Solid angle orientation formula_9, and distance from the viewer as: where the surface area of a sphere is . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2, is the area of a spherical cap on a unit sphere For small such that , this reduces to the area of a circle . The above is found by computing the following double integral using the unit surface element in spherical coordinates: This formula can also be derived without the use of calculus. Over 2200 years ago Archimedes proved that the
Accessible surface area is a numerical method that draws a mesh of points equidistant from each atom of the molecule and uses the number of these points that are solvent accessible to determine the surface area. The points are drawn at a water molecule's estimated radius beyond the van der Waals radius, which is effectively similar to ‘rolling a ball’ along the surface. All points are checked against the surface of neighboring atoms to determine whether they are buried or accessible. The number of points accessible is multiplied by the portion of surface area each point represents to calculate the ASA. The choice