Konformalt

Konformalt is a term used in some linguistic and mathematical contexts to denote the property of conformality—preserving angles locally between geometric figures under a transformation. In those contexts, konformalt describes maps, metrics, or structures that preserve the shape of infinitesimal angles, often up to a position-dependent scale factor. While conformal is the standard English term, konformalt appears in various language traditions as a direct cognate or transliteration.

In mathematics, a function f between domains in the plane or in higher dimensions is called conformal if it preserves angles locally and is differentiable with a nonzero derivative (or Jacobian). In complex analysis, holomorphic functions with nonzero derivative are conformal; Möbius transformations are conformal on the extended complex plane. In dimensions greater than two, Liouville’s theorem implies that global conformal maps are limited to Möbius transformations on suitable domains.

Examples include the maps z → az + b, which are conformal whenever a ≠ 0, and many complex-analytic mappings away from critical points. Functions with vanishing derivative at a point are not conformal there. The exponential function is conformal wherever its derivative is nonzero, but care must be taken at points where the derivative vanishes.

Applications of conformality span cartography (conformal map projections preserve angles locally), computer graphics (conformal parameterizations for textures), and theoretical physics (conformal field theories and scaling symmetries).

Terminology note: konformalt is not standard in English-language references; in English, the conventional term is conformal. The concept, however, aligns with the broader mathematical notion of angle-preserving transformations.