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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special c...
Curve - Wikipedia
Arc length
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Algebraic curve
Curve - Wikipedia
Pi Day Hits a Milestone That Comes Only Once a Century: 3/14/15
Pi Day was dreamed up 27 years ago to celebrate 3.14 on 3/14, but this year the geek dial is being turned up to 15 — as in 3/14/15. And this'll be the only year until 2115 that you can turn the dial u...
Hilbert's twenty-first problem - Slideshow
Matrix representation of conic sections - Slideshow
Arc length
Determining the length of an irregular arc segment is also called rectification of a curve. Historically, many methods were used for specific curves. The advent of infinitesimal calculus led to a ge...
Arc length - Wikipedia
Algebraic curve
In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.For example, the unit circle is ...
Algebraic curve - Wikipedia
Pi Day Hits a Milestone That Comes Only Once a Century: 3/14/15
Pi Day was dreamed up 27 years ago to celebrate 3.14 on 3/14, but this year the geek dial is being turned up to 15 — as in 3/14/15. And this'll be the only year until 2115 that you can turn the dial u...
Truncus (mathematics)
In analytic geometry, a truncus is a curve in the Cartesian plane consisting of all points (x,y) satisfying an equation of the form where a, b, and c are given constants. The two asymptotes ...
Truncus (mathematics) - Wikipedia
Swastika curve
The swastika curve is the name given by Cundy and Rollett to the quartic plane curve with the Cartesian equationor, equivalently, the polar equationThe curve looks similar to the right-handed swastika...
Swastika curve - Wikipedia
Symmetric product of an algebraic curve
In mathematics, the n-fold symmetric product of an algebraic curve C is the quotient space of the n-fold cartesian productor C by the group action of the symmetric group on n letters permuting the fac...
Sierpinski triangle
The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an ...
Sierpinski triangle - Wikipedia
Generalised logistic function
The generalised logistic function or curve, also known as Richards' curve, originally developed for growth modelling, is an extension of the logistic or sigmoid functions, allowing for more flexible S...
Generalised logistic function - Wikipedia
Elkies trinomial curves
In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials givin...
Elkies trinomial curves - Wikipedia
Golden spiral
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every q...
Golden spiral - Wikipedia
Center of curvature
In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if th...
Chord (geometry)
A chord of a circle is a geometric line segment whose endpoints both lie on the circle. A secant line, or just secant, is the line extension of a chord. More generally, a chord is a line segment joini...
Chord (geometry) - Wikipedia
Epicycloid
In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping around a fixed circle. It is a particular kin...
Epicycloid - Wikipedia
Triple spiral
The triple spiral or triskele is a Celtic and pre-Celtic symbol found on a number of Irish Megalithic and Neolithic sites, most notably inside the Newgrange passage tomb, on the entrance stone, and o...
Triple spiral - Wikipedia
Hilbert's twenty-first problem
The twenty-first problem of the 23 Hilbert problems, from the celebrated list put forth in 1900 by David Hilbert, concerns the existence of a certain class of linear differential equations with spec...
Spline (mathematics)
In mathematics, a spline is a numeric function that is piecewise-defined by polynomial functions, and which possesses a sufficiently high degree of smoothness at the places where the polynomial pieces...
Spline (mathematics) - Wikipedia
Modular curve
In number theory and algebraic 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 by the action of a...
Modular curve - Wikipedia
Superegg
In geometry, a superegg is a solid of revolution obtained by rotating an elongated super-ellipse with exponent greater than 2 around its longest axis. It is a special case of super-ellipsoid. Unlik...
Superegg - Wikipedia
De Rham curve
In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham.The Cantor function, Cesàro curve, Minkowski's question mark function, the Lévy C curve, the blancm...
De Rham curve - Wikipedia
Bitangents of a quartic
In real algebraic geometry, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These lines exist in the complex projective plane, but it is possib...
Bitangents of a quartic - Wikipedia
Intrinsic equation
In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location an...
Intrinsic equation - Wikipedia
Fundamental theorem of curves
In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size) completely determined by...
Conchoid of Dürer
The conchoid of Dürer, also called Dürer's shell curve, is a variant of a conchoid or plane algebraic curve, named after Albrecht Dürer. It is not a true conchoid.
Let Q and R be points moving on...
Conchoid of Dürer - Wikipedia
Hodge bundle
In mathematics, the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves. Furthermore, it has a...
Pascal's theorem
In projective geometry, Pascal's theorem (also known as the Hexagrammum Mysticum Theorem) states that if six arbitrary points are chosen on a conic (i.e., ellipse, parabola or hyperbola) and joined by...
Pascal's theorem - Wikipedia
Sierpiński curve
Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit completely fill the unit square: thus their limit cu...
Sierpiński curve - Wikipedia