Conformális

Conformális is a term used in mathematics, particularly in geometry and complex analysis, to describe a type of mapping or transformation. A conformal mapping, or conformal transformation, is a function that preserves angles locally. This means that if two curves intersect at a certain angle at a point, their images under the conformal mapping will intersect at the same angle at the corresponding point.

More formally, a differentiable function is conformal at a point if its derivative at that point is non-zero. This non-zero derivative ensures that the transformation scales and rotates, but does not distort, the infinitesimal geometry around the point. In the context of complex numbers, a complex analytic function is conformal wherever its derivative is non-zero.

The concept of conformality is crucial in various areas of mathematics and physics. In complex analysis, it is used to solve differential equations and understand the behavior of functions. In differential geometry, conformal mappings play a role in studying the properties of surfaces. In physics, they appear in areas like fluid dynamics, electromagnetism, and general relativity, often for simplifying problems by transforming complex geometries into simpler ones while preserving essential physical properties related to angles.

Conformal geometry is the study of geometric properties that are preserved under conformal mappings. This field explores shapes and spaces where only the angles matter, and not the lengths or areas, which can be distorted by conformal transformations.