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===C series=== The C series formats are geometric means between the B series and A series formats with the same number (e.g. C2 is the geometric mean between B2 and A2). The width to height ratio of C series formats is {{math|{{sqrt|2}}}} as in the A and B series. A, B, and C series of paper fit together as part of a [[geometric progression]], with ratio of successive side lengths of {{math|{{sqrt|2|8}}}}, though there is no size half-way between B''n'' and {{Nowrap|A(''n'' β 1)}}: A4, C4, B4, "D4", A3, ...; there is such a D-series in the [[Paper size#Swedish extensions|Swedish extensions]] to the system. The lengths of ISO C series paper are therefore {{math|{{sqrt|2|8}}}} β 1.09 times those of A-series paper. The C series formats are used mainly for [[envelope]]s. An unfolded A4 page will fit into a C4 envelope. Due to same width to height ratio, if an A4 page is folded in half so that it is A5 in size, it will fit into a C5 envelope (which will be the same size as a C4 envelope folded in half). Any {{math|C''n''}} paper can be defined as {{math|1=C''n'' = ''S'' Γ ''L''}}, where (measuring in metres) :<math>\text{C}_n = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{n + \frac{1}{4}}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{n - \frac{3}{4}} \end{cases}</math> Therefore :<math>\text{C0} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{0 + \frac{1}{4}} \approx 0.917\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{0 - \frac{3}{4}} \approx 1.297\,\text{m} \end{cases}</math>, {{pad}} <math>\text{C1} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{1 + \frac{1}{4}} \approx 0.648\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{1 - \frac{3}{4}} \approx 0.917\,\text{m} \end{cases}</math> {{pad}} <math>\text{C2} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{2 + \frac{1}{4}} \approx 0.458\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{2 - \frac{3}{4}} \approx 0.648\,\text{m} \end{cases}</math> {{pad}} Etc.
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