Did you understand that international document sizes (like A3, A4, etc) are based upon the square source of 2?
Because the square source of 2 has this cool property:
1 × √2 × √2 = 2
Which allows us have this:

So we can have sheets the have specifically the same proportions (their ratio of next lengths room the same) and also also to the right in each various other perfectly:

This makes things yes, really efficient:
Don"t have any A3? Tape 2 A4"s together.Don"t have any A5? reduced an A4 in half.And due to the fact that they have the exact same proportions, any type of artwork or file can it is in resized to fit on any kind of sheet:

Another benefit is the you have the right to print something the end at 70% size and also fit 2 pages side-by-side on simply one sheet favor this:

Why 70%? because 1/√2 = 0.7071... which is close come 70%
A comparable enlargement is √2 = 1.4142... i m sorry is close to 140%
Sizes
The famous A4 dimension is 210 mm broad by 297 mm high:

With a width of 210 the height is: 210 × √2 ≈ 297
Here are all the sizes cut from an A0 paper (which has an area the 1.0 m2):

Lastly below are the official sizes:
A0 | 841 × 1189 | table top | 1.0 m2 | |
A1 | 594 × 841 | 0.5 m2 | ||
A2 | 420 × 594 | monitor | 0.25 m2 | |
A3 | 297 × 420 | 0.125 m2 | ||
A4 | 210 × 297 | writing sheet | 0.0624 m2 | |
A5 | 148 × 210 | 0.0311 m2 | ||
A6 | 105 × 148 | 0.0155 m2 | ||
A7 | 74 × 105 | note | 0.00777 m2 | |
A8 | 52 × 74 | 0.003848 m2 | ||
A9 | 37 × 52 | 0.001924 m2 | ||
A10 | 26 × 37 | stamp | 0.000962 m2 |
Note: you can think of the "A-number" as how numerous folds (or cuts-in-half) far from one A0 we are. For this reason an A3 demands 3 crease of one A0, and so is ½×½×½ = 1/8th the size.