unit circle in complex plane
GPTKB entity
Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:borders |
gptkb:unit_disk
|
| gptkbp:centralTo |
origin
|
| gptkbp:definedIn |
set of complex numbers with modulus 1
|
| gptkbp:diameter |
1
|
| gptkbp:dimensions |
1
|
| gptkbp:groupStructure |
multiplicative group of complex numbers of modulus 1
|
| gptkbp:hasEquation |
|z| = 1
|
| gptkbp:hasSubgroup |
complex numbers
|
| gptkbp:homotopyGroup |
π₁(S^1) = ℤ
|
| https://www.w3.org/2000/01/rdf-schema#label |
unit circle in complex plane
|
| gptkbp:isomorphicTo |
gptkb:circle_group
|
| gptkbp:locatedIn |
gptkb:complex_plane
|
| gptkbp:parameter |
z = e^{iθ}, θ ∈ [0, 2π)
|
| gptkbp:relatedTo |
gptkb:Euler's_formula
gptkb:unit_disk trigonometric functions roots of unity |
| gptkbp:symbol |
gptkb:S^1
|
| gptkbp:topology |
compact
connected 1-dimensional manifold |
| gptkbp:usedIn |
gptkb:signal_processing
Fourier analysis complex analysis trigonometry |
| gptkbp:bfsParent |
gptkb:circle_group_S^1
|
| gptkbp:bfsLayer |
6
|