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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
Hyperbolic analogues of trigonometric functions
respectively. Hyperbolic functions are used to express the angle of parallelism in hyperbolic geometry. They are used to express Lorentz boosts as hyperbolic rotations
Hyperbolic_functions
Region of the Cartesian plane bounded by a hyperbola and two radii
defines a circular angle. In other words, the hyperbolic angle is the argument of hyperbolic functions in the same way that the circular angle is the argument
Hyperbolic_sector
Type of non-Euclidean geometry
not equivalent in hyperbolic geometry; new concepts need to be introduced. Further, because of the angle of parallelism, hyperbolic geometry has an absolute
Hyperbolic_geometry
Mathematical functions
). For a given value of a hyperbolic function, the inverse hyperbolic function provides the corresponding hyperbolic angle measure, for example arsinh
Inverse_hyperbolic_functions
Angle in certain right triangles in the hyperbolic plane
In hyperbolic geometry, angle of parallelism Π ( a ) {\displaystyle \Pi (a)} is the angle at the non-right angle vertex of a right hyperbolic triangle
Angle_of_parallelism
Figure formed by two rays meeting at a common point
t|g_{ij}V^{i}V^{j}\right|}}}.} A hyperbolic angle is an argument of a hyperbolic function just as the circular angle is the argument of a circular function
Angle
Mathematical function relating circular and hyperbolic functions
mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called the gudermannian
Gudermannian_function
Geometric mean and hyperbolic angle as coordinates in quadrant I
and v = x y {\displaystyle v={\sqrt {xy}}} . The parameter u is the hyperbolic angle to (x, y) and v is the geometric mean of x and y. The inverse mapping
Hyperbolic_coordinates
Linear map that preserves areas
measure of a hyperbolic angle associated with the sector. The hyperbolic angle concept is quite independent of the ordinary circular angle, but shares
Squeeze_mapping
Concept in astrodynamics
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit (from Newtonian theory: hyperbola shape) is the trajectory of any
Hyperbolic_trajectory
Triangle in hyperbolic geometry
sides or edges and three points called angles or vertices. Just as in the Euclidean case, three points of a hyperbolic space of an arbitrary dimension always
Hyperbolic_triangle
Geometric figure
t,\sinh t).} This parameter t is the hyperbolic angle, which is the argument of the hyperbolic functions. One finds an early expression of the
Unit_hyperbola
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
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
Two geometries based on axioms closely related to those specifying Euclidean geometry
quadrilateral with three right angles. The fourth angle of a Lambert quadrilateral is acute if the geometry is hyperbolic, a right angle if the geometry is Euclidean
Non-Euclidean_geometry
Equation used in relativistic physics
accounted in terms of the hyperbolic tangent function tanh which takes hyperbolic angle (rapidity) as an argument. In fact, the hyperbolic tangent of rapidity
Velocity-addition_formula
functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side
List of trigonometric identities
List_of_trigonometric_identities
Various meanings of the terms
self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality. In the case of function spaces, families of functions are
Orthogonality
Concept in mathematics
geometric transformation. For examples, circular angle is invariant under rotation, hyperbolic angle is invariant under squeeze mapping, and a difference
Invariant_measure
Measure of relativistic velocity
light being infinite. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each
Rapidity
Shape with three sides
above, the internal angles of a triangle in Euclidean space always add up to 180°. However, the sum of the internal angles of a hyperbolic triangle is less
Triangle
Plane curve: conic section
circular sector which that angle subtends. The analogous hyperbolic angle is likewise defined as twice the area of a hyperbolic sector. Let a {\displaystyle
Hyperbola
Input to a mathematical function
The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle. A mathematical function has one or more arguments
Argument_of_a_function
Cylindrical conformal map projection
integral of the secant function up to an angle φ {\displaystyle \varphi } is an associated hyperbolic angle called the anti-gudermannian or lambertian
Mercator_projection
Fundamental result in geometry
the lengths of two sides and their angle, or the length of one side and the two adjacent angles (see hyperbolic trigonometry). Once again, the Euclidean
Sum_of_angles_of_a_triangle
2.71828…, base of natural logarithms
logarithmus hyperbolicus est = 1), … " ( … (e denotes that number whose hyperbolic [i.e., natural] logarithm is equal to 1) … ) Remmert, Reinhold (1991)
E_(mathematical_constant)
Relates the tangent of half of an angle to trigonometric functions of the entire angle
tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle. The tangent of half an angle is the stereographic
Tangent_half-angle_formula
Mutation of quaternions where unit vectors square to +1
Sophus Lie. An example of a one-parameter group is the hyperbolic versor with the hyperbolic angle parameter. This parameter is part of the polar decomposition
Hyperbolic_quaternion
Mathematical description of spacetime used in relativity
Lorentz boost and in mathematics it is a hyperbolic rotation. Each reference frame is associated with a hyperbolic angle, which is zero for the rest frame in
Minkowski_spacetime
SI derived unit of angle
considering the basis for hyperbolic angle which is analogously defined. As Paul Quincey et al. write, "The status of angles within the International System
Radian
S-shaped curve
into the logistic distribution. Geometrically, the hyperbolic tangent function is the hyperbolic angle on the unit hyperbola x 2 − y 2 = 1 {\displaystyle
Logistic_function
Category of coordinate systems
radial coordinate or radius, and the angle is called the angular coordinate, or polar angle. From the hyperbolic law of cosines, we get that the distance
Coordinate systems for the hyperbolic plane
Coordinate_systems_for_the_hyperbolic_plane
Quadric surface with one axis of symmetry and no center of symmetry
} If the hyperbolic paraboloid z = x 2 a 2 − y 2 b 2 {\displaystyle z={\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}} is rotated by an angle of π/4 in
Paraboloid
Mathematical function that preserves angles
are conformal since hyperbolic rotations preserve hyperbolic angle, (called rapidity) and the other rotations preserve circular angle. The introduction
Conformal_map
lengths, angles, and other geometric figures, constructions can also be made in hyperbolic geometry. There are a couple of models for hyperbolic geometry
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
Möbius transformation generalized to rings other than the complex numbers
{\displaystyle \exp(yi)=\cos y+i\sin y,\quad i^{2}=-1.} The "angle" y is hyperbolic angle, slope, or circular angle according to the host ring. Linear fractional transformations
Linear fractional transformation
Linear_fractional_transformation
Generalization of perpendicularity
self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality. In the case of function spaces, families of functions are
Orthogonality_(mathematics)
Line intersecting 2 coplanar lines at 2 points
geometry (hence valid in both hyperbolic and Euclidean Geometry), proves that if the angles of a pair of alternate angles of a transversal are congruent
Transversal_(geometry)
Space in mathematics and theoretical physics
of angle: the definite case corresponds to ciricular angle while the isotropic case yields hyperbolic angle. Just as a rotation by a circular angle can
Pseudo-Euclidean_space
Concept in mathematical group theory
by rapidity, a hyperbolic angle. One way to describe a Lorentz boost is as a hyperbolic rotation which preserves the differential angle between rapidities
Conformal_group
Relation between sides of a right triangle
{b}{R}}\,\cos \gamma ,} with γ the angle at the vertex opposite the side c. By using the Maclaurin series for the hyperbolic cosine, cosh x ≈ 1 + x2/2, it
Pythagorean_theorem
Upper-half plane model of hyperbolic non-Euclidean geometry
way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically, each point in the hyperbolic plane is represented using
Poincaré_half-plane_model
Quantity in relativistic physics
as the hyperbolic angle φ {\displaystyle \varphi } : tanh φ = β {\displaystyle \tanh \varphi =\beta } also leads to γ (by use of hyperbolic identities):
Lorentz_factor
Mathematical term
angular invariant measure, on a par with circular angle (invariant under rotation) and hyperbolic angle, with invariance group of squeeze mappings. The
Slope
Graduated markings, generally logarithmic, on slide rule
coefficients (e.g. ρ" at 180*60*60/π or 206.3×103 to find sine and tan of small angles). A cursor may have subsidiary hairlines beside the main one. For example
Slide_rule_scale
Natural logarithm e (mathematical constant) Exponential function Hyperbolic angle Hyperbolic function Stirling's approximation Bernoulli numbers See also
List_of_calculus_topics
Triangle containing a 90-degree angle
sides are perpendicular, forming a right angle (1⁄4 turn or 90 degrees). The side opposite to the right angle is called the hypotenuse (side c {\displaystyle
Right_triangle
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
Model of hyperbolic geometry
model of hyperbolic space of constant curvature −1. The model has the conformal property that the angle between two intersecting curves in hyperbolic space
Poincaré_disk_model
Horizontal angle from north or other reference cardinal direction
اَلسُّمُوت, romanized: as-sumūt, lit. 'the directions') is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric
Azimuth
Change in the position of an object
Velocity is then interpreted as rapidity, the hyperbolic angle φ {\displaystyle \varphi } for which the hyperbolic tangent function tanh φ = v ÷ c {\displaystyle
Motion
Lie group homomorphism from the real numbers
determine a world-line. Using the parametrization of the hyperbola with hyperbolic angle, the theory of special relativity provided a calculus of relative motion
One-parameter_group
Subset of real numbers that are greater than zero
{\displaystyle {\sqrt {xy}},} while a change along H indicates a new hyperbolic angle. Semifield – Algebraic structure Sign (mathematics) – Number property
Positive_real_numbers
Mathematical term for squaring a plane figure
computation of a univariate definite integral. Gaussian quadrature Hyperbolic angle Numerical integration Quadratrix Tanh-sinh quadrature Lindemann, F
Quadrature_(mathematics)
Theory of interwoven space and time by Albert Einstein
Lorentz boosts represent hyperbolic rotations in Minkowski spacetime.[citation needed] The advantages of using hyperbolic functions are such that some
Special_relativity
Functions of an angle
the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend
Trigonometric_functions
Study of Lie groups, Lie algebras and differential equations
cases the Lie algebra parameters have names: angle, hyperbolic angle, and slope. These species of angle are useful for providing polar decompositions
Lie_theory
Property of all triangles on a Euclidean plane
equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, a sin α = b sin β = c sin γ = 2 R , {\displaystyle
Law_of_sines
Polynomial whose roots are the eigenvalues of a matrix
polynomial of A . {\displaystyle A.} Another example uses hyperbolic functions of a hyperbolic angle φ. For the matrix take A = ( cosh ( φ ) sinh ( φ )
Characteristic_polynomial
Family of linear transformations
4-dimensional Minkowski space. The parameter ζ is the hyperbolic angle of rotation, analogous to the ordinary angle for circular rotations. This transformation
Lorentz_transformation
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
Quaternion of norm 1 (unit quaternion)
rotation, and has the angle 2 a {\displaystyle \ 2\ a\ } about the axis r {\displaystyle \ \mathbf {r} \ } in axis–angle representation. The collection
Versor
Method of drawing geometric objects
construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass
Straightedge and compass construction
Straightedge_and_compass_construction
Geometric axiom
interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum
Parallel_postulate
Trigonometric result for hyperbolic triangles
In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar
Hyperbolic_law_of_cosines
Mathematical model combining space and time
primed and unprimed frames are mutually rotated by a hyperbolic angle (analogous to ordinary angles in Euclidean geometry). Because of this rotation, the
Spacetime
Area interpreted positively or negatively
{-t}{2}}\right|_{0}^{\theta }=-{\frac {\theta }{2}},} giving a negative hyperbolic angle as a negative sector area. Mikhail Postnikov's 1979 textbook Lectures
Signed_area
Generalization of mass, length, area and volume
measure is invariant under rotations preserving the circle. Similarly, hyperbolic angle measure is invariant under squeeze mapping. The Haar measure for a
Measure_(mathematics)
(standard) harmonic series Highly composite number Area of hyperbolic sector, basis of hyperbolic angle Infinite series convergence of the geometric series with
List_of_mathematical_proofs
Quadrilateral with four right angles
its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have
Rectangle
Symmetric subdivision in hyperbolic geometry
In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
Fundamental trigonometric functions
functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the
Sine_and_cosine
Branch of mathematics
assuming that some of the angles of these figures were acute of obtuse, embodied the first few theorems of the hyperbolic and the elliptic geometries
Geometry
Group of real 2×2 matrices with unit determinant
\\&\lambda ^{-1}\end{smallmatrix}}\right)\times \{\pm I\}} ; the hyperbolic angle of the hyperbolic rotation is given by arcosh of half of the trace, but the
SL2(R)
Quadrilateral symmetric across a diagonal
have three right angles and one non-right angle, forming a special case of a Lambert quadrilateral. The fourth angle is acute in hyperbolic geometry and obtuse
Kite_(geometry)
Type of matrix representation
unit hyperbola through (1, 0). This branch is parametrized by the hyperbolic angle a and is written cosh a + j sinh a = exp ( a j ) = e a j , {\displaystyle
Polar_decomposition
Type of curve in hyperbolic geometry
= 1 induces a quasi-symmetry of the hyperbolic plane by inversion. (Such a hypercycle meets its axis at an angle of π/4.) Specifically, a point P in an
Hypercycle_(geometry)
figure's angle defect: 1 p + 1 q > 1 2 : Polyhedron (existing in Euclidean 3-space) 1 p + 1 q = 1 2 : Euclidean plane tiling 1 p + 1 q < 1 2 : Hyperbolic plane
List_of_regular_polytopes
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
Lie group of Lorentz transformations
preservation of angles. Lorentz boosts act by hyperbolic rotation of a spacetime plane, and such "rotations" preserve hyperbolic angle, the measure of
Lorentz_group
Type of unbounded quadratic surface-shaped building or work
Shukhov Tower in Polibino, Dankovsky District, Lipetsk Oblast, Russia. Hyperbolic structures have a negative Gaussian curvature, meaning they curve inward
Hyperboloid_structure
Quaternions with complex number coefficients
with the hyperboloid model of hyperbolic geometry. In special relativity, the hyperbolic angle parameter of a hyperbolic versor is called rapidity. Thus
Biquaternion
View of mathematicians to consolidate two or more theories into a more generalized one
Erlangen programme. The general theory of angle can be unified with invariant measure of area. The hyperbolic angle is defined in terms of area, very nearly
Unifying theories in mathematics
Unifying_theories_in_mathematics
Shape with four equal sides and angles
geometry. Although spherical geometry and hyperbolic geometry both lack polygons with four equal sides and right angles, they have square-like regular polygons
Square
Change of variable for integrals involving trigonometric functions
The tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions
Tangent half-angle substitution
Tangent_half-angle_substitution
Inverse functions of sin, cos, tan, etc.
z} , the definitions allow for hyperbolic angles as outputs and can be used to further define the inverse hyperbolic functions. It's possible to algebraically
Inverse trigonometric functions
Inverse_trigonometric_functions
relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory. This article provides a
Derivations of the Lorentz transformations
Derivations_of_the_Lorentz_transformations
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
Study of geometries as axiomatic systems
three right angles. The fourth angle of a Lambert quadrilateral is acute if the geometry is hyperbolic, and a right angle if the geometry is Euclidean.
Foundations_of_geometry
Irish physicist (1873–1936)
works he used a hyperbolic angle ω to introduce the concept of rapidity and showed that the kinematic space of velocities is hyperbolic, so that "instead
Alfred_Robb
Ratio in relativity
each of these is also simply related to a traveling object's hyperbolic velocity angle or rapidity η by η = sinh − 1 w c = tanh − 1 v c = ± cosh
Proper_velocity
Mathematical functions of split-complex numbers
by hyperbolic angle in its polar coordinates, and this angle is preserved by motor variable linear fractional transformations just as circular angle is
Motor_variable
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
American electrical engineer and mathematician (1861–1939)
advanced applied mathematics by communicating the theory of the hyperbolic angle and hyperbolic functions, first in a course at the University of London and
Arthur_Edwin_Kennelly
Curve that winds around a central point
(Archimedean, hyperbolic, Fermat's, lituus spirals) and the logarithmic spiral r = a e k φ {\displaystyle r=ae^{k\varphi }} . Polar slope angle The angle α {\displaystyle
Spiral
Tiling of euclidean or hyperbolic space of three or more dimensions
the plane. In 3-dimensional hyperbolic space, the dihedral angle of a polyhedron depends on its size. The regular hyperbolic honeycombs thus include two
Honeycomb_(geometry)
Amount by which an orbit deviates from a perfect circle
for open curves (an angle covered by velocity vector). Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of
Orbital_eccentricity
Antiderivative of the secant function
for some arguments. An alternative expression in terms of the inverse hyperbolic sine arsinh is numerically well behaved for real arguments | ϕ | < 1 2
Integral of the secant function
Integral_of_the_secant_function
Rational function of the form (az + b)/(cz + d)
angle-preserving and orientation-preserving) maps D → D. By introducing a suitable metric, the open disk turns into another model of the hyperbolic plane
Möbius_transformation
HYPERBOLIC ANGLE
HYPERBOLIC ANGLE
Girl/Female
Tamil
Angle, Of noble kind
Surname or Lastname
English
English : occupational name for a hornblower or worker in horn, from an agent derivative of Old French corne ‘horn’ (see Corne).English : metonymic occupational name for a maker of hand mills, from an agent derivative of Old English cweorn ‘hand mill’ (see Corn 3).English : topographic name for someone who lived on the corner of two streets or tracks, (Middle English corner, from Old French cornier ‘angle’, ‘corner’).Americanized spelling of German Körner (see Koerner) or Swiss Korner.
Girl/Female
Hindu
Angle, Of noble kind
Boy/Male
Hindu
Feminine
Girl/Female
Indian
Pari fairy
Girl/Female
Tamil
Pari fairy
Surname or Lastname
English
English : from the Middle English personal name Ingelot, a pet form of any of various names such as Ingelbald ‘Angle bold’, Ingelbert ‘Angle bright’, or Ingelard ‘Angle hardy’. These were names of Germanic origin, introduced to Britain by the Normans or possibly by the Danish invaders a century earlier.
Girl/Female
German, Swedish
Bright Angle
Surname or Lastname
English
English : topographic name for someone who lived near a place used for archery practice, from Middle English butte ‘mark for archery’, ‘target’, ‘goal’. In the Middle Ages archery practice was a feudal obligation, and every settlement had its practice area.English : topographic name from Middle English butte ‘strip of land abutting on a boundary’, ‘short strip or ridge at right angles to other strips in a common field’.English : from Middle English butte, bott ‘butt’, ‘cask’, applied as a metonymic occupational name for a cooper or as a nickname possibly for a heavy drinker or for a large, fat man.English : from a Middle English personal name, But(t), of unknown origin, perhaps originally a nickname meaning ‘short and stumpy’, and akin to late Middle English butt ‘thick end’, ‘stump’, ‘buttock’ (of Germanic origin).German and English : in both Middle Low German and Middle English the word but(te) denoted various types of marine fish, originally a fish with a blunt head, for example halibut (German Heilbutt) or turbot (German Steinbutt), and the surname may in some cases be a metonymic occupational name for a seller of fish or salt fish.Kashmiri : variant of Bhatt.Robert Butt came from Kent, England, to NC in 1640.
Boy/Male
Danish, German, Swedish
Angle Bright
Surname or Lastname
English
English : Americanized form of French Anglais ‘English(man)’.
Surname or Lastname
English
English : habitational name from a place in Staffordshire named Engleton, from Old English Engla (genitive plural of Engle ‘Angle’) + tūn ‘settlement’.
Girl/Female
Biblical, Christian, Danish, German, Hawaiian, Hebrew
Superficies; The Angle; Cassia; Name for a Variety of Trees and Shrubs; One of which Produces Cinnamon; Sweet Scented Spice; Super; Cinnamon Tree
Surname or Lastname
English and Irish (of Norman origin)
English and Irish (of Norman origin) : topographic name from Middle English and Old French angle ‘angle’, ‘corner’ (Latin angulus). As an Irish surname, it can also be habitational, from a place in Pembrokeshire, South Wales, named with this word.Americanized spelling of German Angel or Engel.
Surname or Lastname
English
English : habitational name from a place in Devon called Huxford (preserved in the name of Huxford Farm), from the Old English personal name HÅcc or the Old English word hÅc ‘hook or angle of land’ + ford ‘ford’.
Surname or Lastname
English
English : from Old English Englisc. The word had originally distinguished Angles (see Engel) from Saxons and other Germanic peoples in the British Isles, but by the time surnames were being acquired it no longer had this meaning. Its frequency as an English surname is somewhat surprising. It may have been commonly used in the early Middle Ages as a distinguishing epithet for an Anglo-Saxon in areas where the culture was not predominantly English--for example the Danelaw area, Scotland, and parts of Wales--or as a distinguishing name after 1066 for a non-Norman in the regions of most intensive Norman settlement. However, explicit evidence for these assumptions is lacking, and at the present day the surname is fairly evenly distributed throughout the country.Irish : see Golightly.
Girl/Female
Biblical Hebrew
Superficies, the angle, cassia.
Boy/Male
German, Swedish
Angel; Bright Angle
Boy/Male
British, English
From Anglesey
Surname or Lastname
Scottish
Scottish : variant of Whan.English : topographic name for someone who lived in a corner or angle or land, from Old English hwamm ‘corner’, or a habitational name from Wham in County Durham, named with this word.
HYPERBOLIC ANGLE
HYPERBOLIC ANGLE
Boy/Male
Hindu
Age
Boy/Male
Biblical
Plant, verdure, moist, pot.
Boy/Male
English
From the White Cliff
Boy/Male
Tamil
Rampratap | ராமபà¯à®°à®¤à®¾à®ª
Lord Rama
Girl/Female
Tamil
Raj Kumari | ராஜகà¯à®®à®¾à®°à¯€
Princess
Girl/Female
Irish
Devotion to St. Catherine came to Ireland with Christianity. Revered for her courage and purity, Catherine in the Irish form, Cathleen, became such a popular name that W. B. Yeats chose it for the heroine of his 1899 play “The Countess Cathleen†which was inspired by an Irish folktale. In a time of famine the Devil offers food to the starving poor in exchange for their souls. But Cathleen convinces Satan to take her soul instead. When she dies the Devil comes to collect her soul but God intervenes and carries Cathleen to heaven, saying that “such a sacrificial act cannot justly lead to evil consequences.â€
Girl/Female
Tamil
Lajjawati | லஜà¯à®œà®¾à®µà®¤à¯€
A sensitive plant, Modest woman
Boy/Male
Australian, Romanian, Turkish
Marvelous
Girl/Female
Hindu
Name of a Raga
Girl/Female
Tamil
Faith
HYPERBOLIC ANGLE
HYPERBOLIC ANGLE
HYPERBOLIC ANGLE
HYPERBOLIC ANGLE
HYPERBOLIC ANGLE
a.
Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression.
n.
Diminution; a species of hyperbole, representing a thing as being less than it really is.
n.
The use of hyperbole.
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.
p. pr. & vb. n.
of Hyperbolize
a.
Exaggerated; excessive; hyperbolical.
imp. & p. p.
of Hyperbolize
a.
Having the form, or nearly the form, of an hyperbola.
v. i.
To speak or write with exaggeration.
a.
Alt. of Hyperbolical
n.
A figure by which a grave and magnificent word is put for the proper word; amplification; hyperbole.
a.
Belonging to the hyperbola; having the nature of the hyperbola.
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.
v. t.
To state or represent hyperbolically.
adv.
In the form of an hyperbola.
a.
Having some property that belongs to an hyperboloid or hyperbola.
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.
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.
One who uses hyperboles.
a.
Of or pertaining to an hyperbaton; transposed; inverted.