OFFSET
0,1
COMMENTS
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.
LINKS
EXAMPLE
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%)
MATHEMATICA
RealDigits[2^(-9/4), 10, 88][[1]] (* James C. McMahon, Feb 26 2024 *)
PROG
(PARI) default(realprecision, 100); 2^(-9/4)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jianing Song, May 20 2019
EXTENSIONS
Edited by Jon E. Schoenfield, Feb 25 2024
STATUS
approved