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{{Short description|none}}
This is a '''gallery of [[curve]]s''', by Wikipedia page. See also [[list of curves]].
This is a '''gallery of [[curve]]s''' used in [[mathematics]], by Wikipedia page. See also [[list of curves]].


==[[Algebraic curve]]s==
==[[Algebraic curve]]s==
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====[[Degree of a polynomial|Degree]] 1====
====[[Degree of a polynomial|Degree]] 1====
<gallery>
<gallery class=center>
File:FuncionLineal01.svg|[[Line (mathematics)|Line]]
File:FuncionLineal01.svg|[[Line (mathematics)|Line]]
</gallery>
</gallery>


====Degree 2====
====Degree 2====
<gallery>
<gallery class=center>
File:Circle-withsegments.svg|[[Circle]]
File:Circle-withsegments.svg|[[Circle]]
File:Ellipse Properties of Directrix and String Construction.svg|[[Ellipse]]
File:Ellipse Properties of Directrix and String Construction.svg|[[Ellipse]]
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====Degree 3====
====Degree 3====
<gallery>
<gallery class=center>
File:CubeChart.svg|[[Cube (algebra)|Cubic curve]]
File:CubeChart.svg|[[Cube (algebra)|Cubic curve]]
File:Polynomialdeg3.svg|[[Cubic polynomial]]
File:Polynomialdeg3.svg|[[Cubic polynomial]]
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====Degree 4====
====Degree 4====
<gallery>
<gallery class=center>
File:Ampersandcurve.svg|[[Ampersand curve]]
File:Ampersandcurve.svg|[[Ampersand curve]]
File:Bean_curve.svg|[[Bean curve]]
File:Bean_curve.svg|[[Bean curve]]
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File:Spiric section.svg|[[Spiric section]]s
File:Spiric section.svg|[[Spiric section]]s
File:Squircle2.svg|[[Squircle]]
File:Squircle2.svg|[[Squircle]]
File:Swastika curve.svg|[[Swastika curve]]
File:Three-leaved_clover_polar.svg|[[Quartic plane curve#Three-leaved clover|Trifolium Curve]]
File:Three-leaved_clover_polar.svg|[[Quartic plane curve#Three-leaved clover|Trifolium Curve]]
File:Trott.png|[[Trott curve]]
<!-- Commented out: File:Trott.png|[[Trott curve]] -->
</gallery>
</gallery>


====Degree 5====
====Degree 5====
<gallery>
File:Example of a hyperelliptic curve.svg|[[Hyperelliptic curve]]
</gallery>


====Degree 6====
====Degree 6====
<gallery>
<gallery class=center>
File:HypotrochoidOn4.gif|[[Astroid]]
File:HypotrochoidOn4.gif|[[Astroid]]
File:Atriph05.svg|[[Atriphtaloid]]
File:Atriph05.svg|Atriphtaloid
File:Neph0b.png|[[Nephroid]]
File:Neph0b.png|[[Nephroid]]
File:Quadrifolium.svg|[[Quadrifolium]]
File:Quadrifolium.svg|[[Quadrifolium]]
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====Families of variable degree====
====Families of variable degree====
<gallery>
<gallery class=center>
File:EpitrochoidOn3-generation.gif|[[Epicycloid]]
File:EpitrochoidOn3-generation.gif|[[Epicycloid]]
File:Epispiral.svg|[[Epispiral]]
File:Epispiral.svg|[[Epispiral]]
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===Curves of genus one===
===Curves of genus one===
<gallery>
<gallery class=center>
File:Bicuspid_curve.svg|[[Bicuspid curve]]
File:Bicuspid_curve.svg|[[Bicuspid curve]]
File:Line_of_Cassini.svg|[[Cassini oval]]
File:Line_of_Cassini.svg|[[Cassini oval]]
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===Curves with genus greater than one===
===Curves with genus greater than one===
<gallery>
<gallery class=center>
File:Butterfly_curve.png|[[Butterfly curve (algebraic)]]
File:Butterfly_curve.png|[[Butterfly curve (algebraic)]]
File:C168.svg|[[Elkies trinomial curves]]
File:C168.svg|[[Elkies trinomial curves]]
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===Curve families with variable genus===
===Curve families with variable genus===
<gallery>
<gallery class=center>
⚫
File:Cyc7.png|[[Polynomial lemniscate]]
File:Erdos5.png|[[Polynomial lemniscate|Erdős lemniscate]]
File:Erdos5.png|[[Polynomial lemniscate|Erdős lemniscate]]
⚫
File:Order-7 triangular tiling.svg|[[Hurwitz surface]]
File:Mandelcurve2.png|[[Polynomial lemniscate|Mandelbrot curve]]
File:Mandelcurve2.png|[[Polynomial lemniscate|Mandelbrot curve]]
⚫
File:Cyc7.png|[[Polynomial lemniscate]]
File:Sinusoidal_spirals.svg|[[Sinusoidal spiral]] <!-- Not actually a spiral -->
File:Sinusoidal_spirals.svg|[[Sinusoidal spiral]] <!-- Not actually a spiral -->
File:Superellipse_chamfered_square.svg|[[Superellipse]]
File:Superellipse_chamfered_square.svg|[[Superellipse]]
⚫
File:Order-7 triangular tiling.svg|[[Hurwitz surface]]
</gallery>
</gallery>


==Transcendental curves==
==Transcendental curves==
<gallery>
<gallery class=center>
File:Lissajous_curve_5by4.svg|[[Bowditch curve]]
File:Lissajous_curve_5by4.svg|[[Bowditch curve]]
File:Brachistochrone.svg|[[Brachistochrone]]
File:Brachistochrone.svg|[[Brachistochrone]]
File:Butterfly_trans01.svg|[[Butterfly curve (transcendental)]]
File:Butterfly transcendental curve.svg|[[Butterfly curve (transcendental)]]
File:Catenary-pm.svg|[[Catenary]]
File:Catenary-pm.svg|[[Catenary]]
File:Clelies_curve.png|[[Clélies]]
File:Clelies_curve.png|[[Clélies]]
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=== Spirals ===
=== Spirals ===
<gallery>
<gallery class=center>
File:Archimedean_spiral_polar.svg|[[Archimedean spiral]]
File:Archimedean_spiral_polar.svg|[[Archimedean spiral]]
File:Euler_spiral.svg|[[Cornu spiral]]
File:Euler_spiral.svg|[[Cornu spiral]]
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==Piecewise constructions==
==Piecewise constructions==
<gallery>
<gallery class=center>
File:Maurer_roses.svg|[[Maurer rose]]
File:Maurer_roses.svg|[[Maurer rose]]
File:ReuleauxTriangle.svg|[[Reuleaux triangle]]
File:ReuleauxTriangle.svg|[[Reuleaux triangle]]
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==Fractal curves==
==Fractal curves==
<gallery>
<gallery class=center>
File:Blancmange-function.svg|[[Blancmange curve]]
File:Blancmange-function.svg|[[Blancmange curve]]
File:Cesaro-0.5.png|[[De Rham curve]]
File:Cesaro-0.5.png|[[De Rham curve]]
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File:KochFlake.svg|[[Koch snowflake|Koch curve]]
File:KochFlake.svg|[[Koch snowflake|Koch curve]]
File:Levy_C_construction.png|[[Lévy C curve]]
File:Levy_C_construction.png|[[Lévy C curve]]
File:Peanocurve.svg|[[space-filling curve|Peano curve]]
File:Peanocurve.svg|[[Peano curve]]
File:Sierpinski-Curve-3.png|[[Sierpiński curve]]
File:Sierpinski-Curve-3.png|[[Sierpiński curve]]
</gallery>
</gallery>
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[[Species-area curve]]
[[Species-area curve]]
[[Stress-strain curve]]-->
[[Stress-strain curve]]-->

==Curves in art==
<gallery>
File:Slow Curve by artist Julian Hatton.jpeg|Curves in abstract expressionism: ''Slow Curve'' by [[Julian Hatton]]
File:Van Gogh - Starry Night - Google Art Project.jpg|Curves in Post-impressionism: ''Starry Night'' by [[ Vincent van Gogh]]
</gallery>


==External links==
==External links==
* [http://xahlee.org/SpecialPlaneCurves_dir/specialPlaneCurves.html Visual Dictionary of Special Plane Curves]
* [http://xahlee.info/SpecialPlaneCurves_dir/specialPlaneCurves.html Visual Dictionary of Special Plane Curves]


{{Curves}}
{{Curves}}


[[Category:Curves|*]]
[[Category:Curves|*]]
[[Category:Image galleries]]

Latest revision as of 01:55, 24 July 2024

This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves.

Algebraic curves

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Rational curves

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Degree 1

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Degree 2

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Degree 3

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Degree 4

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Degree 5

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Degree 6

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Families of variable degree

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Curves of genus one

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Curves with genus greater than one

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Curve families with variable genus

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Transcendental curves

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Spirals

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Piecewise constructions

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Fractal curves

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