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
Square root of 2 widely used constant. formula_81 The (approximate) aspect ratio of paper sizes under ISO 216 (A4, A0, etc.) is 1:. This ratio of lengths of the shorter over the longer side guarantees that cutting a sheet in half along a line parallel to its shorter side results in the smaller sheets having the same (approximate) ratio as the original sheet. Proof: Let formula_82 shorter length and formula_83 longer length of the sides of a sheet of paper, with Let formula_85 be the analogue ratio of the halved sheet, then Square root of 2 The square root of 2, or the (1/2)th