Points on the Curve is the second studio album by the English new wave band Wang Chung, released in 1984. Points on the Curve is Wang Chung's first studio...

unions of curves and isolated points), and algebraic curves (see below). Level curves and algebraic curves are sometimes called implicit curves, since they...

and describes points in K2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described...

A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines...

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

such curves has singular points (see Genus–degree formula). A non-plane curve is often called a space curve or a skew curve. An algebraic curve in the Euclidean...

the rational points on the curve, from which all further rational points may be generated. If the number of rational points on a curve is infinite then...

a point on the frontier indicates efficient use of the available inputs (such as points B, D and C in the graph), a point beneath the curve (such as A)...

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints...

defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is tangent to the curve y = f(x) at a point...

at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector...

Control points are always either connected directly to the curve or surface, or else act as if they were connected by a rubber band. Depending on the type...

the type of curve being studied. Algebraic curves in the plane may be defined as the set of points (x, y) satisfying an equation of the form f ( x ,...

point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function...

in the study of elliptic curves is devising effective ways of counting points on the curve. There have been several approaches to do so, and the algorithms...

(known as the elliptic curve discrete logarithm problem by analogy to other cryptographic systems). This is because the addition of two points on an elliptic...

computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features. The following...

In microeconomics, the contract curve or Pareto set is the set of points representing final allocations of two goods between two people that could occur...

Hasse's theorem on elliptic curves, also referred to as the Hasse bound, provides an estimate of the number of points on an elliptic curve over a finite...

used to express the coordinates of the points that make up a geometric object such as a curve or surface, called a parametric curve and parametric surface...

system, a superellipse is defined as the set of all points ( x , y ) {\displaystyle (x,y)} on the curve that satisfy the equation | x a | n + | y b | n =...

are plotted on the two axes; the curve is the locus of points showing the consumption bundles chosen at each of various levels of income. The income effect...

of rational points. On the other hand, if the rank of the curve is greater than 0, then the curve has an infinite number of rational points. Although Mordell's...

phrased in terms of smooth curves joining pairs of points. Conditions on the tangent vectors of the curves then define the causal relationships. If (...

projective curves, the behavior of rational points depends strongly on the genus of the curve. Every smooth projective curve X of genus zero over a field k is isomorphic...

plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally...

more variables, and the interval of integration is replaced by a curve connecting two points in space. In a surface integral, the curve is replaced by a...

connecting up the geometries of points on a curve is tantamount to providing a connection. In fact, the usual notion of connection is the infinitesimal...

In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent...

assure the point is on the curve. One can define Addition of two points on the curve, to define a group. The addition laws are given in the article on elliptic...