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gptkbp:instanceOf
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gptkb:mathematical_concept
mathematical discipline
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gptkbp:alternativeName
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Geometric_shape
Geometrie
Geometry
Projective_space
computational_geometry
finite_geometry
geodesic
geometric_construction
geometric_figure
geometric_object
geometric_shape
geometric_structure
projective_geometry
projective_space
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|
gptkbp:application
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gptkb:algebraic_geometry
computer vision
physics
perspective in art
projective transformations
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gptkbp:appliesTo
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gptkb:architecture
gptkb:art
gptkb:astronomy
gptkb:navigation
computer graphics
engineering
geography
physics
robotics
|
|
gptkbp:built
|
lines through the origin
quotient of vector space minus zero by scalar multiplication
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|
gptkbp:category
|
gptkb:algebraic_geometry
gptkb:topology
incidence geometry
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gptkbp:definedIn
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gptkb:Field
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gptkbp:dimension_1
|
projective line
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gptkbp:dimension_2
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projective plane
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gptkbp:dimension_3
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projective 3-space
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gptkbp:dimensions
|
n
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gptkbp:etymology
|
Greek: geo (earth) + metron (measure)
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gptkbp:field
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gptkb:mathematics
|
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gptkbp:generalizes
|
projective plane
projective line
|
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gptkbp:hasApplication
|
gptkb:navigation
robotics
surveying
|
|
gptkbp:hasConcept
|
gptkb:Vector
gptkb:aircraft
gptkb:butter
gptkb:music
gptkb:region
gptkb:stone
gptkb:street
gptkb:train
gptkb:Polygon
gptkb:symmetry
gptkb:transformation
gptkb:Riemannian_manifold
gptkb:intersection
cube
coordinate system
cone
parallelism
congruence
cylinder
Angle
dimension
quadrilateral
similarity
perimeter
|
|
gptkbp:hasSubfield
|
gptkb:algebraic_geometry
gptkb:geometry
gptkb:Euclidean_geometry
gptkb:Topology
gptkb:Algebraic_geometry
gptkb:Analytic_geometry
gptkb:Computational_geometry
gptkb:Differential_geometry
gptkb:Discrete_geometry
gptkb:Projective_geometry
Non-Euclidean geometry
|
|
gptkbp:homogeneous_coordinates
|
[x_0:x_1:...:x_n]
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
geometry
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gptkbp:introduced
|
gptkb:Jean-Victor_Poncelet
|
|
gptkbp:notableFigure
|
gptkb:Archimedes
gptkb:Carl_Friedrich_Gauss
gptkb:Euclid
gptkb:Pythagoras
gptkb:René_Descartes
|
|
gptkbp:notableWork
|
gptkb:Elements
|
|
gptkbp:notation
|
P^n
[mathbb{P}^n
|
|
gptkbp:originatedIn
|
gptkb:Ancient_Egypt
Ancient Greece
|
|
gptkbp:over_complex_numbers
|
complex projective space
|
|
gptkbp:over_finite_field
|
finite projective space
|
|
gptkbp:over_real_numbers
|
real projective space
|
|
gptkbp:property
|
gptkb:algebraic_geometry
gptkb:topology
quotient space
connected
homogeneous space
incidence structure
compact (over complex numbers)
every pair of lines meets
non-orientable (real projective space)
points at infinity
smooth manifold (over real or complex numbers)
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gptkbp:relatedConcept
|
gptkb:Euclidean_space
homogeneous coordinates
|
|
gptkbp:relatedTo
|
gptkb:algebra
gptkb:logic
calculus
Grassmannian
projective variety
trigonometry
projective bundle
projective group
|
|
gptkbp:studiedBy
|
gptkb:David_Hilbert
gptkb:Felix_Klein
gptkb:Oswald_Veblen
|
|
gptkbp:studies
|
positions
shapes
sizes
properties of space
relative positions of figures
|
|
gptkbp:theory
|
gptkb:Euler's_formula
gptkb:Euclid's_postulates
gptkb:Pythagorean_theorem
gptkb:Thales'_theorem
Triangle sum theorem
|
|
gptkbp:uses
|
gptkb:logic
axioms
postulates
proofs
theorems
|
|
gptkbp:bfsParent
|
gptkb:David_Hilbert
|
|
gptkbp:bfsLayer
|
3
|