International Standard Paper sizes and square roots: The most common size of printer paper (in Europe anyway) is A4 (about 8.3 x 11.7 inches or 210 x 297 mm). A piece of A4 is twice the area of an A5 sheet and half the area of an A3 sheet.
If you want to be able to cut a sheet of paper in half like this and get two smaller pieces with the same proportions as the original, then the height to length ratio has to be the square root of two (about 1.414).
ISO paper sizes begin with A0 which is defined as having an area of one square metre. When A0 is cut in half you get A1 and so on until after 4 divisions you end up with A4 which is therefore 1/16 of a square metre in area.
It's possible to buy sheets of paper larger than A0. One of twice the area is called 2A0 and one twice as big as that is called 4A0. This system of naming the larger formats doesn't fit well with the naming scheme of the smaller sizes - the person who came up with those large format designations was no mathematician.
