Konformális

Konformális refers to a property in geometry. A mapping or transformation is considered konformális if it preserves angles locally. This means that if two curves intersect at a certain angle in one space, their images under a konformális mapping will intersect at the same angle in the transformed space. More precisely, the angle between the tangent vectors of the curves at the intersection point is preserved.

Konformális mappings are crucial in various fields of mathematics and physics. In complex analysis, conformal maps play a central role. A complex function is conformal if it is analytic and its derivative is non-zero. These mappings have applications in fluid dynamics, electrostatics, and cartography, where preserving angles is often desirable for accurate representation.

The concept of konformális geometry extends beyond complex analysis. In differential geometry, konformális transformations are a type of geometric transformation that preserves angles but not necessarily lengths. A key characteristic of konformális mappings is their ability to "zoom in" on a point without distorting the angular relationships between nearby lines. This property makes them powerful tools for solving problems involving shapes and their distortions.