 28 June 2022 |
Order-5-3 square honeycomb (category Honeycombs (geometry)) infinite cell consists of a pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 12 KB (704 words) - 00:14, 28 January 2024 |
Order-4-3 pentagonal honeycomb (category Honeycombs (geometry)) infinite cell is an order-4 pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 10 KB (619 words) - 00:08, 28 January 2024 |
 | Equidistant (category Elementary geometry) all points. In hyperbolic geometry the set of points that are equidistant from and on one side of a given line form a hypercycle (which is a curve not a... 4 KB (445 words) - 16:03, 12 February 2024 |
 | Poincaré disk model (category Multi-dimensional geometry) In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside... 26 KB (3,970 words) - 23:55, 1 March 2024 |
Order-8-3 triangular honeycomb (category Honeycombs (geometry)) infinite cell consists of an octagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 25 KB (1,293 words) - 00:14, 28 January 2024 |
Order-4-4 pentagonal honeycomb (category Honeycombs (geometry)) infinite cell consists of a pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 7 KB (416 words) - 00:08, 28 January 2024 |
Order-3-6 heptagonal honeycomb (category Honeycombs (geometry)) infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 8 KB (457 words) - 00:08, 28 January 2024 |
Order-6-3 square honeycomb (category Honeycombs (geometry)) infinite cell consists of a hexagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 9 KB (546 words) - 00:14, 28 January 2024 |
 | Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate... 14 KB (1,901 words) - 14:53, 28 September 2022 |
 | Hyperbolic triangle (category Hyperbolic geometry) horocycle or hypercycle. Hyperbolic triangles have some properties that are analogous to those of triangles in spherical or elliptic geometry: Two triangles... 13 KB (1,759 words) - 18:14, 1 April 2024 |
Heptagonal tiling honeycomb (category Honeycombs (geometry)) infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 9 KB (469 words) - 00:04, 24 January 2024 |
Order-infinite-3 triangular honeycomb (category Honeycombs (geometry)) infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 31 KB (1,578 words) - 00:14, 28 January 2024 |
Order-3-5 heptagonal honeycomb (category Honeycombs (geometry)) infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 7 KB (412 words) - 00:07, 28 January 2024 |
Order-3-4 heptagonal honeycomb (category Honeycombs (geometry)) infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli... 8 KB (421 words) - 00:07, 28 January 2024 |
Circle Limit III (section Geometry) the squares and triangles are formed by arcs of hypercycles, which are not straight in hyperbolic geometry, but which connect smoothly to each other without... 10 KB (1,174 words) - 21:01, 2 September 2023 |
 | List of regular polytopes (category Multi-dimensional geometry) the Euclidean plane, with the vertices circumscribed by horocycles or hypercycles rather than circles. Regular apeirogons that are scaled to converge at... 97 KB (5,294 words) - 16:02, 26 March 2024 |
 | Beltrami–Klein model (category Hyperbolic geometry) not distorted. All other circles are distorted, as are horocycles and hypercycles Chords that meet on the boundary circle are limiting parallel lines.... 21 KB (2,709 words) - 22:18, 14 January 2024 |
Laguerre transformations (category Projective geometry) Möbius geometry, where lines and circles can be mapped to each other, but neither can be mapped to points. Both Möbius geometry and Laguerre geometry are... 22 KB (3,424 words) - 23:07, 25 July 2023 |
epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid, isocyclic, mesocyclone, monocyclic, polycyclic, pseudocyclosis... 1 KB (1,495 words) - 06:14, 16 April 2024 |
 | Alternated octagonal tiling (section Geometry) angle at each vertex, while in Escher's woodcut they appear to be smooth hypercycles. Circle Limit III Square tiling Uniform tilings in hyperbolic plane List... 3 KB (309 words) - 21:56, 12 December 2023 |