In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases...

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 plane of a homogeneous...

In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation ⁠ F ( x , y , z ) = 0 {\displaystyle F(x,y,z)=0} ⁠ applied...

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...

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...

differentiable curve. A plane algebraic curve is the zero set of a polynomial in two indeterminates. More generally, an algebraic curve is the zero set...

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...

Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides the plane into an...

line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined...

characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: y 2 = x 3...

the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal...

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...

differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the osculating plane. Taken together, the...

invariants – any two plane curves with the same turning number are regular homotopic. Every immersed plane curve lifts to an embedded space curve via separating...

In mathematics, a real plane curve is usually a real algebraic curve defined in the real projective plane. The field of real numbers is not algebraically...

dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to...

geometry, an osculating curve is a plane curve from a given family that has the highest possible order of contact with another curve. That is, if F is a family...

one, space-filling curves in the 2-dimensional plane are sometimes called Peano curves, but that phrase also refers to the Peano curve, the specific example...

winding index of a closed curve in the plane around a given point is an integer representing the total number of times that the curve travels counterclockwise...

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential...

every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint...

An oval (from Latin ovum 'egg') is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas of...

In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without...

The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989. The curve is given by the...

every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint...

convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going...

In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the...

In Euclidean geometry, the Neuberg cubic is a special cubic plane curve associated with a reference triangle with several remarkable properties. It is...

algebraic geometry, the Tschirnhausen cubic, or Tschirnhaus' cubic is a plane curve defined, in its left-opening form, by the polar equation r = a sec 3...

Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each...