egységdiszknek
The egységdiszk (unit disk) is a basic object in geometry and complex analysis. It is the set of points in the Euclidean plane whose distance from the origin is at most 1. In mathematical notation, the closed unit disk is D̄ = { (x, y) ∈ R^2 : x^2 + y^2 ≤ 1 } or { z ∈ C : |z| ≤ 1 } in the complex plane. The open unit disk is D = { (x, y) ∈ R^2 : x^2 + y^2 < 1 } or { z ∈ C : |z| < 1 }.
Key properties include its center at the origin, radius 1, and boundary the unit circle S^1 = {
In complex analysis, the unit disk serves as a standard domain for function theory. It is common
Applications of the unit disk include serve as a simple test domain for convergence, mapping properties of