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
Penrose square root law voting, including the Jagiellonian Compromise designed for the Council of the European Union. Penrose square root law In the mathematical theory of games, the Penrose square root law, originally formulated by Lionel Penrose, concerns the distribution of the voting power in a voting body consisting of "N" members. It states that the "a priori" voting power of any voter, measured by the Penrose–Banzhaf index formula_1 scales like formula_2. This result was used to design the Penrose method of for allocating the voting weights of representatives in a decision-making bodies proportional to the square root of the population represented. To estimate