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Non-Euclidean geometry
added to distinguish it from complex hyperbolic spaces. Hyperbolic space serves as the prototype of a Gromov hyperbolic space, which is a far-reaching notion
Hyperbolic_space
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
Concept in mathematics
In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number
Hyperbolic_metric_space
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
symmetric spaces is a generalization of the well known duality between spherical and hyperbolic geometry. A symmetric space with a compatible complex structure
Simple_Lie_group
Isometric automorphisms of a hyperbolic space
In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous
Hyperbolic_motion
Parametrizes complex structures on a surface
S {\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
Teichmüller_space
Mathematical space with two coordinates
Lorentz surface appear locally like the complex plane or hyperbolic number plane, respectively. Mathematical spaces are often defined or represented using
Two-dimensional_space
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
Reals with an extra square root of +1 adjoined
In 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
Smooth manifold with an inner product on each tangent space
Euclidean space, the n {\displaystyle n} -sphere, hyperbolic space, and smooth surfaces in three-dimensional space, such as ellipsoids and paraboloids, are all
Riemannian_manifold
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
Relation of space and time in relativity theory
relativity of simultaneity. Keeping time and space axes hyperbolically orthogonal, as in Minkowski space, gives a constant result when measurements are
Hyperbolic_orthogonality
2D surface which extends indefinitely
the real projective plane. One may also conceive of a hyperbolic plane, which obeys hyperbolic geometry and has a negative curvature. Abstractly, one
Plane_(mathematics)
This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. There
List_of_regular_polytopes
Pseudometric of complex manifolds
introduced by Shoshichi Kobayashi in 1967. Kobayashi hyperbolic manifolds are an important class of complex manifolds, defined by the property that the Kobayashi
Kobayashi_metric
Three dimensional analogue of uniformization conjecture
(Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization
Geometrization_conjecture
One-dimensional complex manifold
otherwise called hyperbolic. This class of hyperbolic surfaces is further subdivided into subclasses according to whether function spaces other than the
Riemann_surface
Upper-half plane model of hyperbolic non-Euclidean geometry
the hyperbolic plane is associated with a complex number. The half-plane model can be thought of as a map projection from the curved hyperbolic plane
Poincaré_half-plane_model
Quadratic form for which there is a non-zero vector on which the form evaluates to zero
orthogonal when B(u, v) = 0. In the case of the hyperbolic plane, such u and v are hyperbolic-orthogonal. A space with quadratic form is split (or metabolic)
Isotropic_quadratic_form
Argument of the hyperbolic functions
In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane
Hyperbolic_angle
Complex numbers with non-negative imaginary part
half-plane becomes a metric space. The generic name of this metric space is the hyperbolic plane. In terms of the models of hyperbolic geometry, this model is
Upper_half-plane
Mutation of quaternions where unit vectors square to +1
the split-complex number plane. Furthermore, just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic quaternion
Hyperbolic_quaternion
Triangle in hyperbolic geometry
Euclidean case, three points of a hyperbolic space of an arbitrary dimension always lie on the same plane. Hence planar hyperbolic triangles also describe triangles
Hyperbolic_triangle
Topological space formed from distances
homology theory from simplicial complexes to metric spaces. After Eliyahu Rips applied the same complex to the study of hyperbolic groups, its use was popularized
Vietoris–Rips_complex
complete as a metric space, if and only if all geodesics can be infinitely extended. Complete metric space Completion Complex hyperbolic space Conformal map
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Isogonal polytope with regular facets
semi-check), There are also hyperbolic uniform honeycombs composed of only regular cells (Coxeter & Whitrow 1950), including: Hyperbolic uniform honeycombs, 3D
Semiregular_polytope
Mathematical space
unit complex numbers with multiplication). Group multiplication on the torus is then defined by coordinate-wise multiplication. Hyperbolic space is a
3-manifold
Group of unitary complex matrices with determinant of 1
\operatorname {SU} (2,1;\mathbb {Z} [i])} which acts (projectively) on complex hyperbolic space of dimension two, in the same way that SL ( 2 , 9 ; Z ) {\displaystyle
Special_unitary_group
functions Hyperbolic functions Logarithmic functions Inverse trigonometric functions Inverse hyperbolic functions Residue theory Isometries in the complex plane
List of complex analysis topics
List_of_complex_analysis_topics
Topics referred to by the same term
hyperbolic geometry using a Euclidean half-space Siegel upper half-space, a set of complex matrices with positive definite imaginary part Half-space (punctuation)
Half-space
real, complex, or hyperbolic projective space into a sphere, introduced by Ioan James. James, I. M. (1958). "Embeddings of real projective spaces". Mathematical
James_embedding
Rational function of the form (az + b)/(cz + d)
orientation-preserving isometries of hyperbolic 3-space and therefore plays an important role when studying hyperbolic 3-manifolds. In physics, the identity
Möbius_transformation
Two geometries based on axioms closely related to those specifying Euclidean geometry
portion of hyperbolic space and in a second paper in the same year, defined the Klein model, which models the entirety of hyperbolic space, and used this
Non-Euclidean_geometry
Belgian mathematician
hypergeometric differential equations in two- and three-dimensional complex hyperbolic spaces, etc. He was awarded the Fields Medal in 1978, the Crafoord Prize
Pierre_Deligne
Quaternion of norm 1 (unit quaternion)
of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend the concept to 4-space. Problems
Versor
Pictorial representation of symmetry
represents a hyperplane within a spherical, Euclidean, or hyperbolic space of given dimension. (In 2D spaces, a mirror is a line; in 3D, a mirror is a plane.)
Coxeter–Dynkin_diagram
to any geometry or space. This includes spherical trigonometry, hyperbolic trigonometry, gyrotrigonometry, and universal hyperbolic trigonometry. Geometric
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Type of vector space in math
Euclidean space: that a series that converges absolutely also converges in the ordinary sense. Hilbert spaces are often taken over the complex numbers.
Hilbert_space
Embedding of data within a manifold based on a similarity function
black-box nature of these models often makes the latent space unintuitive, while its high-dimensional, complex, and nonlinear characteristics further complicate
Latent_space
Type of Riemannian manifold with constant Jacobi operator spectrum
, hyperbolic spaces H n {\displaystyle \mathbb {H} ^{n}} , complex projective spaces C P n {\displaystyle \mathbb {CP} ^{n}} , complex hyperbolic spaces
Osserman_manifold
to prove. It was proved by Masur and Minsky that the complex of curves is a Gromov hyperbolic space. Later work by various authors gave alternate proofs
Curve_complex
Russian-American mathematician (1963–2026)
topology, Kleinian groups, hyperbolic geometry, geometric group theory, geometric representation theory in Lie groups, spaces of nonpositive curvature [de]
Michael_Kapovich
considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that
List_of_mathematical_shapes
Concept in geometry
the complex projective line, CP1, also called the Riemann sphere (when complex numbers are mapped to each point). In the case of a hyperbolic space, each
Point_at_infinity
Study of complex manifolds and several complex variables
concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions
Complex_geometry
Branch of topology
other words, it is the quotient of three-dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely and properly discontinuously
Low-dimensional_topology
Mathematical set with some added structure
Euclidean spaces are also Riemann spaces. Smooth surfaces in Euclidean spaces are Riemann spaces. A hyperbolic non-Euclidean space is also a Riemann space. A
Space_(mathematics)
Three-holed sphere
Clifford J.; Harvey, William J.; Recillas-Pishmish, Sevín (eds.). Complex Manifolds and Hyperbolic Geometry. Contemporary Mathematics. Vol. 311. Providence, RI:
Pair_of_pants_(mathematics)
acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric space. This notion
Acylindrically hyperbolic group
Acylindrically_hyperbolic_group
Relation between sides of a right triangle
{b}{2R}}-2\sin ^{2}{\frac {a}{2R}}\,\sin ^{2}{\frac {b}{2R}}.} In a hyperbolic space with uniform Gaussian curvature −1/R2, for a right triangle with legs
Pythagorean_theorem
French-American mathematician
ISBN 0-387-96508-4. MR 0890960. Lang, Serge (1987). Introduction to complex hyperbolic spaces. New York: Springer-Verlag. doi:10.1007/978-1-4757-1945-1. ISBN 0-387-96447-9
Serge_Lang
Space in mathematics and theoretical physics
space and it does not have the properties of the dot product of Euclidean vectors. If x and y are orthogonal and q(x)q(y) < 0, then x is hyperbolic-orthogonal
Pseudo-Euclidean_space
Critical point on a surface graph which is not a local extremum
then a point is hyperbolic if and only if the differential of ƒ n (where n is the period of the point) has no eigenvalue on the (complex) unit circle when
Saddle_point
Number with a real and an imaginary part
well as the hyperbolic functions sinh and cosh, also carry over to complex arguments without change. For the other trigonometric and hyperbolic functions
Complex_number
hyperbolic 3-manifold is, by definition, covered by the hyperbolic 3-space H3, hence aspherical. As is any n-manifold whose universal covering space is
Aspherical_space
simplicial complexes and CW complexes in the computation of the homology of topological spaces. Non-positively curved and CAT(0) cube complexes appear with
Cubical_complex
Framework of distances and directions
four-dimensional spacetime, called Minkowski space (see special relativity). The idea behind spacetime is that time is hyperbolic-orthogonal to each of the three spatial
Space
Introduction to Complex Hyperbolic Spaces. New York: Springer. ISBN 978-1-4419-3082-8. Zalcman, L. (1975). "Heuristic principle in complex function theory"
Bloch's_principle
Mathematical function relating circular and hyperbolic functions
In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called
Gudermannian_function
instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space H 3 {\displaystyle \mathbb {H} ^{3}} by an arithmetic
Arithmetic hyperbolic 3-manifold
Arithmetic_hyperbolic_3-manifold
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
Möbius transformation generalized to rings other than the complex numbers
finite points of the generalized circles in the complex plane. To construct models of the hyperbolic plane the unit disk and the upper half-plane are
Linear fractional transformation
Linear_fractional_transformation
Area of mathematics
American Mathematical Society. Lang, Serge (1987). Introduction to complex hyperbolic spaces. New York: Springer-Verlag. ISBN 978-0-387-96447-8. Zbl 0628.32001
Nevanlinna_theory
Branch of mathematics
between points in the Euclidean plane, while the hyperbolic metric measures the distance in the hyperbolic plane. Other important examples of metrics include
Geometry
Group of real 2×2 matrices with unit determinant
considered the boundary of the hyperbolic plane, PSL(2, R) expresses hyperbolic motions. Elements of PSL(2, R) act on the complex plane by Möbius transformations:
SL2(R)
Indian mathematician and monk of the Ramakrishna Order (born 1968)
He is best known for his work in hyperbolic geometry, geometric group theory, low-dimensional topology and complex geometry. Mahan Mitra studied at St
Mahan_Mj
Type of topological space
mathematics, and specifically in topology, a CW complex (also cellular complex or cell complex) is a topological space that is built by gluing together topological
CW_complex
Geometrical structure
non-Euclidean spaces such as hyperbolic space. A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible
Sphere_packing
Discrete group of Möbius transformations
orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable with PSL(2, C), is the quotient group of the 2 by 2 complex matrices of determinant
Kleinian_group
Mathematical space used to study hyperbolic geometry
gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in
Gyrovector_space
nodes are sprinkled according to a probability density function into a hyperbolic space of constant negative curvature and (2) an edge between two nodes is
Hyperbolic_geometric_graph
Mathematical space with a notion of distance
Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A
Metric_space
complex numbers is changed to the split-complex numbers, then a similar formalism can be developed for representing oriented lines on the hyperbolic plane
Laguerre_transformations
Overview of and topical guide to geometry
plane geometry Angle excess Hyperbolic geometry Pseudosphere Tractricoid Elliptic geometry Spherical geometry Minkowski space Thurston's conjecture Parametric
Outline_of_geometry
complex Hodge theory pseudodifferential operator Klein geometry, Erlangen programme symmetric space space form Maurer–Cartan form Examples hyperbolic
List of differential geometry topics
List_of_differential_geometry_topics
Model of the extended complex plane plus a point at infinity
simplest complex manifolds. In projective geometry, the sphere is an example of a complex projective space and can be thought of as the complex projective
Riemann_sphere
Geometric figure
pseudo-Euclidean space. There the asymptotes of the unit hyperbola form a light cone. Further, the attention to areas of hyperbolic sectors by Gregoire
Unit_hyperbola
Branch of mathematics
Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the
Differential_geometry
Class of algebraic theorems
Millson, John (1987), "Local rigidity of discrete groups acting on complex hyperbolic space", Inventiones Mathematicae, 88 (3): 495–520, Bibcode:1987InMat
Local_rigidity
Property of a mathematical space
Euclidean space is defined. While analysis usually assumes a manifold to be over the real numbers, it is sometimes useful in the study of complex manifolds
Dimension
Mathematical space
two geometries here real-hyperbolic 4-space H R 4 {\displaystyle \mathbf {H} _{\mathbb {R} }^{4}} and the complex hyperbolic plane H C 2 {\displaystyle
4-manifold
Metric space
which every simplex has a flat metric. (Other spaces of interest are spherical and hyperbolic polyhedral spaces, where every simplex has a metric of constant
Polyhedral_space
Mathematical description of spacetime used in relativity
spaces with positive curvature are just spheres in Euclidean space of one higher dimension. Hyperbolic spaces can be isometrically embedded in spaces
Minkowski_spacetime
Well studied projective geometries over finite fields
{\displaystyle PG(3,q)} a hyperbolic fibration is a partition of the space into q − 1 {\displaystyle q-1} pairwise disjoint hyperbolic quadrics and two lines
Spread_(projective_geometry)
between the boundaries of two hyperbolic metric spaces extending a discrete isometric actions of the group on those spaces. The notion originated from a
Cannon–Thurston_map
Type of geometry
eventually demonstrated to have models, such as the Klein model of hyperbolic space, relating to projective geometry. In 1855 A. F. Möbius wrote an article
Projective_geometry
Topological space of dimension zero
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several
Zero-dimensional_space
Linear map that preserves areas
split-complex number multiplications and the diagonal basis which corresponds to the pair of light lines. Formally, a squeeze preserves the hyperbolic metric
Squeeze_mapping
Length of a line segment
Psychophysics, 7 (2): 103–107, doi:10.3758/bf03210143 Milnor, John (1982), "Hyperbolic geometry: the first 150 years" (PDF), Bulletin of the American Mathematical
Euclidean_distance
The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1] From hyperbolic 2-space to Euclidean 3-space: Tilings and patterns via topology Stephen Hyde
Uniform tiling symmetry mutations
Uniform_tiling_symmetry_mutations
Concept in mathematics
boundary) the Teichmüller space T ( S ) {\displaystyle T(S)} is the space of marked complex (equivalently, conformal or complete hyperbolic) structures on S {\displaystyle
Mapping class group of a surface
Mapping_class_group_of_a_surface
Euclidean plane but one can also consider the system in the hyperbolic plane or in other spaces that suitably generalize the plane. Outer billiards differs
Outer_billiards
– inverse hyperbolic cosecant function. (Also written as arcsch.) arcosh – inverse hyperbolic cosine function. arcoth – inverse hyperbolic cotangent function
List of mathematical abbreviations
List_of_mathematical_abbreviations
Area in mathematics devoted to the study of finitely generated groups
CAT(0) spaces and CAT(0) cubical complexes, motivated by ideas from Alexandrov geometry. Interactions with low-dimensional topology and hyperbolic geometry
Geometric_group_theory
Locally spherical point on a mathematical surface
parabolic umbilics and hyperbolic umbilics. Elliptical umbilics have the three ridge lines passing through the umbilic and hyperbolic umbilics have just one
Umbilical_point
Space with one dimension
is a one-dimensional space. In particular, if the field is the complex numbers C , {\displaystyle \mathbb {C} ,} then the complex projective line P 1 (
One-dimensional_space
Iranian mathematician (1977–2017)
mathematics at Stanford University. Her research focused on hyperbolic geometry, dynamical systems, complex analysis, and topology. In 2014, she was awarded the
Maryam_Mirzakhani
Model of hyperbolic geometry
model and the Poincaré half-space model, it was proposed by Eugenio Beltrami who used these models to show that hyperbolic geometry was equiconsistent
Poincaré_disk_model
open unit disc in the complex plane C, thought of as the Poincaré disc model for 2-dimensional real/1-dimensional complex hyperbolic geometry. Let the Poincaré
Complex_geodesic
Set of points at distance less than one from a given point
are preserved by motions of their isometry groups. Another model of hyperbolic space is also built on the open unit disk: the Beltrami–Klein model. It is
Unit_disk
COMPLEX HYPERBOLIC-SPACE
COMPLEX HYPERBOLIC-SPACE
Girl/Female
Tamil
Complete
Girl/Female
Tamil
Complete
Girl/Female
Bengali, Indian
Good Complex
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Boy/Male
Tamil
Complete
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Girl/Female
Tamil
Complete
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Girl/Female
Muslim
Complex, Zigzag, Curling
Boy/Male
Indian
Complete
Girl/Female
Hindu, Indian
Complex
Boy/Male
Tamil
Complete
Boy/Male
Indian
Complete
COMPLEX HYPERBOLIC-SPACE
COMPLEX HYPERBOLIC-SPACE
Girl/Female
Tamil
Best, The Goddess who is above the five elements
Male
Hungarian
Hungarian form of Latin Desiderius, DEZSÖ means "longing."
Boy/Male
Tamil
An idol, All auspicious Lord, Lord Vishnu, Statue
Surname or Lastname
English
English : from an Old Breton personal name, derived from an element meaning ‘high’, ‘mighty’, which was introduced into England by followers of William the Conqueror and subsequently into Ireland, where it still has some currency as a personal name.Scottish : habitational name from a place in Kincardineshire. The place name is of uncertain origin, possibly from an early Celtic name, Conona ‘hound stream’.Roger Conant led a secession from Plymouth colony in about 1627 and founded the settlement that became Salem, MA. He was probably the son of Christopher Connant, who came over from England aboard the Anne in 1623.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Profit; Gain
Boy/Male
Hindu, Indian
Desired; Done with Intention
Boy/Male
Arabic, Australian, German, Turkish
One who Serves a Capable Man
Boy/Male
Indian, Punjabi, Sikh
Gem of Truth
Girl/Female
Muslim/Islamic
Gem name of a female companion
Girl/Female
Australian, Irish
Pure; Similar to Katherine
COMPLEX HYPERBOLIC-SPACE
COMPLEX HYPERBOLIC-SPACE
COMPLEX HYPERBOLIC-SPACE
COMPLEX HYPERBOLIC-SPACE
COMPLEX HYPERBOLIC-SPACE
imp. & p. p.
of Comply
n.
One who uses hyperboles.
imp. & p. p.
of Compile
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
imp. & p. p.
of Couple
a.
Complex, complicated.
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.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Not complex; uncompounded; simple.
n.
The use of hyperbole.
a.
Intricate; entangled; complicated; complex.
a.
Belonging to the hyperbola; having the nature of the hyperbola.
adv.
In a complex manner; not simply.
a.
Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression.
a.
Alt. of Hyperbolical
a.
Having some property that belongs to an hyperboloid or hyperbola.
n.
A complex; an aggregate of parts; a complication.
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.
a.
Repeatedly compound; made up of complex constituents.
a.
See Couple-close.