Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:geometry
|
| gptkbp:alsoKnownAs |
2-norm ball
L2 ball |
| gptkbp:borders |
gptkb:Euclidean_sphere
|
| gptkbp:centralTo |
point in Euclidean space
|
| gptkbp:contains |
all points whose Euclidean distance from center is less than or equal to radius
|
| gptkbp:definedIn |
gptkb:Euclidean_space
|
| gptkbp:diameter |
non-negative real number
|
| gptkbp:dimensions |
n (for n-dimensional space)
|
| gptkbp:generalizes |
disk (2D)
solid sphere (3D) |
| gptkbp:hasSpecialCase |
unit ball (radius = 1)
|
| gptkbp:hasSubgroup |
gptkb:Euclidean_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
Euclidean ball (p=2)
|
| gptkbp:isClosed |
true (if includes boundary)
|
| gptkbp:isConvex |
true
|
| gptkbp:openDays |
true (if excludes boundary)
|
| gptkbp:relatedTo |
gptkb:Lp_ball
|
| gptkbp:surfaceAreaFormula |
A = (2 * π^{n/2} / Γ(n/2)) * r^{n-1}
|
| gptkbp:usedIn |
gptkb:geometry
gptkb:machine_learning functional analysis mathematical analysis optimization |
| gptkbp:volume |
V = (π^{n/2} / Γ(n/2 + 1)) * r^n
|
| gptkbp:bfsParent |
gptkb:Lp_ball
|
| gptkbp:bfsLayer |
6
|