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{{short description|Online mathematics resource for cubic plane curves}} ...umber of the first entry in the catalogue is "K001" which is the [[Neuberg cubic]] of the reference triangle {{mvar|ABC}}. The catalogue provides, among oth ...

...plane of a reference [[triangle]] and associated with it. It is the third cubic curve in Bernard Gilbert's [[Catalogue of Triangle Cubics]] and it is assig {{legend-line|solid red|'''McCay cubic''': [[Locus (mathematics)|locus]] of {{mvar|P}} such that the pedal circle ...

...cil (mathematics)|pencil]] (one-dimensional family) of [[Cubic plane curve|cubic plane]] [[elliptic curve]]s in the [[complex projective plane]], defined by ...or | author2-link = Igor Dolgachev | title=The Hesse pencil of plane cubic curves | arxiv = math/0611590 | mr = 2583779 | year=2009 | journal=L'Enseignement ...

...rch and Swinnerton-Dyer conjecture]] for a positive proportion of elliptic curves. ...

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

{{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]] ...

{{Short description|Mathematical curves that are isomorphic over algebraic closures}} ...is an invertible isogeny. Some curves have higher order twists such as '''cubic''' and '''quartic twists'''. The curve and its twists have the same [[j-inv ...

...The genus–degree formula is a generalization of this fact to higher genus curves. The basic idea would be to use higher degree equations. Consider the quart ...a line). When the points of infinity are added, we get a line meeting the cubic in 3 points. The complex picture of this reducible curve looks like a torus ...

Given four [[space]] curves ''c''₀(''s''), ''c''₁(''s''), ''d''₀(''t'' ...rves. To fix this problem, the linear interpolation can be replaced with [[cubic Hermite spline]]s with the weights chosen to match the partial derivatives ...

...identification number K001,<ref name="K001">{{cite web |title=K001 Neuberg cubic |url=http://bernard-gibert.fr/Exemples/k001.html|access-date=29 November 20 [[File:NeubergCurve.png|thumb|Neuberg cubic of triangle {{math|△''ABC''}} showing one of the defining properties of an ...

In [[projective geometry]], the '''Laguerre–Forsyth invariant''' is a cubic differential that is an invariant of a projective plane curve. It is named A key property of {{math|''P''}} is that the cubic differential {{math|''P''(''dt'')³}} is invariant under the auto ...

*[[Cubic surface]] (The union of a cubic surface and a plane is another particular type of quartic surface) ...

...al computer graphics applications.<ref name=":0" /> Its advantage over the cubic spline curve is its stability with respect to outliers.<ref>{{Cite book |la ...hose value between <math>x_i</math> and <math>x_{i+1}</math> is the unique cubic polynomial <math>P_i(x)</math>, ...

...]] of genus 2 curves with level 2 structure. It is the dual of the [[Segre cubic]]. ...

...e they are [[Two-dimensional space|bi-dimensional]] [[Spline interpolation|cubic splines]].<ref name="mitchell-netravali">{{cite conference |last1=Mitchell ...le filters from this family, such as [[Continuous function|discontinuous]] curves, two parameters <math>B</math> and <math>C</math> remain, through which the ...

...torsion conjecture has been completely resolved in the case of [[elliptic curves]]. ==Elliptic curves== ...

The ''tangent-chord process'' (one form of [[addition theorem]] on a [[cubic curve]]) had been known as far back as the seventeenth century. The process ...up the subject, producing the generalisation to Jacobians of higher genus curves over arbitrary number fields in his doctoral dissertation<ref>{{cite thesis ...

...', in short '''PN triangle''', is an interpolation algorithm to retrieve a cubic [[Bézier triangle]] from the vertex coordinates of a regular [[Triangle|fla ...ngle page the nomenclature follows G. Farin (2002),<ref>{{Cite book |title=Curves and surfaces for CAGD : a practical guide |last=Farin |first=Gerald E. |dat ...

# The [[cubic curve]] through 9 points; # The cubic curve with a [[double point]] through 6 points; ...

...al lattice vectors. This results in a very complicated set intersecting of curves when the dispersion relations are calculated because there is a large numbe ...three kinds of crystal structures: the BCC and FCC [[cubic crystal system|cubic crystal structures]] and the [[hexagonal crystal system|hexagonal]] close-p ...