A0….A3, A4, …… etc. paper sizes all have a ratio of there short to long sides of 1: square root of 2. With this ratio, 2 sheets of portrait A4 placed side by side will fit exactly on a sheet of landscape A3, 2 sheets of A3 on A2 and so on. The ratio doesn't give nice clean whole numbers for side lengths, either in metric or imperial units, but the sizes are based on A0 having an area of 1 square metre.

For a fuller explanation see ISO paper sizes