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:

Two A4s do an A3and have the very same proportions

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:

size mm × mmabout the dimension of aarea
A0841 × 1189table top1.0 m2
A1594 × 8410.5 m2
A2420 × 594monitor0.25 m2
A3297 × 4200.125 m2
A4210 × 297writing sheet0.0624 m2
A5148 × 2100.0311 m2
A6105 × 1480.0155 m2
A774 × 105note0.00777 m2
A852 × 740.003848 m2
A937 × 520.001924 m2
A1026 × 37stamp0.000962 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.