spherical coordinates (in 3D)

URI: https://gptkb.org/entity/spherical_coordinates_(in_3D)
GPTKB entity
Statements (30)
Predicate Object
gptkbp:instanceOf coordinate system
gptkbp:azimuthalAngleDescription angle from positive x-axis in x-y plane
gptkbp:azimuthalAngleSymbol φ
gptkbp:conversionFromCartesian r = sqrt(x^2 + y^2 + z^2)
θ = arccos(z/r)
φ = arctan2(y, x)
gptkbp:conversionToCartesian x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ
gptkbp:coordinate3 gptkb:azimuthal_angle_(φ)
gptkbp:coordinates polar angle (θ)
radius (r)
gptkbp:dimensions 3
gptkbp:firstDescribed gptkb:Leonhard_Euler
18th century
gptkbp:generalizes gptkb:polar_coordinates
https://www.w3.org/2000/01/rdf-schema#label spherical coordinates (in 3D)
gptkbp:polarAngleDescription angle from positive z-axis
gptkbp:polarAngleSymbol θ
gptkbp:radiusDescription distance from origin
gptkbp:radiusSymbol r
gptkbp:relatedTo gptkb:cylindrical_coordinates
Cartesian coordinates
gptkbp:usedFor problems with spherical symmetry
gptkbp:usedIn gptkb:mathematics
engineering
physics
gptkbp:volumeElement r^2 sinθ dr dθ dφ
gptkbp:bfsParent gptkb:finite-dimensional_Euclidean_space
gptkbp:bfsLayer 5