Square root of 3 billion digits. The fraction (…) for the square root of three can be used as an approximation. Despite having a denominator of only 56, it differs from the correct value by less than (approximately ). The rounded value of 1.732 is correct to within 0.01% of the actual value. Archimedes reported , accurate to (six decimal places) and (four decimal places), respectively. It can be expressed as the continued fraction , expanded on the right. It can also be expressed by generalized continued fractions such as which is evaluated at every second term. The following nested square expressions converge to
Root-mean-square deviation of atomic positions the context of docking, as well as in other methods to study the configuration of ligands when bound to macromolecules. Note that, for the case of ligands (contrary to proteins, as described above), their structures are most commonly not superimposed prior to the calculation of the RMSD. Root-mean-square deviation of atomic positions In bioinformatics, the root-mean-square deviation of atomic positions (or simply root-mean-square deviation, RMSD) is the measure of the average distance between the atoms (usually the backbone atoms) of superimposed proteins. Note that RMSD calculation can be applied to other, non-protein molecules, such as small organic molecules. In the