3-dimensional Euclidean space

URI: https://gptkb.org/entity/3-dimensional_Euclidean_space
GPTKB entity
Statements (51)
Predicate Object
gptkbp:instanceOf gptkb:Euclidean_space
gptkb:Vector
gptkbp:basisFor standard basis (e1, e2, e3)
gptkbp:coordinates gptkb:cylindrical_coordinates
gptkb:spherical_coordinates
Cartesian coordinates
gptkbp:dimensions 3
gptkbp:field real numbers
gptkbp:hasApplication gptkb:architecture
computer graphics
mechanics
robotics
gptkbp:hasConnection yes
gptkbp:hasGroupOfIsometries gptkb:Euclidean_group_E(3)
gptkbp:hasInnerProduct dot product
gptkbp:hasNorm Euclidean norm
gptkbp:hasSubspaces lines
points
planes
https://www.w3.org/2000/01/rdf-schema#label 3-dimensional Euclidean space
gptkbp:includesMetric Euclidean metric
gptkbp:isAffineSpace yes
gptkbp:isBanachSpace yes
gptkbp:isFiniteDimensional yes
gptkbp:isFlat yes
gptkbp:isHausdorff yes
gptkbp:isHilbertSpace yes
gptkbp:isHomogeneous yes
gptkbp:isInnerProductSpace yes
gptkbp:isIsotropic yes
gptkbp:isLocallyCompact yes
gptkbp:isManifold yes
gptkbp:isMetricSpace yes
gptkbp:isNormedVectorSpace yes
gptkbp:isOrientable yes
gptkbp:isParacompact yes
gptkbp:isRealVectorSpace yes
gptkbp:isSecondCountable yes
gptkbp:isSeparable yes
gptkbp:isSmoothManifold yes
gptkbp:isStandardModelFor physical space
gptkbp:isTopologicalVectorSpace yes
gptkbp:notation R^3
gptkbp:numberOfIssues yes
gptkbp:originatedIn (0,0,0)
gptkbp:subclassOf gptkb:n-dimensional_Euclidean_space
gptkbp:usedIn gptkb:geometry
engineering
physics
gptkbp:bfsParent gptkb:knot
gptkbp:bfsLayer 5