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unit disk (Definition)

The unit disk in the complex plane, denoted $ \Delta$, is defined as $ \{ z \in {\mathbb{C}}: \vert z\vert < 1 \}$. The unit circle, denoted $ \partial\Delta$ or $ S^1$ is the boundary $ \{z \in {\mathbb{C}}: \vert z\vert=1 \}$ of the unit disk $ \Delta$. Every element $ z \in \partial\Delta$ can be written as $ z=e^{i \theta}$ for some real value of $ \theta$.



"unit disk" is owned by brianbirgen.
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See Also: conformal Möbius circle map theorem, Schwarz lemma, complex, upper half plane, unit disk upper half plane conformal equivalence theorem, unit disc

Other names:  unit disc
Also defines:  unit circle
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Cross-references: real, boundary, complex plane
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This is version 5 of unit disk, born on 2003-05-12, modified 2003-05-13.
Object id is 4277, canonical name is UnitDisk.
Accessed 7014 times total.

Classification:
AMS MSC: 30A99 (Functions of a complex variable :: General properties :: Miscellaneous)
Pending Errata and Addenda
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