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...

curve. Topologically, a complex elliptic curve is a torus, while a complex ellipse is a sphere. Although the formal definition of an elliptic curve requires...

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...

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...

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

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

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...

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

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

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...

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

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 ⁡...

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:...

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

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...

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

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

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...

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...

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...

proved Thurston's ending lamination conjecture and as a student of curve complex geometry. Minsky obtained his Ph.D. from Princeton University in 1989...

unit hyperbola group. 4-manifold Clifford-Klein form Closed timelike curve Complex spacetime Geometrodynamics Gravitational singularity Hantzsche-Wendt...

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...

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...

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...