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A308321
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Decimal expansion of 2^(-9/4); exact width of the A4 paper size measured in meters according to the ISO 216 standard.
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2, 1, 0, 2, 2, 4, 1, 0, 3, 8, 1, 3, 4, 2, 8, 6, 3, 5, 7, 5, 7, 7, 8, 1, 3, 6, 9, 0, 5, 8, 3, 0, 3, 7, 2, 3, 7, 6, 0, 0, 0, 8, 5, 6, 5, 5, 8, 9, 1, 9, 6, 1, 2, 7, 7, 0, 3, 3, 0, 6, 5, 2, 1, 4, 9, 3, 7, 3, 1, 1, 8, 8, 7, 3, 8, 4, 7, 5, 5, 5, 9, 9, 5, 3, 5, 8, 1, 0
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OFFSET
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0,1
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COMMENTS
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Also exact length of the A5 paper size measured in meters.
According to the ISO 216 standard, the A0 paper size is defined to have an area of 1 square meter where the ratio of the length to the width is sqrt(2), so the length is 2^(1/4) m and the width is 2^(-1/4) m. For each n >= 0, the length of the size A(n+1) is equal to the width of the size A(n) and the width of the size A(n+1) is equal to half of the length of the size A(n), so the area of the size A(n+1) is half of that of A(n). Equivalently, the length of the A(n) size is 2^(-n/2 + 1/4) m and the width is 2^(-n/2 - 1/4) m. For the A4 size, the exact length and width are 2^(-7/4) m = 297.301... mm (A308320) and 2^(-9/4) m = 210.224... mm, and the actual length and width are 297 mm and 210 mm.
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LINKS
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EXAMPLE
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The exact lengths and widths (rounded to the nearest 1/10 mm) and areas of the A-series are as follows:
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size | exact length | exact width | exact area (mm^2)
A0 | 2^( 1/4) m = 1189.2 mm | 2^(- 1/4) m = 840.9 mm | 1000000
A1 | 2^(- 1/4) m = 840.9 mm | 2^(- 3/4) m = 594.6 mm | 500000
A2 | 2^(- 3/4) m = 594.6 mm | 2^(- 5/4) m = 420.4 mm | 250000
A3 | 2^(- 5/4) m = 420.4 mm | 2^(- 7/4) m = 297.3 mm | 125000
A4 | 2^(- 7/4) m = 297.3 mm | 2^(- 9/4) m = 210.2 mm | 62500
A5 | 2^(- 9/4) m = 210.2 mm | 2^(-11/4) m = 148.7 mm | 31250
A6 | 2^(-11/4) m = 148.7 mm | 2^(-13/4) m = 105.1 mm | 15625
A7 | 2^(-13/4) m = 105.1 mm | 2^(-15/4) m = 74.3 mm | 7812.5
A8 | 2^(-15/4) m = 74.3 mm | 2^(-17/4) m = 52.6 mm | 3906.25
A9 | 2^(-17/4) m = 52.6 mm | 2^(-19/4) m = 37.2 mm | 1953.125
A10 | 2^(-19/4) m = 37.2 mm | 2^(-21/4) m = 26.3 mm | 976.5625
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And the actual lengths, widths and areas (note that the actual areas are always smaller than the exact areas) are as follows:
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size | actual length (mm) | actual width (mm) | actual area (mm^2)
A0 | 1189 | 841 | 999949 (99.9949%)
A1 | 841 | 594 | 499554 (99.9108%)
A2 | 594 | 420 | 249480 (99.7920%)
A3 | 420 | 297 | 124740 (99.7920%)
A4 | 297 | 210 | 62370 (99.7920%)
A5 | 210 | 148 | 31080 (99.4560%)
A6 | 148 | 105 | 15540 (99.4560%)
A7 | 105 | 74 | 7770 (99.4560%)
A8 | 74 | 52 | 3848 (98.5088%)
A9 | 52 | 37 | 1924 (98.5088%)
A10 | 37 | 26 | 962 (98.5088%)
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 100); 2^(-9/4)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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