Släta

Släta is a Swedish verb meaning to make something smooth, flat, or even, or to remove roughness or irregularities from a surface. It is used both literally, for example “släta ut en yta” (to smooth out a surface) or “släta ut huden” (to smooth the skin), and figuratively, such as “släta över en konflikt” (to gloss over a conflict) or “släta ut skillnader” (to smooth differences). The term is commonly used in crafts, construction, and everyday speech.

In mathematics and related fields, the term “släta funktioner” refers to smooth functions, i.e., functions that are differentiable to all orders (often denoted as C∞). This contrasts with functions that are only continuous or have a finite number of derivatives. The concept is central in analysis and differential geometry, where smoothness describes the quality of a function's behavior.

In data analysis, statistics, and signal processing, to släta means to apply smoothing to data or curves to reduce noise and reveal underlying trends. Common methods include moving-average filters, LOESS (local regression), and spline smoothing. Smoothing aims to balance fidelity to the original data with a reduction of random variation, producing a more interpretable trend line or curve.

Etymology links the verb to the Swedish adjective slät, meaning smooth, with the verb form describing the action of making something smooth. The phrases “släta ut” (to smooth out) and “släta över” (to gloss over) are widely used in both literal and figurative Swedish.