The A series of paper sizes are designed so that when you cut one in half, you get two pieces of the next-smallest-size, and every size has height and width in the same proportion.
A little math reveals that one can achieve this by having the height and width in the ratio sqrt(2):1, or approximately 1.414:1. So once you've decided that this is the ratio you want for your page, how do you decide the absolute size? In the case of the A series of paper sizes, an A0 piece of paper is exactly 1 square metre, requiring width x width x 1.414 = 1, which gives a width of 84.1cm and height of 118.9cm (to the nearest mm). An A1 piece of paper has a length that's the same as the width of A0, or 84.1cm, and a width of 84.1cm / sqrt (2) = 59.5cm. Which you'll notice is half the height of the A0 size (118.9cm). These relationships hold true going all the way down to A10:
