2-dimensional Euclidean space

URI: https://gptkb.org/entity/2-dimensional_Euclidean_space
GPTKB entity
Statements (50)
Predicate Object
gptkbp:instanceOf gptkb:Euclidean_space
gptkbp:basisFor standard basis (i, j)
gptkbp:connectedTo gptkb:complex_plane
affine plane
vector space over R
gptkbp:coordinates gptkb:polar_coordinates
Cartesian coordinates
gptkbp:describedBy axioms of Euclidean geometry
gptkbp:dimensions 2
gptkbp:hasAngleMeasure degrees
radians
gptkbp:hasArea area = base × height for rectangles
area = πr^2 for circles
gptkbp:hasDistanceFormula sqrt((x2-x1)^2 + (y2-y1)^2)
gptkbp:hasInnerProduct dot product
gptkbp:hasSubgroup gptkb:n-dimensional_Euclidean_space
lines
points
polygons
curves
gptkbp:includesMetric Euclidean metric
gptkbp:isomorphicTo R^2
gptkbp:originatedIn (0, 0)
gptkbp:represents ordered pairs (x, y)
gptkbp:symmetry Euclidean group E(2)
gptkbp:usedFor gptkb:computer_graphics
gptkb:algebraic_geometry
gptkb:navigation
gptkb:topology
gptkb:data_visualization
complex analysis
differential geometry
physics simulations
robotics
statistics
optimization
vector calculus
linear algebra
analytic geometry
map projections
trigonometry
artificial intelligence (spatial reasoning)
machine learning (feature spaces)
gptkbp:usedIn gptkb:geometry
engineering
physics
gptkbp:visualizes gptkb:aircraft
gptkbp:bfsParent gptkb:4-dimensional_Euclidean_space
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label 2-dimensional Euclidean space