Determining the length of an irregular arc segment is also called rectification of a curve. Historically, many methods were used for specific curves...
of a curve. For polyhedra (objects with flat polygonal faces
In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
, are assigned surface area using their representation as parametric surface
A parametric surface is a surface in the Euclidean space R3 which is defined by a parametric equation with two parameters. Parametric representation is the most general way to specify a surface. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence...