cp's OEIS Frontend

A308321 Decimal expansion of 2^(-9/4); exact width of the A4 paper size measured in meters according to the ISO 216 standard.

%I A308321 #26 Mar 09 2024 11:17:27
%S A308321 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,
%T A308321 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,
%U A308321 1,1,8,8,7,3,8,4,7,5,5,5,9,9,5,3,5,8,1,0
%N A308321 Decimal expansion of 2^(-9/4); exact width of the A4 paper size measured in meters according to the ISO 216 standard.
%C A308321 Also exact length of the A5 paper size measured in meters.
%C A308321 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.
%H A308321 Prepressure, <a href="https://www.prepressure.com/library/paper-size/din-a4">A4</a>.
%H A308321 Wikipedia, <a href="https://en.wikipedia.org/wiki/ISO-216">ISO 216</a>.
%e A308321 The exact lengths and widths (rounded to the nearest 1/10 mm) and areas of the A-series are as follows:
%e A308321 .
%e A308321   size |       exact length      |       exact width      | exact area (mm^2)
%e A308321    A0  | 2^(  1/4) m = 1189.2 mm | 2^(- 1/4) m = 840.9 mm |  1000000
%e A308321    A1  | 2^(- 1/4) m =  840.9 mm | 2^(- 3/4) m = 594.6 mm |   500000
%e A308321    A2  | 2^(- 3/4) m =  594.6 mm | 2^(- 5/4) m = 420.4 mm |   250000
%e A308321    A3  | 2^(- 5/4) m =  420.4 mm | 2^(- 7/4) m = 297.3 mm |   125000
%e A308321    A4  | 2^(- 7/4) m =  297.3 mm | 2^(- 9/4) m = 210.2 mm |    62500
%e A308321    A5  | 2^(- 9/4) m =  210.2 mm | 2^(-11/4) m = 148.7 mm |    31250
%e A308321    A6  | 2^(-11/4) m =  148.7 mm | 2^(-13/4) m = 105.1 mm |    15625
%e A308321    A7  | 2^(-13/4) m =  105.1 mm | 2^(-15/4) m =  74.3 mm |     7812.5
%e A308321    A8  | 2^(-15/4) m =   74.3 mm | 2^(-17/4) m =  52.6 mm |     3906.25
%e A308321    A9  | 2^(-17/4) m =   52.6 mm | 2^(-19/4) m =  37.2 mm |     1953.125
%e A308321    A10 | 2^(-19/4) m =   37.2 mm | 2^(-21/4) m =  26.3 mm |      976.5625
%e A308321 .
%e A308321 And the actual lengths, widths and areas (note that the actual areas are always smaller than the exact areas) are as follows:
%e A308321 .
%e A308321   size | actual length (mm) | actual width (mm) | actual area (mm^2)
%e A308321    A0  |        1189        |        841        |  999949 (99.9949%)
%e A308321    A1  |         841        |        594        |  499554 (99.9108%)
%e A308321    A2  |         594        |        420        |  249480 (99.7920%)
%e A308321    A3  |         420        |        297        |  124740 (99.7920%)
%e A308321    A4  |         297        |        210        |   62370 (99.7920%)
%e A308321    A5  |         210        |        148        |   31080 (99.4560%)
%e A308321    A6  |         148        |        105        |   15540 (99.4560%)
%e A308321    A7  |         105        |         74        |    7770 (99.4560%)
%e A308321    A8  |          74        |         52        |    3848 (98.5088%)
%e A308321    A9  |          52        |         37        |    1924 (98.5088%)
%e A308321    A10 |          37        |         26        |     962 (98.5088%)
%t A308321 RealDigits[2^(-9/4),10,88][[1]] (* _James C. McMahon_, Feb 26 2024 *)
%o A308321 (PARI) default(realprecision, 100); 2^(-9/4)
%Y A308321 Cf. A010767 (2^(1/4)), A228497 (2^(-1/4)), A308320 (2^(-7/4)).
%K A308321 nonn,cons
%O A308321 0,1
%A A308321 _Jianing Song_, May 20 2019
%E A308321 Edited by _Jon E. Schoenfield_, Feb 25 2024