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....

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...

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...

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...

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...

complex analysis, geometric topology, differential geometry, and physics (such as in string theory). Suppose we are given a closed, oriented curve in...

smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose...

A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay, French pronunciation: [bezje]) is a parametric curve used in computer graphics and related fields. A set of discrete...

where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour...

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...

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:...

In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way...

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...

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...

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...

evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible...

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...

{\displaystyle \mathbb {C} /(\mathbb {Z} +\tau \mathbb {Z} )} (a complex elliptic curve) for a complex number τ ∈ H {\displaystyle \tau \in \mathbb {H} } where...

geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map, from a Riemann surface into an almost complex manifold, that satisfies the...

Laffer curve illustrates a theoretical relationship between rates of taxation and the resulting levels of the government's tax revenue. The Laffer curve assumes...

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 ⁡...

the j-invariant for which a complex elliptic curve has complex multiplication. The complex elliptic curves with complex multiplication are those for...

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...

memorizing the word set. (More detail about the complex processes of learning are discussed in the Learning curve article.) This was later more generalized...

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...

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...

A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have...

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...

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...

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC...