For general access to the Wolfram Knowledgebase, use entities of type PlaneCurve instead of PlaneCurveData.


gives the value of the specified property for the plane curve entity.


gives a list of property values for the specified plane curve entities.


gives the specified annotation associated with the given property.


  • PlaneCurveData[] gives a list of all plane curve entities.
  • PlaneCurveData["Properties"] gives a list of available properties.
  • PlaneCurveData["SampleEntities"] gives a list of sample entities.
  • The specified entity in PlaneCurveData can be an Entity, EntityClass, entity canonical name, or list thereof.
  • The specified property can be an EntityProperty, EntityPropertyClass, property canonical name, or list of properties.
  • Properties that do not apply or are not known in a particular case are indicated by Missing[].
  • Properties include:
  • "Acnodes"acnodes
    "AlgebraicDegree"algebraic degree
    "AlgebraicEquation"algebraic equation
    "AlternateNames"alternate names
    "ArcLength"arc length
    "ArcLengthFunction"arc length function
    "Area"area enclosed
    "AreaImage"area enclosed plot
    "AreaMomentOfInertiaTensor"area moment of inertia tensor of enclosed lamina
    "AssociatedEntities"associated entities
    "AssociatedPeople"associated people
    "CartesianEquation"Cartesian equation
    "Centroid"centroid of enclosed lamina
    "CesaroEquation"Cesàro equation
    "ChordLength"chord length
    "Curvature"parametric curvature
    "DifferentialEquation"differential equation
    "FilledRegion"filled region
    "FocalParameter"focal parameter
    "Graphics"graphics expression
    "ImplicitCurvature"implicit curvature
    "ImplicitSlope"implicit slope
    "ImplicitVectorLength"implicit vector length
    "InfinitePoints"infinite points
    "InflectionPoints"inflection points
    "LatusRectum"latus rectum
    "LineSegmentLengthCDF"CDF of lengths
    "LineSegmentLengthMean"mean line segment length
    "LineSegmentLengthPDF"PDF of lengths
    "MajorAxis"major axis length (major diameter)
    "MinorAxis"minor axis length (minor diameter)
    "NaturalParametricEquations"natural parametric equations
    "NodeCount"node count
    "NormalVector"normal vector
    "NotationTable"notation table
    "ParallelCurve"parallel curve
    "ParametricEquations"parametric equations
    "PedalCurve"pedal curve
    "PolarCurvature"polar curvature
    "PolarEquation"polar equation
    "PolarSlope"polar slope
    "QuadruplePoints"quadruple points
    "RamphoidCusps"ramphoid cusps
    "RelatedWolframLanguageSymbols"related symbols in the Wolfram Language
    "SalientPoints"salient points
    "SemialgebraicDescription"semialgebraic description
    "SemilatusRectum"semilatus rectum
    "SemimajorAxis"semimajor axis length (major radius)
    "SemiminorAxis"semiminor axis length (minor radius)
    "SignedArea"signed area enclosed
    "SingularPoints"singular points
    "Slope"parametric slope
    "SpecialAffineCurvature"special affine curvature
    "SpecialCases"special cases
    "TangentialAngle"tangential angle
    "TangentVector"tangent vector
    "TriplePoints"triple points
    "VariableConstraints"variable constraints
    "VariableDescriptions"description of variables
    "VectorLength"vector length
    "WhewellEquation"Whewell equation


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Basic Examples  (8)

Use for entity discovery:

Find a list of sample entities of plane curves:

Use to discover properties of a plane curve:

Find properties of a plane curve:

Display an image of a plane curve:

Return people associated with a plane curve:

Find a list of sample entity classes of plane curves:

Find plane curves in a given class:

Properties & Relations  (2)

Using PlaneCurveData is equivalent to calling EntityValue on the corresponding entity and property:

Evaluate PlaneCurveData with "Classes" argument:

The above is equivalent to evaluating EntityClassList of the entity type "PlaneCurve":

Possible Issues  (1)

Entity classes cannot be given as bare strings:

Specifying an explicit EntityClass works as intended:

This is equivalent to calling EntityList on the EntityClass:

Interactive Examples  (1)

Dynamically plot the tangent and normal vectors of the trifolium curve as a function of parameter:

Neat Examples  (1)

Draw a set of sextic curves:

Wolfram Research (2014), PlaneCurveData, Wolfram Language function, (updated 2019).


Wolfram Research (2014), PlaneCurveData, Wolfram Language function, (updated 2019).


Wolfram Language. 2014. "PlaneCurveData." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019.


Wolfram Language. (2014). PlaneCurveData. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_planecurvedata, author="Wolfram Research", title="{PlaneCurveData}", year="2019", howpublished="\url{}", note=[Accessed: 13-June-2024 ]}


@online{reference.wolfram_2024_planecurvedata, organization={Wolfram Research}, title={PlaneCurveData}, year={2019}, url={}, note=[Accessed: 13-June-2024 ]}