In every office and most households you will find A4 paper, the standard paper for printing documents. Most people don't give it a second thought. But there are a few reasons why A4 paper is beautiful.
The main reason that A4 paper is beautiful is the ratio of the two sides: 1 to the square root of 2 (√2).
This is the only possible ratio which results in paper which, when cut in half, produces a sheet with the same ratio (A5)
And the square root of 2 is beautiful because it is an irrational number: when expressed as a decimal, there are no repeating patterns after the decimal point. There is even a published book which shows the square root of 2 to a million decimal paces. It's 446 pages long.
The A-series of paper sizes is also designed so that the area of the largest standard size - A0 - is exactly one square metre.
Developed in Germany in the 1920s, the 'DIN' standard of paper sizes has been gradually adopted across Europe and around the world - a perfect example of post-war international co-operation. It's now used in almost every country - except the United States which, of course, sticks to its strange collection of unrelated sizes, including Letter, Legal, Tabloid and Executive.