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Topics referred to by the same term
Hyperbolic structure may refer to: Hyperboloid structure Hyperbolic set This disambiguation page lists mathematics articles associated with the same title
Hyperbolic_structure
Type of unbounded quadratic surface-shaped building or work
purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features. A hyperbolic structure is beneficial
Hyperboloid_structure
Manifold of dimension 3 equipped with a hyperbolic metric
topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric
Hyperbolic_3-manifold
Parametrizes complex structures on a surface
{\displaystyle S} to itself. It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it with a natural topology for which
Teichmüller_space
American mathematician (1946–2012)
union of two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched up correctly and gave the hyperbolic structure on the figure-eight knot
William_Thurston
Space where every point locally resembles a hyperbolic space
In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in
Hyperbolic_manifold
systems theory, a subset Λ of a smooth manifold M is said to have a hyperbolic structure with respect to a smooth map f if its tangent bundle may be split
Hyperbolic_set
Type of non-Euclidean geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Normalized hyperbolic volume of the complement of a hyperbolic knot
link complement has a hyperbolic structure, this structure is uniquely determined, and any geometric invariants of the structure are also topological invariants
Hyperbolic_volume
Study of mathematical knots
particular that of hyperbolic geometry. The hyperbolic structure depends only on the knot so any quantity computed from the hyperbolic structure is then a knot
Knot_theory
Mathematical space
additional structure given by a particular Thurston model geometry (of which there are eight). The most prevalent geometry is hyperbolic geometry. Using
3-manifold
Mathematical software
description of the hyperbolic structure on a link complement, SnapPea can then perform hyperbolic Dehn filling on the cusps to obtain more hyperbolic 3-manifolds
SnapPea
Mathematics award
Contributed idea that a very large class of closed 3-manifolds carry a hyperbolic structure." Shing-Tung Yau Institute for Advanced Study, US Tsinghua University
Fields_Medal
24 mathematical problems stated in 1982
influential 1982 paper Three-dimensional manifolds, Kleinian groups and hyperbolic geometry published in the Bulletin of the American Mathematical Society
Thurston's_24_questions
Theorem in geometry
complete hyperbolic structure of finite volume. The Mostow rigidity theorem implies that if a manifold of dimension at least 3 has a hyperbolic structure of
Hyperbolization_theorem
Spacetime manifold
global hyperbolicity is a certain condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold). It is called hyperbolic in analogy
Globally_hyperbolic_spacetime
Theorem in geometric topology
manifold has a thick-thin decomposition, whose thick piece has a hyperbolic structure, and whose thin piece is a graph manifold. Due to Perelman's and
Poincaré_conjecture
Characterizes homeomorphisms of a compact orientable surface
a hyperbolic structure on the mapping torus of a pseudo-Anosov homeomorphism is a deep and difficult theorem (also due to Thurston). The hyperbolic 3-manifolds
Nielsen–Thurston classification
Nielsen–Thurston_classification
Mathematical concept
precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group
Hyperbolic_group
Geometric mean and hyperbolic angle as coordinates in quadrant I
analytic function. Since HP carries the metric space structure of the Poincaré half-plane model of hyperbolic geometry, the bijective correspondence Q ↔ H P
Hyperbolic_coordinates
Iranian mathematician (1977–2017)
professor of mathematics at Stanford University. Her research focused on hyperbolic geometry, dynamical systems, complex analysis, and topology. In 2014,
Maryam_Mirzakhani
Shukhov (1853–1939). Shukhov built his first example as a water tower (hyperbolic shell) for the 1896 All-Russian Exposition. Subsequently, more have been
List of hyperboloid structures
List_of_hyperboloid_structures
not enough to determine the manifold: one also needs to know the hyperbolic structure on the surfaces at the "ends" of the manifold, and also the ending
Ending_lamination_theorem
least two has a hyperbolic structure. Mostow's rigidity theorem does not apply in this case. In fact, there are many hyperbolic structures on any such manifold;
Topological_rigidity
One-dimensional complex manifold
Picard theorem: maps from hyperbolic to parabolic to elliptic are easy, but maps from elliptic to parabolic or parabolic to hyperbolic are very constrained
Riemann_surface
Quadric surface with one axis of symmetry and no center of symmetry
example of a hyperbolic paraboloid structure Surface illustrating a hyperbolic paraboloid Restaurante Los Manantiales, Xochimilco, Mexico Hyperbolic paraboloid
Paraboloid
In mathematics, the complex hyperbolic space is a Hermitian manifold which is the equivalent of the real hyperbolic space in the context of complex manifolds
Complex_hyperbolic_space
Diffeomorphism that has a hyperbolic structure on the tangent bundle
definitions must be distinguished: If a differentiable map f on M has a hyperbolic structure on the tangent bundle, then it is called an Anosov map. Examples
Anosov_diffeomorphism
American mathematician
under the supervision of William Paul Thurston, with the thesis Hyperbolic Structures on 3-Manifolds with Compressible Boundaries. He received a Sloan
Richard_Canary
Fixed point that does not have any center manifolds
systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds. Near a hyperbolic point the
Hyperbolic_equilibrium_point
Mathematical tree in the hyperbolic plane
A hyperbolic tree (often shortened as hypertree) is an information visualization and graph drawing method inspired by hyperbolic geometry. Displaying hierarchical
Hyperbolic_tree
Three linked but pairwise separated rings
Robert (1979), "An elliptical path from parabolic representations to hyperbolic structures", in Fenn, Roger (ed.), Topology of Low-Dimensional Manifolds: Proceedings
Borromean_rings
Distinguished surfaces of dynamic trajectories
coherent structures they form should also be objective. A sample application is shown in Fig. 9, where the sudden appearance of a hyperbolic core (strongest
Lagrangian_coherent_structure
Theorem in hyperbolic geometry
(complete) hyperbolic structures on a finite volume hyperbolic n {\displaystyle n} -manifold (for n > 2 {\displaystyle n>2} ) is a point, for a hyperbolic surface
Mostow_rigidity_theorem
Conjecture in knot theory relating quantum invariants and hyperbolic geometry
conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry of their complements. Let O denote the unknot. For any knot K
Volume_conjecture
Covering by shapes without overlaps or gaps
made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for
Tessellation
Spiral asymptotic to a line
A hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmic spirals
Hyperbolic_spiral
Local and global geometry of the universe
than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H3. Curved geometries are in the domain of non-Euclidean geometry
Shape_of_the_universe
Function of a knot that takes the same value for equivalent knots
Mostow–Prasad rigidity, the hyperbolic structure on the complement of a hyperbolic link is unique, which means the hyperbolic volume is an invariant for
Knot_invariant
2D surface which extends indefinitely
conceive of a hyperbolic plane, which obeys hyperbolic geometry and has a negative curvature. Abstractly, one may forget all structure except the topology
Plane_(mathematics)
Structure whose members are only in tension
curved from is the saddle shape, which can be a hyperbolic paraboloid (not all saddle shapes are hyperbolic paraboloids). This is a double ruled surface
Tensile_structure
Theory of text organization
Rhetorical structure theory (RST) is a theory of text organization that describes relations that hold between parts of text. It was originally developed
Rhetorical_structure_theory
Technique of creating lace or fabric from thread using a hook
creations apply hyperbolic (curved) geometric shapes—distinguished from Euclidean (flat) geometry—to emulate natural structures. Extending hyperbolic crochet
Crochet
Classification of a two-dimensional repetitive pattern
(spherical) structure; if it is zero then it has a parabolic structure, i.e. a wallpaper group; and if it is negative it will have a hyperbolic structure. When
Wallpaper_group
torus T {\displaystyle \mathbb {T} } with a complete, finite-volume hyperbolic structure is given by ∑ γ 1 1 + e ℓ ( γ ) = 1 2 {\displaystyle \sum _{\gamma
McShane's_identity
Pseudometric of complex manifolds
manifold. It was introduced by Shoshichi Kobayashi in 1967. Kobayashi hyperbolic manifolds are an important class of complex manifolds, defined by the
Kobayashi_metric
Fractal named after mathematician Benoit Mandelbrot
known as density of hyperbolicity, is one of the most important open problems in complex dynamics. Hypothetical non-hyperbolic components of the Mandelbrot
Mandelbrot_set
Generalized manifold
covering space has a hyperbolic, Euclidean, or spherical structure. The compact 2-dimensional connected orbifolds that are not hyperbolic are listed in the
Orbifold
Three dimensional analogue of uniformization conjecture
different hyperbolic metrics.) More precisely, if M is a manifold with a finite volume geometric structure, then the type of geometric structure is almost
Geometrization_conjecture
Three-holed sphere
proof of the fact that it is finitely presented. The interesting hyperbolic structures on a pair of pants are easily classified. For all ℓ 1 , ℓ 2 , ℓ
Pair_of_pants_(mathematics)
Two geometries based on axioms closely related to those specifying Euclidean geometry
forms associated with metric geometry. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries
Non-Euclidean_geometry
Glue the face 0, 2, 3 to the face 3, 2, 1 in that order. In the hyperbolic structure of the Gieseking manifold, this ideal tetrahedron is the canonical
Gieseking_manifold
American mathematician
discover the hyperbolic structure on the complement of the figure-eight knot and some others. This was one of the few examples of hyperbolic 3-manifolds
Robert_Riley_(mathematician)
Type of roof structure
roof. Gallery of hyperbolic paraboloid structures A hyperbolic paraboloid saddle roof: Church Army Chapel, Blackheath A hyperbolic paraboloid saddle
Saddle_roof
Subfield of mathematical topology
normal surface theory. The Manning algorithm is an algorithm to find hyperbolic structures on 3-manifolds whose fundamental group have a solution to the word
Computational_topology
hyperbolic plane, with an algebraic structure as a field. It was introduced by German mathematician David Hilbert. In a hyperbolic plane, one can define an ideal
Hilbert's_arithmetic_of_ends
Mutation of quaternions where unit vectors square to +1
In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form q = a + b i + c
Hyperbolic_quaternion
A hyperbolic geometric graph (HGG) or hyperbolic geometric network (HGN) is a special type of spatial network where (1) latent coordinates of nodes are
Hyperbolic_geometric_graph
Causal relationships between points in a manifold
whose Cauchy development is M {\displaystyle M} . A metric is globally hyperbolic if it can be foliated by Cauchy surfaces. The chronology violating set
Causal_structure
Tiling of the hyperbolic plane
Böröczky tiling) is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane model of the hyperbolic plane. The tiles are congruent
Binary_tiling
Geometrical structure
hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space. A typical sphere packing problem is to find an arrangement in which
Sphere_packing
American mathematician (born 1956)
University of Wisconsin–Madison in 1983. His dissertation was titled "Hyperbolic Structures on Link Complements" and was supervised by James Cannon. Among his
Colin_Adams_(mathematician)
Standard hostname for a networked device's loopback interface
model Watts–Strogatz Exponential random (ERGM) Random geometric (RGG) Hyperbolic (HGN) Hierarchical Stochastic block Blockmodeling Maximum entropy Soft
Localhost
Personality disorder involving excessive emotionality and attention-seeking
wants. Histrionic personality disorder is also linked with hyperbolic language and hyperbolic communication. People diagnosed with HPD may be dramatic.
Histrionic personality disorder
Histrionic_personality_disorder
Shape in hyperbolic geometry
along lines of the hyperbolic space. The Platonic solids and Archimedean solids have ideal versions, with the same combinatorial structure as their more familiar
Ideal_polyhedron
Shape with three sides
discovered in several spaces, as in hyperbolic space and spherical geometry. A triangle in hyperbolic space is called a hyperbolic triangle, and it can be obtained
Triangle
Social structure made up of a set of social actors
A social network is a social structure consisting of a set of social actors (such as individuals or organizations), networks of dyadic ties, and other
Social_network
Mathematical space with two coordinates
Two-dimensional spaces can also be curved, for example the sphere and hyperbolic plane, sufficiently small portions of which appear like the flat plane
Two-dimensional_space
Smith conjecture knot theory Based on work of William Thurston on hyperbolic structures on 3-manifolds, with results by William Meeks and Shing-Tung Yau
List_of_conjectures
On tangency patterns of circles
as a hyperbolic manifold. By Mostow rigidity, the hyperbolic structure of this domain is uniquely determined, up to isometry of the hyperbolic space;
Circle_packing_theorem
American mathematician
of hyperbolic structures. I. Ann. of Math. (2) 120 (1984), no. 3, 401–476. Morgan, John W.; Shalen, Peter B. Degenerations of hyperbolic structures. II
Peter_Shalen
Theorem in topology
3-manifold theory, In particular the work of William Thurston on hyperbolic structures on 3-manifolds, and results by William Meeks and Shing-Tung Yau
Smith_conjecture
itself is not a hyperbolic group, the fact that C ( S ) {\displaystyle C(S)} is hyperbolic still has implications for its structure and geometry. There
Curve_complex
American mathematician
combinatorial structure of cocompact discrete hyperbolic groups" was one of the forerunners in the development of the theory of word-hyperbolic groups, a
James_W._Cannon
Centre, Sesto San Giovanni, 1980 "Symbols and Structure", Galleria Spazia, Bologna, 1981 "Hyperbolic Structures", Galleria Lorenzelli, Milan, 1981 "Experimental
Franco_Grignani
are called regulatory enzymes. Generally, it is considered that a hyperbolic structured protein in specific media conditions is ready to do its task, it
Regulatory_enzyme
Network whose degree distribution follows a power law
x_{i}x_{j}}{1+\delta x_{i}x_{j}}}.} Assuming that a network has an underlying hyperbolic geometry, one can use the framework of spatial networks to generate scale-free
Scale-free_network
Approximate nearest neighbor search algorithm
The algorithm repeatedly chooses locally better nodes, using the graph structure to approach the query point. The HNSW graph is built incrementally. When
Hierarchical navigable small world
Hierarchical_navigable_small_world
Awarded every year by the American Mathematical Society
Publishing Company. ISBN 9780720407570. Thurston, William P. (1986). "Hyperbolic structures on 3-manifolds I: Deformation of acylindrical manifolds". Annals
Leroy_P._Steele_Prize
Tiling of euclidean or hyperbolic space of three or more dimensions
space. They may also be constructed in non-Euclidean spaces, such as hyperbolic honeycombs. Any finite uniform polytope can be projected to its circumsphere
Honeycomb_(geometry)
Church in Norton Shores, Michigan
surrounding Muskegon area. The parish's current building, noted for its hyperbolic paraboloid form and brutalist design, was designed by modernist architect
St. Francis de Sales Church (Norton Shores, Michigan)
St._Francis_de_Sales_Church_(Norton_Shores,_Michigan)
Dutch graphic artist (1898–1972)
reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical
M._C._Escher
Knowledge base that represents semantic relations between concepts in a network
who in 1960 had published descriptions of algorithms for using a phrase structure grammar to generate syntactically well-formed nonsense sentences. Sheldon
Semantic_network
Diagram to visually organize information
tree-like structure. Concept maps: Mind maps differ from concept maps in that mind maps are based on a radial hierarchy (tree structure) denoting relationships
Mind_map
Building in Markham Moor junction services
by Scorer which included hyperbolic structures. These structures (sometimes known as 'hypars') were experimental structures with the intention of making
Markham_Moor_Scorer_Building
Analysis of social structures using network and graph theory
process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes (individual
Social_network_analysis
Smallest closed orientable hyperbolic 3-manifold
manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead
Weeks_manifold
Arrangement of a communication network
fieldbusses and computer networks. Network topology is the topological structure of a network and may be depicted physically or logically. It is an application
Network_topology
Mathematical space used to study hyperbolic geometry
space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry
Gyrovector_space
Group of real 2×2 matrices with unit determinant
a circle bundle, and has a natural contact structure induced by the symplectic structure on the hyperbolic plane. SL(2, R) is a 2-fold cover of PSL(2
SL2(R)
Plane curve: conic section
ellipses and hyperbolas. Hyperbolic growth Hyperbolic partial differential equation Hyperbolic sector Hyperboloid structure Hyperbolic trajectory Hyperboloid
Hyperbola
Concept in graph theory
PMID 33191975. Bruno, Matteo (21 Jun 2019). "Community Detection in the Hyperbolic Space". arXiv:1906.09082 [physics.soc-ph]. Condon, A.; Karp, R. M. (2001)
Community_structure
Clustering and community detection algorithm
and Newman, M. E. J. and Moore, Cristopher (2004). "Finding community structure in very large networks". Phys. Rev. E. 70 (6) 066111. arXiv:cond-mat/0408187
Leiden_algorithm
Multi-scale chaotic motions
distributions advected by an unsteady flow. LCSs can be classified as hyperbolic (locally maximally attracting or repelling material surfaces), elliptic
Coherent_turbulent_structure
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, exponentials, and
CORDIC
same structure can be mutated between different symmetry classes, including across curvature domains from spherical, to Euclidean to hyperbolic. This
Uniform tiling symmetry mutations
Uniform_tiling_symmetry_mutations
Reals with an extra square root of +1 adjoined
algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1 {\displaystyle
Split-complex_number
Branch of topology
admitting a constant positively curved metric), parabolic (flat), and hyperbolic (negatively curved) according to their universal cover. The uniformization
Low-dimensional_topology
Constantin Weber) is a closed hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral space and hyperbolic dodecahedral space. It is one
Seifert–Weber_space
Electronic communication subsystem on an integrated circuit
model Watts–Strogatz Exponential random (ERGM) Random geometric (RGG) Hyperbolic (HGN) Hierarchical Stochastic block Blockmodeling Maximum entropy Soft
Network_on_a_chip
HYPERBOLIC STRUCTURE
HYPERBOLIC STRUCTURE
Girl/Female
Hindu, Indian, Telugu
The Structure of God
Girl/Female
Tamil
Shape, Structure
Girl/Female
Indian, Kashmiri
Body Structure
Boy/Male
Indian
Solid structure
Girl/Female
Indian
Shape, Structure
Boy/Male
Indian
Good Structure
Girl/Female
Tamil
Shape, Structure
Girl/Female
Indian
Shape, Structure
Boy/Male
Afghan, Arabic, Gujarati, Indian, Muslim
Solid Structure; Lifetime
Girl/Female
Indian
Structure
Boy/Male
Muslim
Solid structure
HYPERBOLIC STRUCTURE
HYPERBOLIC STRUCTURE
Girl/Female
Hindu
Strong
Surname or Lastname
English
English : variant of Balham, a habitational name from a place in Surrey (now part of south London), named with Old English bealg ‘smooth’ or ‘round’ + hamm ‘water meadow’, ‘land hemmed in by water’.
Girl/Female
Hindu, Indian
Victorious; Carrying
Boy/Male
Hindu
Meek, Friend of Krishna, Another name of Kuchela
Boy/Male
Hindu, Indian, Punjabi, Sikh, Traditional
Exalted Way of Life
Boy/Male
Muslim
Early Imam (Leader) of Islam; grandson of Prophet Muhammad.
Girl/Female
Latin
Grace.
Girl/Female
American, Australian, British, English
White Waves; Combination of Jenna and Lee; Modern Variant of Jenny and Jennifer
Female
English
Anglicized form of Hebrew Abiyshag, ABISHAG means "my father is a wanderer" or "father of error." In the bible, this is the name of a young girl who cared for David in his old age.Â
Girl/Female
Hindu, Indian, Traditional
Fame
HYPERBOLIC STRUCTURE
HYPERBOLIC STRUCTURE
HYPERBOLIC STRUCTURE
HYPERBOLIC STRUCTURE
HYPERBOLIC STRUCTURE
a.
Having the form, or nearly the form, of an hyperbola.
a.
Alt. of Hyperbolical
n.
A figure of speech in which the expression is an evident exaggeration of the meaning intended to be conveyed, or by which things are represented as much greater or less, better or worse, than they really are; a statement exaggerated fancifully, through excitement, or for effect.
adv.
In the form of an hyperbola.
imp. & p. p.
of Hyperbolize
n.
A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
a.
Of or pertaining to an hyperbaton; transposed; inverted.
n.
Diminution; a species of hyperbole, representing a thing as being less than it really is.
v. t.
To state or represent hyperbolically.
a.
Belonging to the hyperbola; having the nature of the hyperbola.
n.
A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.
n.
One who uses hyperboles.
v. i.
To speak or write with exaggeration.
n.
The act of exaggerating; the act of doing or representing in an excessive manner; a going beyond the bounds of truth reason, or justice; a hyperbolical representation; hyperbole; overstatement.
n.
The use of hyperbole.
a.
Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression.
a.
Having some property that belongs to an hyperboloid or hyperbola.
a.
Exaggerated; excessive; hyperbolical.
n.
A figure by which a grave and magnificent word is put for the proper word; amplification; hyperbole.
p. pr. & vb. n.
of Hyperbolize