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Type of curve in hyperbolic geometry
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight
Hypercycle_(geometry)
Topics referred to by the same term
Hypercycle may refer to: Hypercycle (chemistry), a kind of reaction network prominent in a theory of the self-organization of matter Hypercycle (geometry)
Hypercycle
Type of non-Euclidean geometry
Euclidean geometry, each hyperbolic triangle has an incircle. In hyperbolic space, if all three of its vertices lie on a horocycle or hypercycle, then the
Hyperbolic_geometry
Curve whose normals converge asymptotically
geometry have some properties similar to those of circles in Euclidean geometry: No three points of a horocycle are on a line, circle or hypercycle.
Horocycle
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
Distance from one geometric object to another along a line perpendicular to both
fitting and for defining offset surfaces. Distance between sets Hypercycle (geometry) Moment of inertia Signed distance Ballantine, J. P.; Jerbert, A
Perpendicular_distance
Study of geometries as axiomatic systems
in hyperbolic geometry (they form a hypercycle.) Advocates of the position that Euclidean geometry is the one and only "true" geometry received a setback
Foundations_of_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
Order-4-4 pentagonal honeycomb
Order-4-4_pentagonal_honeycomb
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
Order-4-3 pentagonal honeycomb
Order-4-3_pentagonal_honeycomb
Equation for radii of tangent circles
also holds for mutually tangent configurations in hyperbolic geometry including hypercycles and horocycles, if k j {\displaystyle k_{j}} is the geodesic
Descartes'_theorem
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
Order-3-5 heptagonal honeycomb
Order-3-5_heptagonal_honeycomb
1959 woodcut by M. C. Escher
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
Circle_Limit_III
Concept in 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
Equidistant
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
Order-6-3_square_honeycomb
Model of 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
Beltrami–Klein_model
Model of hyperbolic 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
Poincaré_disk_model
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
Order-7-3 triangular honeycomb
Order-7-3_triangular_honeycomb
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
Order-8-3 triangular honeycomb
Order-8-3_triangular_honeycomb
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
Order-5-3_square_honeycomb
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
Order-3-6 heptagonal honeycomb
Order-3-6_heptagonal_honeycomb
Fundamental result in geometry
pairs of curves called hypercycles, and the foliation is non-singular. In Taxicab Geometry, a type of non-Euclidean geometry where distance is measured
Sum_of_angles_of_a_triangle
Hypersurface in hyperbolic space
the surface would be an (N − 1)-dimensional hypercycle. Roberto Bonola (1906), Non-Euclidean Geometry, translated by H.S. Carslaw, Dover, 1955; p. 63
Horosphere
Upper-half plane model of hyperbolic non-Euclidean geometry
projection of the sphere it projects generalized circles (geodesics, hypercycles, horocycles, and circles) in the hyperbolic plane to generalized circles
Poincaré_half-plane_model
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
Laguerre_transformations
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
Order-3-4 heptagonal honeycomb
Order-3-4_heptagonal_honeycomb
Triangle in hyperbolic geometry
horocycle or hypercycle. Hyperbolic triangles have some properties that are analogous to those of triangles in spherical or elliptic geometry: Two triangles
Hyperbolic_triangle
Uniform tiling of the hyperbolic plane
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
Alternated_octagonal_tiling
boundary. Lines parallel to the boundaries of the band within the band are hypercycles whose common axis is the line through the middle of the band. Mercator
Band_model
the Euclidean plane, with the vertices circumscribed by horocycles or hypercycles rather than circles. Regular apeirogons that are scaled to converge at
List_of_regular_polytopes
Characterizes spherical triangles with fixed base and area
also be proven for hyperbolic triangles, for which the apex lies on a hypercycle. Given a fixed base A B , {\displaystyle AB,} an arc of a great circle
Lexell's_theorem
Category of coordinate systems
(see Lambert quadrilateral). Also in hyperbolic geometry there are no equidistant lines (see hypercycles). This all has influences on the coordinate systems
Coordinate systems for the hyperbolic plane
Coordinate_systems_for_the_hyperbolic_plane
honeycomb. The order-4 hexagonal tiling honeycomb contains , which tile 2-hypercycle surfaces and are similar to the truncated infinite-order triangular tiling
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
pairs of ultraparallel mirrors: . This honeycomb contains that tile 2-hypercycle surfaces, which are similar to the paracompact order-3 apeirogonal tiling
Square_tiling_honeycomb
Isometric automorphisms of a hyperbolic space
perpendicular to the given line; points off the given line move along hypercycles; three degrees of freedom. Orientation reversing reflection through a
Hyperbolic_motion
and with all vertices on the ideal surface. It contains and that tile 2-hypercycle surfaces, which are similar to these paracompact order-4 apeirogonal tilings
Order-4 square tiling honeycomb
Order-4_square_tiling_honeycomb
domain, [((3,∞,3)),((3,∞,3))]: . This honeycomb contains and that tile 2-hypercycle surfaces, which are similar to the paracompact infinite-order triangular
Order-4_octahedral_honeycomb
and with all vertices on the ideal surface. It contains and that tile 2-hypercycle surfaces, which are similar to the paracompact tilings and (the truncated
Order-6 hexagonal tiling honeycomb
Order-6_hexagonal_tiling_honeycomb
Polyhedron with regular congruent polygons as faces
honeycomb {7,3,3}; they are inscribed in an equidistant surface (a 2-hypercycle), which has two ideal points. Another group of regular polyhedra comprise
Regular_polyhedron
All Latin and Greek roots beginning with G
epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid, isocyclic, mesocyclone, monocyclic, polycyclic, pseudocyclosis
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
HYPERCYCLE GEOMETRY
HYPERCYCLE GEOMETRY
HYPERCYCLE GEOMETRY
Surname or Lastname
English
English : habitational name from Shrewsbury in Shropshire, which is named from an ancient district name derived from Old English scrobb ‘scrub’, ‘brushwood’, + Old English byrig, dative case of burh ‘fortified place’.
Girl/Female
Tamil
Neelkamala | நீலகமாலா
Blue lotus
Female
English
French form of Latin Susanna, SUZANNE means "lily."
Boy/Male
Muslim/Islamic
Supervising guardian, protector
Girl/Female
Hebrew
She is my delight.
Girl/Female
Tamil
Silk cotton tree
Boy/Male
Hindu
Fabric markar, Cloth merchant
Girl/Female
American, Australian, British, Christian, English, French, Gaelic, German, Scottish
Small Meadow; The Gray Castle; Holly Garden; Dwells at the Gray Fortress; Garden of Hollies; Garden in the Paradise
Girl/Female
Tamil
The best, Knowledge of truth
Surname or Lastname
English
English : patronymic from Mander 1.Dutch : variant of Mandel.
HYPERCYCLE GEOMETRY
HYPERCYCLE GEOMETRY
HYPERCYCLE GEOMETRY
HYPERCYCLE GEOMETRY
HYPERCYCLE GEOMETRY
v. i.
To investigate or apprehend geometrical quantities or laws; to make geometrical constructions; to proceed in accordance with the principles of geometry.
a.
Well versed in any branch of learning; qualified by study; learned; as, a man well studied in geometry.
n.
the science or art of conducting ships or vessels from one place to another, including, more especially, the method of determining a ship's position, course, distance passed over, etc., on the surface of the globe, by the principles of geometry and astronomy.
n.
A treatise on this science.
n.
Related to Euclid, or to the geometry of Euclid.
n.
That branch of applied geometry which gives rules for finding the length of lines, the areas of surfaces, or the volumes of solids, from certain simple data of lines and angles.
n.
The act of superposing, or the state of being superposed; as, the superposition of rocks; the superposition of one plane figure on another, in geometry.
n.
That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.
n.
One skilled in geometry; a geometer; a mathematician.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
a.
Having familiar knowledge united with readiness and dexterity in its application; familiarly acquainted with; expert; skillful; -- often followed by in; as, a person skilled in drawing or geometry.
n.
The art of delineating the forms of solid bodies on a plane; a branch of solid geometry which shows the construction of all solids which are regularly defined.
pl.
of Geometry
n.
The doctrine of the sphere; the science of the properties and relations of the circles, figures, and other magnitudes of a sphere, produced by planes intersecting it; spherical geometry and trigonometry.
v. t.
To determine the form, extent, position, etc., of, as a tract of land, a coast, harbor, or the like, by means of linear and angular measurments, and the application of the principles of geometry and trigonometry; as, to survey land or a coast.
n.
Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
n.
That branch of geometry which treats of the cone and the curves which arise from its sections.
n.
That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.
n.
A Greek geometer of the 3d century b. c.; also, his treatise on geometry, and hence, the principles of geometry, in general.
n.
The four "liberal arts," arithmetic, music, geometry, and astronomy; -- so called by the schoolmen. See Trivium.