Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
higher-dimensional geometry
|
| gptkbp:definedIn |
set of points at constant distance from a center in n-dimensional space
|
| gptkbp:dimensions |
n-dimensional
|
| gptkbp:generalizes |
gptkb:butter
|
| gptkbp:hasEquation |
x1^2 + x2^2 + ... + xn^2 = r^2
|
| gptkbp:hasSpecialCase |
circle (n=2)
sphere (n=3) |
| gptkbp:hasSurfaceAreaFormula |
A_n = (2 * π^{n/2} * r^{n-1}) / Γ(n/2)
|
| https://www.w3.org/2000/01/rdf-schema#label |
hypersphere
|
| gptkbp:isA |
n-sphere
|
| gptkbp:relatedTo |
gptkb:Euclidean_space
unit sphere |
| gptkbp:surface |
hypersurface
|
| gptkbp:usedIn |
gptkb:geometry
gptkb:topology physics |
| gptkbp:volume |
V_n = (π^{n/2} * r^n) / Γ(n/2 + 1)
|
| gptkbp:bfsParent |
gptkb:7-sphere
gptkb:4-dimensional_Euclidean_space gptkb:5-dimensional_sphere |
| gptkbp:bfsLayer |
7
|