GeometricScene

Symbolic representations of notable constructions and theorems from plane geometry.

Entity [ "GeometricScene" , name ] or

represents an entity of type "GeometricScene" .

[ prop ]

gives the value of a specified property.

[ { prop i , } ]

gives the value of a list of properties.

EntityClass [ "GeometricScene" , { prop i spec i , } ]

represents a class of entities with values of prop i defined by spec i .

Sample Entities

Properties

  • AlternateNames alternate names
    AlternateScenes alternate scenes
    AlternateStatements alternate statements
    EntityClasses entity classes
    EponymousPeople eponymous people
    FormulationDates formulation dates
    FormulationSources formulation sources
    Formulators formulators
    GreekStatement statement in Greek
    HeathsStatement Heath's translation of Greek statement
    MathWorld related MathWorld terms
    Name name
    ProofDates proof dates
    ProofSources proof sources
    Provers provers
    RelatedDemonstrations related Wolfram Demonstrations
    RelatedScenes related geometric scenes
    Scene scene
    Statement statement

Details

  • "GeometricScene" entities include constructions and theorems from 2D Euclidean geometry.
  • ["Scene"] gives the GeometricScene object representing the scene.
  • "GeometricScene" entity classes include classes that describe the logical structure of a scene, such as "Constructions" and "Theorems", classes that describe the important geometric objects of a scene, such as "Lines" and "Circles", and classes of scenes coming from certain sources, such as "EuclidsElements" and "MathWorld" .
  • Some properties are available for the "GeometricScene" type as a whole and can be given using the form EntityValue [ "GeometricScene" , 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)
    "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
    "PropertyCount" number of properties available
  • The following annotations can be used in the third argument of EntityValue [ "GeometricScene" , property , annotation ] for a property or list of properties:
  • "Association" a nested association with entity keys on the first level and property keys on the second level
    "Dataset" a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
    "EntityAssociation" an association of entities and entity-property values
    "NonMissingEntityAssociation" an association of properties and entity-property values with the missing values dropped
  • The following annotations can be used in the third argument of EntityValue [ "GeometricScene" , properties , annotation ] for a list of properties:
  • "EntityPropertyAssociation" an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "NonMissingPropertyAssociation" an association of entities and entity-property values with the missing values dropped
    "PropertyAssociation" an 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
  • The following annotation can be used in the second argument of EntityValue [ property , annotation ] :
  • "Description" a brief textual description of the property

Examples

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Basic Examples    (3)

Use for entity discovery:

Get the underlying GeometricScene for an entity:

Display an interactive instance of that scene:

Find geometric scenes named after Leonhard Euler:

Relations to Other Entity Types    (3)

The properties

,
and
give "Person" entities:

The property

gives "MathWorld" entities, often with the same name:

The property

gives "WolframDemonstration" entities:

Interactive Examples    (1)

Get a list of related Demonstrations from the Wolfram Demonstrations Project:

Get the interactive Demonstration: