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the curve complex is a simplicial complex C(S) associated to a finite-type surface S, which encodes the combinatorics of simple closed curves on S.
Curve_complex
Algebraic curve in mathematics
mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over
Elliptic_curve
Mathematical idealization of the trace left by a moving point
topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is not a curve, but a
Curve
Curve defined as zeros of polynomials
mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective
Algebraic_curve
Concept in mathematics
this paragraph with a slightly different complex instead of the curve complex, called the cut system complex. An example of a relation between Dehn twists
Mapping class group of a surface
Mapping_class_group_of_a_surface
Number of times a curve wraps around a point in the plane
complex analysis, geometric topology, differential geometry, and physics (such as in string theory). Suppose we are given a closed, oriented curve in
Winding_number
Algebraic variety
geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H
Modular_curve
Curve used in computer graphics and related fields
A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay, French pronunciation: [bezje]) is a parametric curve used in computer graphics and related fields. A sequence
Bézier_curve
Definite integral of a scalar or vector field along a path
where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour
Line_integral
Fractal constructible with L-systems
A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. The
Dragon_curve
geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map, from a Riemann surface into an almost complex manifold, that satisfies the
Pseudoholomorphic_curve
Mathematical concept
smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose
Plane_curve
Model of the extended complex plane plus a point at infinity
Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. This extended
Riemann_sphere
Mathematical curve outputted from a specific pair of parametric equations
A Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations x = A sin
Lissajous_curve
Jeffrey Brock and Richard Canary, and for results on the geometry of the curve complex obtained in collaboration with Howard Masur. Minsky obtained his Ph
Yair_Minsky
Mathematical function defined piecewise by polynomials
evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible
Spline_(mathematics)
Theory of a class of elliptic curves
In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way
Complex_multiplication
Representation of the relationship between taxation and government revenue
Laffer curve illustrates a theoretical relationship between rates of taxation and the resulting levels of the government's tax revenue. The Laffer curve assumes
Laffer_curve
Mathematical measure of how much a curve or surface deviates from flatness
the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained
Curvature
Approach to public-key cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC
Elliptic-curve_cryptography
Algebraic curve
In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation:
Fermat_curve
in the field of complex geometry, a holomorphic curve in a complex manifold M is a non-constant holomorphic map f from the complex plane to M. Nevanlinna
Holomorphic_curve
British mathematician
the study of the curve complex, with various applications to 3-manifolds, mapping class groups and Kleinian groups. The curve complex C(S) of a finite
Brian_Bowditch
Mathematical concept
the j-invariant for which a complex elliptic curve has complex multiplication. The complex elliptic curves with complex multiplication are those for
Supersingular_elliptic_curve
Fractal curve
Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which
Koch_snowflake
Parametrizes complex structures on a surface
{\displaystyle \mathbb {C} /(\mathbb {Z} +\tau \mathbb {Z} )} (a complex elliptic curve) for a complex number τ ∈ H {\displaystyle \tau \in \mathbb {H} } where
Teichmüller_space
1893). They are also referred to as Hurwitz curves, interpreting them as complex algebraic curves (complex dimension 1 = real dimension 2). The Fuchsian
Hurwitz_surface
Roulette curve made from circles with radii that differ by factors of 3 or 1.5
In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created
Deltoid_curve
2017 song by Gucci Mane featuring The Weeknd
for New Song "Curve"". Complex. Lamarre, Carl (September 13, 2017). "Listen to Gucci Mane & The Weeknd Kill Every Groupie's Dream on 'Curve'". Billboard
Curve_(song)
Topological structure of 4D spacetime
unit hyperbola group. 4-manifold Clifford-Klein form Closed timelike curve Complex spacetime Geometrodynamics Gravitational singularity Hantzsche-Wendt
Spacetime_topology
American mathematician
1997. As a mathematician, Klarreich proved that the boundary of the curve complex is homeomorphic to the space of ending laminations. As a popular science
Erica_Klarreich
Method of evaluating certain integrals along paths in the complex plane
In complex analysis, a contour is a type of curve in the complex plane. In contour integration, contours provide a precise definition of the curves on
Contour_integration
Relationship between experience producing a good and the efficiency of that production
memorizing the word set. (More detail about the complex processes of learning is discussed in the Learning curve article.) This was later more generalized to:
Experience_curve_effect
Mathematical Sentence
The idea is that one can extend a complex-analytic function (from here on called simply analytic function) along curves starting in the original domain
Monodromy_theorem
Type of spline curve
In mathematics, a Pythagorean hodograph curve or PH curve is a curve defined by a polynomial parametric equation for which the speed (the derivative of
Pythagorean_hodograph_curve
American mathematician and topologist (1935–2022)
American Mathematical Society. He also introduced the study of the curve complex into 3-manifold topology. Hempel wrote a book about 3-manifolds in 1976
John_Hempel
Relationship between proficiency and experience
learning curve Proficiency (test score)Experience (hours spent)01234503691215Proficiency (test score)Example of a steep learning curve A learning curve is a
Learning_curve
Plane algebraic curve
lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n. For
Polynomial_lemniscate
Concept in mathematics
the free factor complex (sometimes also called the complex of free factors) is a free group counterpart of the notion of the curve complex of a finite type
Free_factor_complex
Plane algebraic curve
modular curves are part of the larger theory of modular curves. In particular it has another expression as a compactified quotient of the complex upper
Classical_modular_curve
Mathematical function having a characteristic S-shaped curve or sigmoid curve
mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function. Other
Sigmoid_function
In mathematics, the Tate curve is a curve defined over the ring of formal power series Z [ [ q ] ] {\displaystyle \mathbb {Z} [[q]]} with integer coefficients
Tate_curve
Continuous fractal curve obtained as the image of Cantor space
fractal curves, including the Cantor function, Cesàro–Faber curve (Lévy C curve), Minkowski's question mark function, blancmange curve, and the Koch curve are
De_Rham_curve
Method of representing curves and surfaces in computer graphics
(B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both
Non-uniform_rational_B-spline
Simplicial complex
Tits building is a Coxeter complex. Buildings Weyl group Root system https://dept.math.lsa.umich.edu/~lji/building-curve-complex-handbook.pdf pg. 8, definition
Coxeter_complex
Fractal sets in complex dynamics of mathematics
{\displaystyle z^{2}+c} , where c is a complex number. For such an iteration the Julia set is not in general a simple curve, but is a fractal, and for some values
Julia_set
Mathematical concept
to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex numbers, these
Elliptic_surface
Law of electrical current and voltage
between current and voltage (their I–V curve) is nonlinear (or non-ohmic). An example is the p–n junction diode (curve at right). As seen in the figure, the
Ohm's_law
Figure-eight-shaped curve
(/lɛmˈnɪskɪt/ or /ˈlɛmnɪsˌkeɪt, -kɪt/) is any of several figure-eight or ∞-shaped curves. The word comes from the Latin lēmniscātus, meaning "decorated with ribbons"
Lemniscate
A fish curve is an ellipse negative pedal curve that is shaped like a fish. In a fish curve, the pedal point is at the focus for the special case of the
Fish_curve
equivalent to that of smooth projective curves over the complex numbers. Throughout the article, a curve mean a complete curve (but not necessarily smooth). Let
Complete_algebraic_curve
Theorem in complex analysis
that a curve is homotopic to a constant curve if there exists a smooth homotopy (within U {\displaystyle U} ) from the curve to the constant curve. Intuitively
Cauchy's_integral_theorem
Mathematical curves generated by rolling other curves together
it is the path traced by a curve while rolling on another curve without slipping. Roughly speaking, a roulette is the curve described by a point (called
Roulette_(curve)
Theorem in symplectic topology
pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may
Gromov's compactness theorem (topology)
Gromov's_compactness_theorem_(topology)
Study of complex manifolds and several complex variables
one-dimensional complex manifold classifying possible compact Riemann surfaces of genus 1, so-called elliptic curves, the modular curve. By the uniformization
Complex_geometry
Property of a planar simple closed curve
an orientation of a curve (including polygonal curves) is the choice of one of the two possible senses for travelling on the curve, as in forward and backward
Curve_orientation
Describes when a compact Riemann surface is determined by its Jacobian variety
result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) C is determined
Torelli_theorem
Term in mathematics
of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to a subvariety of J
Jacobian_variety
Theorem stating that smooth algebraic curve has minimum genus its homology class
In mathematics, a smooth algebraic curve C {\displaystyle C} in the complex projective plane, of degree d {\displaystyle d} , has genus given by the genus–degree
Thom_conjecture
Method for determining the concentration of a substance in an unknown sample
In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in
Calibration_curve
Projective variety that is also an algebraic group
abelian variety is the same as that of elliptic curve, and every complex torus gives rise to such a curve; for g > 1 {\displaystyle g>1} it has been known
Abelian_variety
Theorem in topology
topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides the plane
Jordan_curve_theorem
Algebraic surface
It can be defined as an algebraic curve using five complex numbers as projective coordinates, as the space curve in the four-dimensional projective space
Bring's_curve
Curve formed by a hanging chain
gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola. The curve appears in the design of certain
Catenary
Mathematical curve with two cusps
the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation y 2 ( a 2 − x 2
Bicorn
Unproved conjecture in mathematics
continuation to the whole complex plane.[citation needed] This conjecture was first proved by Max Deuring for elliptic curves with complex multiplication. It
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Complex exponential in terms of sine and cosine
mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function
Euler's_formula
Economic model of price determination in a market
Economists distinguish between the supply curve of an individual firm and the market supply curve. The market supply curve shows the total quantity supplied by
Supply_and_demand
Fractal curve resembling a blancmange pudding
mathematics, the blancmange curve is a self-affine fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi
Blancmange_curve
Asymptotically stable in the sense of geometric invariant theory
example, an elliptic curve (a non-singular genus 1 curve with 1 marked point) is stable. Over the complex numbers, a connected curve is stable if and only
Stable_curve
Object in algebraic geometry
curve is an object in algebraic geometry that is roughly an algebraic curve with potentially "fractional points" called stacky points. A stacky curve
Stacky_curve
Type of mathematical curve
In mathematics, a cubic plane curve , often called simply a cubic is a plane algebraic curve defined by a homogeneous polynomial of degree 3 in three variables
Cubic_plane_curve
Algebraic variety in a projective space
(1996), Rational curves on algebraic varieties Mumford, David (1970), Abelian Varieties Mumford, David (1995), Algebraic Geometry I: Complex Projective Varieties
Projective_variety
Relationship between stress and performance
decreases. The process is often illustrated graphically as a bell-shaped curve which increases and then decreases with higher levels of arousal. The original
Yerkes–Dodson_law
Geometric representation of the complex numbers
part of complex analysis. In this context, the direction of travel around a closed curve is important – reversing the direction in which the curve is traversed
Complex_plane
Plane algebraic curve defined by a 4th-degree polynomial
In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: A x 4
Quartic_plane_curve
Relation between genus, degree, and dimension of function spaces over surfaces
is two, but one as a complex manifold. The compactness of a Riemann surface is paralleled by the condition that the algebraic curve be complete, which is
Riemann–Roch_theorem
One-dimensional complex manifold
admit complex structures but the Möbius strip, Klein bottle and real projective plane do not. Every compact Riemann surface is a complex algebraic curve by
Riemann_surface
Concept in complex analysis
a complex curve, that is complex analytic manifold of dimension one (over the complex numbers). The simplest examples of such curves are the complex plane
Zeros_and_poles
Mathematical concept
modular elliptic curve is an elliptic curve E that admits a parametrization X0(N) → E by a modular curve. This is not the same as a modular curve that happens
Modular_elliptic_curve
precast floors. Its two buildings are curved to form two quarter circles, the two arcs of an S-shaped complex, with the radii of the circles lined up
Embassy_of_Australia,_Paris
Generalization of the concept of parallel lines
A parallel curve of a given (progenitor) curve is the envelope of a family of congruent (equal-radius) circles centered on the curve. It generalises the
Parallel_curve
Mathematical function
Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the horizontal position of the center
Gaussian_function
Geometric space
algebraic geometry, a moduli space of curves is a space whose points correspond to isomorphism classes of algebraic curves. The term "modulus" was introduced
Moduli_of_algebraic_curves
Algebraic curve
geometry an imaginary curve is an algebraic curve which does not contain any real points. For example, the set of pairs of complex numbers ( x , y ) {\displaystyle
Imaginary_curve
Integral criterion for holomorphy
piecewise regular curve between the new z0 and the old, and this does not change the derivative. Morera's theorem is a standard tool in complex analysis. It
Morera's_theorem
Curves whose limit does not preserve length
shows that, for curves under uniform convergence, the length of a curve is not a continuous function of the curve. For any smooth curve, polygonal chains
Staircase_paradox
Theorem about zeros of holomorphic functions
same number of times. Let C be a closed, simple curve (i.e., not self-intersecting). By Jordan curve theorem, it delimits a region called its interior
Rouché's_theorem
Type of catenary curve
and thus sometimes called Rankine curve) is a catenary curve, but of a special form: while a catenary is the curve formed by a chain under its own weight
Weighted_catenary
Curve from a cone intersecting a plane
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola
Conic_section
elliptic functions Elliptic integral Complex multiplication Weil pairing Hyperelliptic curve Klein quartic Modular curve Modular equation Modular function
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Point on a curve not given by a smooth embedding of a parameter
In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular
Singular_point_of_a_curve
Cubic plane curve
} Another way of parameterizing the same curve uses complex numbers, each representing a point in the complex plane. For a parameter τ {\displaystyle \tau
Tschirnhausen_cubic
Three-holed sphere
following operations: take a curve α {\displaystyle \alpha } in the decomposition in a one-holed torus and replace it by a curve in the torus intersecting
Pair_of_pants_(mathematics)
Coordinates comprising a distance and an angle
curve is notable as one of the first curves, after the conic sections, to be described in a mathematical treatise, and as a prime example of a curve best
Polar_coordinate_system
Branch of mathematics studying functions of a complex variable
number of curve arcs removed. Many basic and special complex functions are defined in this way, including the complex exponential function, complex logarithm
Complex_analysis
Operation in mathematical calculus
variable x. When a complex function is integrated along a curve γ {\displaystyle \gamma } in the complex plane, the integral is denoted as follows ∫ γ f ( z
Integral
Probability distribution
distributed. A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped (such as the Cauchy,
Normal_distribution
Roadbed that turns 180 degrees
horseshoe curve is a class of climbing curve in a roadbed that reverses turn direction (inflection) twice on either side of a single tight curve that varies
Horseshoe_curve
Number, approximately 3.14
of the key tools in complex analysis is contour integration of a function over a positively oriented (rectifiable) Jordan curve γ. A form of Cauchy's
Pi
CURVE COMPLEX
CURVE COMPLEX
Boy/Male
Arabic, Muslim
Cure
Boy/Male
Arabic
Cure
Surname or Lastname
Scottish and Irish
Scottish and Irish : reduced form of McCure, an Anglicized form of Gaelic Mac Ãomhair (see McIver).English : possibly from Middle English cure ‘charge’, ‘care’, ‘concern’.
Boy/Male
Muslim/Islamic
Cure
Surname or Lastname
English
English : unexplained.
Boy/Male
Muslim
Cure, Treatment
Girl/Female
Muslim
Cure
Boy/Male
Biblical American Hebrew
Physician; cure.
Girl/Female
Arabic
Cure
Boy/Male
Indian
Cure, Treatment
Boy/Male
Arabic
Cure.
Girl/Female
Arabic, Muslim
Cure
Girl/Female
Hindu
Beautiful
Boy/Male
Native American
Curve like foxtail grass.
Boy/Male
Indian
Glitter, Curve, Shine
Boy/Male
Muslim
Glitter, Curve, Shine
Surname or Lastname
English
English : variant spelling of Curl.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Telugu
Curved
Boy/Male
Arabic, Muslim
Glitter; Curve; Shine; Brightness
Boy/Male
Australian, Sindhi
Cure
CURVE COMPLEX
CURVE COMPLEX
Girl/Female
African, Indian, Swahili
Compassion
Boy/Male
Muslim
White Falcon. King of Falcons.
Boy/Male
Hindu
Every where, God
Boy/Male
American, Australian, French, German, Greek, Latin, Shakespearean, Spanish
Light; Illumination; From Lucanus; A Region of Southern Italy; Spanish Form of Luke Light
Girl/Female
Hindu, Indian
Goddess Laxmi; Daughter of Anand
Boy/Male
Arabic, Muslim
Best Friend
Female
German
Pet form of German Elisabeth, ILSE means "God is my oath."Â
Boy/Male
Italian American
He shall add.
Female
French
Possibly a pet form of French Marguerite, MAGALIE means "pearl."
Girl/Female
Muslim/Islamic
Baby lion young lioness, Moon, Beautiful
CURVE COMPLEX
CURVE COMPLEX
CURVE COMPLEX
CURVE COMPLEX
CURVE COMPLEX
adv.
Perpendicularly; at right angles; as, a curve cuts a set of curves orthogonally.
superl.
Having, or consisting of, a gentle curve or curves; not angular or abrupt; as, soft outlines.
p. pr. & vb. n.
of Curve
v. t.
To prepare for preservation or permanent keeping; to preserve, as by drying, salting, etc.; as, to cure beef or fish; to cure hay.
a.
To bend; to crook; as, to curve a line; to curve a pipe; to cause to swerve from a straight course; as, to curve a ball in pitching it.
n.
Spiritual charge; care of soul; the office of a parish priest or of a curate; hence, that which is committed to the charge of a parish priest or of a curate; a curacy; as, to resign a cure; to obtain a cure.
v. i.
To curve upward.
n.
Medical or hygienic care; remedial treatment of disease; a method of medical treatment; as, to use the water cure.
a.
Bent without angles; crooked; curved; as, a curve line; a curve surface.
n.
The curve described by any point in a wheel rolling on a line; a cycloid; a roulette; in general, the curve described by any point fixedly connected with a moving curve while the moving curve rolls without slipping on a second fixed curve, the curves all being in one plane. Cycloids, epicycloids, hypocycloids, cardioids, etc., are all trochoids.
a.
A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.
n.
To make a curvet; to leap; to bound.
a.
A line described according to some low, and having no finite portion of it a straight line.
v. t.
To cause to curvet.
imp. & p. p.
of Curve
v. i.
To bend or turn gradually from a given direction; as, the road curves to the right.
v. i.
To restore health; to effect a cure.
v. t.
To make or shape by cutting, sculpturing, or engraving; to form; as, to carve a name on a tree.
a.
Having the ribs or the veins of the leaves curved; -- called also curvinervate and curve-veined.
v. i.
To cut up meat; as, to carve for all the guests.