Solid angle a solid angle in steradians is the following ratio: where A is the spherical surface area and r is the radius of the considered sphere. Solid angles are often used in physics, in particular astrophysics. The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance. Here "area" means the area of the object when projected along the viewing direction. The solid angle of a sphere measured from any point in its interior is 4 sr, and the solid angle subtended at the center of a cube by one
Surface area of infinitesimal calculus and involves partial derivatives and double integration. A 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. While the areas of many simple surfaces have been known since antiquity, a rigorous mathematical "definition" of area requires a great deal of care. This should provide a function which assigns a positive real number to