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...rface]] all of whose generators are parallel to a fixed [[Plane (geometry)|plane]]. ...same plane, called the ''[[Directrix (rational normal scroll)|directrix]] plane'' of the surface. This can be characterized by the condition: the [[Scalar ...

{{Short description|Mathematical invariants used to classify plane curves}} ...^-</math>, and <math>St</math>—provide ways to classify and understand how curves can be deformed while preserving certain properties.<ref name="mai2022">Mai ...

[[File:Bezier curves.png|thumb|right|Sample curves (red) with their polygons (grey).]] == Variation diminishing property for Bézier curves == ...

...plane curve|cubic plane]] [[elliptic curve]]s in the [[complex projective plane]], defined by the equation ...math>\lambda,\mu</math>) (not both zero) and consists of the points in the plane whose [[homogeneous coordinates]] <math>(x,y,z)</math> satisfy the equation ...

...ed ''principal directions'' which give the directions in which the surface curves the most and the least. The theorem is named for [[Leonhard Euler]] who pr ...vector|unit]]) [[tangent vector]] to ''M'' at ''p'', there passes a normal plane ''P''_''X'' which cuts out a curve in ''M''. That curve has a ce ...

...'Cayley's sextic''' ('''sextic of Cayley''', '''Cayley's sextet''') is a [[plane curve]], a member of the [[sinusoidal spiral]] family, first discussed by [ ...book | first=J. Dennis | last=Lawrence | title=A catalog of special plane curves | publisher=Dover Publications | year=1972 | isbn=0-486-60288-5 | page=[htt ...

...|first=Richard|date=2014-03-25|title=Lectures on Moduli Spaces of Elliptic Curves|class=math.AG|eprint=0812.1803}}</ref> there is a moduli space of principal ...s the upper half plane, which appears prominently in the study of elliptic curves. In general, any point <math>\Omega \in H_g</math> gives a complex torus < ...

The classic [[Spirograph]] toy traces out these curves. [[Category:Plane curves]] ...

{{short description|1=Family of curves of the form r^n = a^n cos(nθ)}} In [[algebraic geometry]], the '''sinusoidal spirals''' are a family of curves defined by the equation in [[polar coordinates]] ...

...s the degree <math>d</math> of an [[Irreducible polynomial|irreducible]] [[plane curve]] <math>C</math> with its [[arithmetic genus]] <math>g</math> via the ...ane curve" means that <math>C</math> is a closed curve in the [[projective plane]] <math>\mathbb{P}^2</math>. If the curve is non-singular the [[geometric g ...

...stein|Bernstein]], Lange, and Kohel.<ref>{{cite web |title=Twisted Hessian curves |url=http://hyperelliptic.org/EFD/g1p/auto-twistedhessian.html |accessdate= ...curves]], and Hessian curves are just the special case of twisted Hessian curves in which {{Math|1=''a'' = 1}}. ...

{{short description|Online mathematics resource for cubic plane curves}} ...ngle Cubics |url=http://bernard-gibert.fr/ |website=Cubics in the Triangle Plane |publisher=Bernard Gibert |access-date=27 November 2021}}</ref> The resourc ...

...]], the '''total curvature''' of an [[immersion (mathematics)|immersed]] [[plane curve]] is the [[integral]] of [[curvature]] along a curve taken with respe It is 2{{pi}} for [[convex curve]]s in the plane, and larger for non-convex curves.<ref>{{citation ...

Given four [[space]] curves ''c''₀(''s''), ''c''₁(''s''), ''d''₀(''t'' ...urfaces to be joined, leading to creases in the joined surface along those curves. To fix this problem, the linear interpolation can be replaced with [[cubic ...

...n {{mvar|n}}-ellipse is the [[locus (mathematics)|locus]] of points of the plane whose sum of distances to the {{mvar|n}} foci is a constant {{mvar|d}}. In ...Vincze (mathematician)|title=On the Approximation of Convex, Closed Plane Curves by Multifocal Ellipses|journal=Journal of Applied Probability|date=1982|vol ...

In mathematics, an '''Artin–Schreier curve''' is a [[plane curve]] defined over an algebraically closed field of characteristic <math> ...pages=139–150 |doi= 10.1007/BF02252872}}</ref> It is common to write these curves in the form ...

{{Short description|Mathematical plane curve}} In mathematics, '''Wiman's sextic''' is a degree 6 [[plane curve]] with four [[Singular point of an algebraic variety|nodes]] studied ...

...oduced separately: [[Möbius plane]]s, [[Laguerre plane]]s, and [[Minkowski plane]]s.<ref>W. Benz, ''Vorlesungen über Geomerie der Algebren'', [[Springer Sci == Möbius plane == ...

{{short description|Plane curve unique to a given triangle}} ...rt |access-date=5 December 2021}}</ref>) is a [[cubic plane curve]] in the plane of a reference [[triangle]] and associated with it. It is the third cubic c ...

[[File:Two cubic curves.png|thumb|The nine intersections of <math>x^3 - x = 10(y^3 - y)</math> and ...oints of intersection of two higher-order curves in the [[plane (geometry)|plane]] can be greater than the number of arbitrary points that are usually neede ...