Square root any nonnegative number, then the principal square root of −"x" is The right side (as well as its negative) is indeed a square root of −"x", since For every non-zero complex number "z" there exist precisely two numbers "w" such that : the principal square root of "z" (defined below), and its negative. There are two complex numbers that square to a given arbitrary non-zero imaginary number formula_11 with real formula_12 where the two-digit pattern {3, 6} repeats over and over again in the partial denominators. Since , the above is also identical to the following generalized continued fractions: The
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