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
Volume Area Dihedral Angle Reporter Volume Area Dihedral Angle Reporter Volume, Area, Dihedral Angle Reporter (VADAR) is a freely available protein structure validation web server that was developed as a collaboration between Dr. Brian Sykes and Dr. David Wishart at the University of Alberta. VADAR consists of >15 different algorithms and programs for assessing and validating peptide and protein structures from their PDB coordinate data. VADAR is capable of determining secondary structure (using three different algorithms), identifying and classifying six different types of beta turns, determining and calculating the strength of C=O -- N-H hydrogen bonds, calculating residue-specific accessible surface areas (ASA), calculating residue volumes,