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Curve - Wikipedia
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is […] the … See more
Interest in curves began long before they were the subject of mathematical study. This can be seen in numerous examples of their decorative use in art and on everyday objects … See more
Roughly speaking a differentiable curve is a curve that is defined as being locally the image of an injective differentiable function $${\displaystyle \gamma \colon I\rightarrow X}$$ from an interval I of the real numbers into a differentiable manifold X, often See more
A topological curve can be specified by a continuous function $${\displaystyle \gamma \colon I\rightarrow X}$$ from an interval I of the real numbers into a topological space X. Properly speaking, the curve is the image of $${\displaystyle \gamma .}$$ See more
Algebraic curves are the curves considered in algebraic geometry. A plane algebraic curve is the set of the points of coordinates x, y such … See more
• Famous Curves Index, School of Mathematics and Statistics, University of St Andrews, Scotland
• Mathematical curves A collection of 874 two-dimensional mathematical curves
• Gallery of Space Curves Made from Circles, includes … See moreWikipedia text under CC-BY-SA license List of curves - Wikipedia
Rational curves are subdivided according to the degree of the polynomial.
• Line
Plane curves of degree 2 are known as conics or conic sections and include
• Circle
• EllipseWikipedia · Text under CC-BY-SA licenseCurvature - Wikipedia
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
List of mathematical shapes - Wikipedia
Following is a list of shapes studied in mathematics. See the list of algebraic surfaces. Monkey saddle (saddle-like surface for 3 legs.) This table shows a summary of regular polytope counts …
Gallery of curves - Wikipedia
This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves.
Differentiable curve - Wikipedia
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 and integral calculus. Many specific curves have been thoroughly investigated …
Algebraic curve - Wikipedia
In 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 plane of a homogeneous …
Curve - Simple English Wikipedia, the free encyclopedia
A curve is a line that turns or bends. A curved line is never straight, and a curved surface is a surface that is never flat. Some curves can be drawn on paper, but some curves, like a helix, …
Differential geometry of surfaces - Wikipedia
Curves on a surface which minimize length between the endpoints are called geodesics; they are the shape that an elastic band stretched between the two points would take. Mathematically they are described using ordinary …
Family of curves - Wikipedia
The Apollonian circles, two orthogonal families of circles.. In geometry, a family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the …
Affine differential geometry - Wikipedia
Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name affine differential geometry follows from Klein's …
Transcendental curve - Wikipedia
In analytical geometry, a transcendental curve is a curve that is not an algebraic curve. [1] Here for a curve, C, what matters is the point set (typically in the plane) underlying C, not a given …
Algebraic geometry - Simple English Wikipedia, the free …
Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and …
Glossary of classical algebraic geometry - Wikipedia
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of …
Line - Simple English Wikipedia, the free encyclopedia
In geometry, the word line means a straight line. A straight line is the shortest distance between two points. A straight line is traced by a point moving in a direction that does not change. A …
Morphism of algebraic varieties - Wikipedia
In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.It is also called a regular map.A morphism from an …
List of curves - Wikipedia, the free encyclopedia - Zubiaga
Aug 2, 2008 · This is a list of curves, by Wikipedia page. See also list of curve topics, list of surfaces, Riemann surface.
Surface (mathematics) - Wikipedia
A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, …
The horizontal curves are, by definition, circular curves of radius R. The elements of a horizontal curve are shown in Figure 7.9 and summarized (with units) in Table 7.2.
Differential geometry - Encyclopedia of Mathematics
Mar 26, 2023 · A branch of geometry dealing with geometrical forms, mainly with curves and surfaces, by methods of mathematical analysis. In differential geometry the properties of …
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