detaarea

Detaarea is a term used in mathematics and geographic information systems to denote the differential or incremental change in area associated with a small change in a region’s boundary. It expresses how area evolves under boundary movement, deformation, or temporal change.

The name blends delta or differential notation with area. In some sources it is presented as a synonym or informal alias for the differential area element dA or for the change in area ΔA. The term is not widely standardized and usage varies by field and author.

When a region R in the plane is perturbed by a small displacement, the resulting detaarea roughly equals the integral of the boundary-normal displacement across ∂R. In simple Cartesian terms, for a small rectangular patch with sides dx and dy, the incremental area is dA = dx dy. For polygons, the area change can be obtained by recomputing the polygon area after moving the vertices, or by applying Green's theorem to relate boundary motion to area change.

Detaarea is local and additive for disjoint regions, scales with uniform scaling (dA scales by factor squared), and changes sign with orientation. In practice, it is used to quantify land-cover change in GIS, assess material deformation under stress, and support mesh adaptation in computational geometry and computer graphics.

See also: Area, differential geometry, Green's theorem, differential element.