From Wikipedia’s paper size entry :

The international paper size standard, ISO 216, is based on the German DIN 476 standard for paper sizes. Its unique quality is its scalalability: The height divided by the width of all formats is the square root of two (1.4142), so folding any sheet in half, the two halves have the same proportions, and any image can be reproduced on the half size paper by reducing it by about 70% (0.707 is the reciprocal of root 2). To double an image area, the multiplication factor is about 140% These options commonly appear on photocopiers and image projectors.

Within the ISO metric system, the base format is a sheet of paper measuring 1 m² in area (A0 paper size). Successive paper sizes in the series A1, A2, A3, and so forth, are defined by halving the preceding paper size parallel to its shorter side. The most frequently used paper size is A4 (210 × 297 mm). An advantage is that standard A4 sheets made from 80 grams/m² paper weighs 5 grams, allowing one to know the weight – and associated postage rate – by counting the number of sheets used.

All those years of using A series paper and I did not know that… It all makes sense now !

I also realize my unabashed taste for engineering trivia…