If you create a rectangle whose sides are in the ratio it has a very interesting property. If you cut it in half across the narrow dimension, the two pieces also have their sides in the ratio . This can of course be continued indefinitely.
In Europe and much of the rest of the world, paper sizes are standardized using this mathematical fact. Each size can be obtained by cutting the next bigger size in half. Because the sizes all have the same ratio of their sides (called the aspect ratio) A copying machine can magnify or shrink a page to another size, and it will fit exactly.
The thing that is fascinating about this ISO standard is that it is based entirely on a purely mathematical foundation. There are eleven A-sizes ranging from A0 (about the size of a table-top) down to A10 which is about the size of a postage stamp. They each can be obtained by cutting the next larger size in half and rotating it 90°.