Sieves

A sieve is a device consisting of a mesh or perforated surface that allows small particles to pass through while retaining larger ones. Sieves can be simple handheld strainers or large industrial screens. The term also denotes mathematical techniques that filter elements from a set according to a rule.

Physical sieves are used to separate particles by size in cooking, mining, agriculture, and manufacturing. Kitchen sieves and strainers use metal or plastic meshes with defined openings to drain liquids or to refine textures. Industrial sieves and screen decks use woven wire cloth or perforated plates and may be operated by hand, mechanically, or by vibration to classify bulk materials such as ore, sand, or grain.

In geology and soil science, sieve analysis measures grain-size distribution by passing a sample through a stack of standardized sieves and weighing the material retained on each sieve. The results describe the material's texture and influence construction properties and drainage. In food processing, sieves separate solids from liquids or remove lumps and kernels.

In mathematics, sieve theory studies how to count or estimate subsets of integers with prescribed properties. The Sieve of Eratosthenes is a foundational algorithm for finding all primes up to a given limit by repeatedly marking multiples of primes. More advanced sieve methods, such as the Brun, Selberg, and large sieve, provide tools for estimating the distribution of primes and related problems.

The term originates from the physical device used to sift and separate solids and liquids; the mathematical use preserves the idea of filtering elements. Across disciplines, sieves vary in material, mesh size, and mechanical design, but share the principle of separating matters by particle size or by a selection rule.