Risks and scribbles, letters and numbers, stains and colors … we do every day of A4 paper a kind of Jack-of-all-trades, from literary to a more simple outline of ideas. But the dimensions of the paper format, so ingrained in our culture, have a real reason to be, more specifically 1.4142.

**PROPORTION INFINITE**

1.4142 is the ratio of the height (297 mm) and width (210 mm) of a sheet of A4 paper.Apparently, this calculation has nothing special, but if we execute the same operation in the dimensions of a sheet of A5, A3, A2 or A1, we obtain, rounded to one decimal place, exactly the same result.

The practical consequence of this phenomenon is simple math: folding the paper in half, we get a sheet with the exact dimensions of the format of paper immediately below. Try it! Take an A4 sheet vertically, fold it in half and turn left or right so to see her in an upright position. Now has in hand a sheet in A5 format. Do the same again, and will be looking at a single A6. And so on, always with the proportion strictly ensured.

In theory, we could carry this size reduction to negligible values, but physics is not on our side.

**ROOT OF A SOLUTION**

Mathematicians are not unrelated to phenomena of this nature, since the search for absolute proportion in the relations between quantities is the most fascinating in the realm of numbers.But it was not until 1786 that the scientist Georg Christoph Lichtenberg suggested publicly in the University of Göttingen, Germany, that the application of 1.4142 (the square root of the number 2) as a reason for a paper to ensure harmony of proportions between the different sizes.

This notion was later echoed by German engineer Walter Porstmann, who in 1922 envisioned the proposal on the basis of DIN 476 for paper formats. Starting from a shape with a square meter (A0), all remaining abated in proportion to the tiny dimensions of A10, little smaller than a postage stamp. So standardizing all sizes and reducing the cost of reproduction, distribution and storage, the standard quickly gained success around Europe – including Portugal, where he arrived in 1954 – and is now adopted worldwide, except U.S. and Canada.

**A4? NOT SO, THERE ARE MANY MORE!**

The A4 is the most familiar, but the standard covers other variants such as B, C or D, all compatible with each other, an A4 letter fits well into a B4 envelope, which in turn fits like a glove in an envelope C4 bulkier. The balance of the standard is such that the shape of the paper in order to subliminally encourages ideas – there is nothing more conducive to inspiration, in fact, than a blank sheet of A4.

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