egységdiszk

egységdiszk is a Hungarian term that translates to "unit disk" in English. It refers to a fundamental concept in mathematics, particularly in geometry and analysis.

In geometry, the unit disk is the set of all points in a plane whose distance from a central point is less than or equal to one. The central point is typically taken to be the origin (0,0) in a Cartesian coordinate system. The boundary of the unit disk is called the unit circle, which consists of all points exactly one unit away from the center. The unit disk is often denoted by D or B.

In complex analysis, the unit disk plays a significant role. It is the set of all complex numbers z such that |z| ≤ 1, where |z| represents the modulus of the complex number z. Many important theorems in complex analysis, such as Liouville's theorem and the Maximum Modulus Principle, are stated or have implications for functions defined on or within the unit disk.

The concept of a unit disk can be generalized to higher dimensions. In n-dimensional Euclidean space, the unit ball is the set of all points whose distance from the origin is less than or equal to one. The boundary of the unit ball is the unit sphere. The unit disk can be considered a 2-dimensional unit ball.

The egységdiszk is a standard object of study in various branches of mathematics due to its simplicity and its role as a building block for more complex mathematical structures and theories.