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===B series=== The B series is defined in the standard as follows: "A subsidiary series of sizes is obtained by placing the [[Geometric mean|geometrical means]] between adjacent sizes of the A series in sequence." The use of the geometric mean makes each step in size: B0, A0, B1, A1, B2 ... smaller than the previous one by the same factor. As with the A series, the lengths of the B series have the ratio {{math|{{sqrt|2}}}}, and folding one in half (and rounding down to the nearest millimetre) gives the next in the series. The shorter side of B0 is exactly 1 metre. There is also an incompatible Japanese B series which the [[Japanese Industrial Standard|JIS]] defines to have 1.5 times the area of the corresponding JIS A series (which is identical to the ISO A series).<ref>{{cite web|url=http://www.paper-sizes.com/uncommon-paper-sizes/japanese-b-series-paper-size|title=Japanese B Series Paper Size|access-date=18 April 2010}}</ref> Thus, the lengths of JIS B series paper are {{math|{{sqrt|1.5}}}} β 1.22 times those of A-series paper. By comparison, the lengths of ISO B series paper are {{math|{{sqrt|2|4}}}} β 1.19 times those of A-series paper. Any {{math|B''n''}} paper (according to the ISO standard) can be defined as {{math|1=B''n'' = ''S'' Γ ''L''}}, where (measuring in metres) :<math>\text{B}_n = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{n}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{n - 1} \end{cases}</math> Therefore :<math>\text{B0} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{0} = 1\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{0 - 1} \approx 1.414\,\text{m} \end{cases}</math>, {{pad}} <math>\text{B1} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{1} \approx 0.707\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{1 - 1} = 1\,\text{m} \end{cases}</math> {{pad}} <math>\text{B2} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{2} = 0.5\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{2 - 1} \approx 0.707\,\text{m} \end{cases}</math> {{pad}} Etc.
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