A308320 Decimal expansion of 2^(-7/4); exact length of the A4 paper size measured in meters according to the ISO 216 standard.

2, 9, 7, 3, 0, 1, 7, 7, 8, 7, 5, 0, 6, 8, 0, 2, 6, 6, 6, 7, 9, 3, 7, 4, 9, 9, 2, 6, 4, 0, 1, 1, 8, 9, 7, 8, 8, 2, 3, 2, 4, 3, 0, 2, 3, 1, 1, 5, 9, 5, 4, 3, 5, 3, 2, 5, 4, 7, 5, 0, 5, 5, 6, 1, 7, 9, 8, 6, 6, 6, 6, 7, 0, 5, 6, 7, 2, 9, 2, 8, 9, 9, 6, 7, 6, 9, 5, 3

Offset: 0

Author

Jianing Song, May 20 2019

Keywords

• nonn
• cons

Comments

Also exact width of the A3 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 and 2^(-9/4) m = 210.224... mm (A308321), and the actual length and width are 297 mm and 210 mm.

Examples

			0.29730177...
The exact lengths and widths (rounded to the nearest 1/10 mm) and areas of the A-series are as follows:
.
  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
.
And the actual lengths, widths and areas (note that the actual areas are always smaller than the exact areas) are as follows:
.
  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%)
		

Links

• Prepressure, A4.
• Wikipedia, ISO 216.

Crossrefs

Cf. A010767 (2^(1/4)), A228497 (2^(-1/4)), A308321 (2^(-9/4)).

Programs

Mathematica

RealDigits[2^(-7/4),10,88][[1]] (* James C. McMahon, Feb 26 2024 *)

PARI

default(realprecision, 100); 2^(-7/4)

Formula

Equals square root of A222066. - R. J. Mathar, Jan 27 2021

Extensions

Edited by Jon E. Schoenfield, Feb 25 2024