coarsest

Coarsest is the superlative form of coarse, used to describe the greatest degree of roughness, texture, or lack of refinement in a material, surface, or model. It is typically contrasted with finest or most refined to indicate differences in granularity or detail.

In physical contexts, coarsest refers to rougher textures or larger particle sizes. For example, coarse sand has larger grains than fine sand, and coarse-textured fabrics feel rougher than smooth ones. In geology, coarse-grained rocks contain visible mineral grains, as opposed to fine-grained rocks where the crystals are too small to see unaided.

In mathematics, computer science, and related fields, coarsest describes the lowest-resolution or most aggregated level in a hierarchy. A coarsest partition splits a set into the fewest blocks while meeting a given criterion. Coarsening is the process of merging elements to reduce detail, producing a coarser representation. The coarsest mesh or grid in numerical methods serves as the starting point for iterative refinement. Coarse-graining in physics and data analysis similarly refers to summarizing detailed information to obtain a simpler, higher-level description.

Etymology note: coarsest derives from the adjective coarse with the comparative and superlative suffixes, reflecting its meaning of greatest roughness or least refinement.