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The precise origins of the dimensions of US letter-size paper (8.5 × 11 in) are not known. The American Forest & Paper Association says that the standard US dimensions have their origin in the days of manual papermaking, the 11-inch length of the standard paper being about a quarter of "the average maximum stretch of an experienced vatman's arms". [2]
Then, the size of A5 paper is half of A4, i.e. 148 mm × 210 mm (5.8 in × 8.3 in). [ 6 ] [ 7 ] The geometric rationale for using the square root of 2 is to maintain the aspect ratio of each subsequent rectangle after cutting or folding an A-series sheet in half, perpendicular to the larger side.
Its D format sits between a B format and the next larger A format (just like C sits between A and the next larger B). The remaining formats fit in between all these formats, such that the sequence of formats A4, E4, C4, G4, B4, F4, D4, *H4, A3 is a geometric progression , in which the dimensions grow by a factor 2 16 {\displaystyle {\sqrt[{16 ...
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The size and proportions of a book depend on the size of the original full sheet. If a sheet 480 by 640 mm (19 by 25 in) is used to print a quarto, the resulting untrimmed pages, will be approximately half as large in each dimension: width 240 mm (9 + 1 ⁄ 2 in) and height 320 mm (12 + 1 ⁄ 2 in).