Surface area is the total area of the faces and curved surface of the a solid figure. Mathematical description of the surface area is considerably more involved than the definition of arc length or polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
General definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.
Famous quotes containing the words surface and/or area:
“In the cold of Europe, under prudish northern fogs, except when slaughter is afoot, you only glimpse the crawling cruelty of your fellow men. But their rottenness rises to the surface as soon as they are tickled by the hideous fevers of the tropics.”
—Louis-Ferdinand Céline (18941961)
“If you meet a sectary, or a hostile partisan, never recognize the dividing lines; but meet on what common ground remains,if only that the sun shines, and the rain rains for both; the area will widen very fast, and ere you know it the boundary mountains, on which the eye had fastened, have melted into air.”
—Ralph Waldo Emerson (18031882)