Notable mathematical surfaces.

Entity["Surface",name] or

represents an entity of type "Surface".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

EntityClass["Surface",{propispeci,}]

represents a class of entities with values of propi defined by speci.

Sample Entities

Sample Entity Classes

Properties

  • AlgebraicDegreealgebraic degree
    AlgebraicEquationalgebraic equation
    AlternateNamesalternate names
    AreaElementarea element
    AssociatedPeopleassociated people
    CartesianEquationCartesian equation
    Centroidcentroid of solid
    ChristoffelSymbolOfTheSecondKindChristoffel symbol of the second kind
    ChromaticNumber(map) chromatic number
    Classesclasses
    CrossSectionscross sections
    EntityClassesentity classes
    EulerCharacteristicEuler characteristic
    FilledRegionfilled region
    FirstFundamentalFormcoefficients of the first fundamental form
    GaussianCurvatureGaussian curvature
    GeneralizedDiametergeneralized diameter
    Genusgenus
    Graphics3D3D graphics
    Imageimage
    ImplicitGaussianCurvatureimplicit Gaussian curvature
    ImplicitMeanCurvatureimplicit mean curvature
    ImplicitNormalVectorimplicit normal vector
    InertiaTensormoment of inertia tensor of solid
    LineSegmentLengthCDFCDF of lengths
    LineSegmentLengthMeanmean line segment length
    LineSegmentLengthPDFPDF of lengths
    MeanCurvaturemean curvature
    MetricTensormetric tensor
    Namename
    NodeCountnumber of nodes
    NormalVectornormal vector
    Parametersparameters
    ParametricEquationsparametric equations
    PrincipalCurvaturesprincipal curvatures
    PunctureCountnumber of punctures
    RelatedWolframLanguageSymbolsrelated Wolfram Language symbols
    RicciTensorRicci tensor
    RiemannTensorRiemann tensor
    SecondFundamentalFormcoefficients of the second fundamental form
    SemialgebraicDescriptionsemialgebraic description
    SingularPointssingular points
    SportObjectssport objects
    SurfaceAreasurface area
    VariableConstraintsvariable constraints
    VariableDescriptionsvariable descriptions
    Variablesvariables
    VectorLengthvector length
    Volumevolume of solid

Details

  • "Surface" entities include named mathematical surfaces.
  • "Surface" entity classes include mathematical classifications based on curvature, algebraic degree, geometric characteristics and topology.
  • Some properties are available for the "Surface" entity type as a whole and can be given using the form EntityValue["Surface",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["Surface",property,annotation]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (4)

Use for entity discovery:

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Find a property value for an entity:

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Retrieve a dataset of all available properties for an entity:

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Retrieve closed surfaces of algebraic degree two:

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