This video is about paper.
Did you know there is a beautiful piece of math involved in every sheet of paper?
In the world there are two major standards regarding paper sizes. First there is ISO-216, more commonly known as the A-series (as in A4, A5). This system is used in all over the world... with some exceptions. The main being the United States of America, they have their own standard, US Letter.
The standard US Letter has a size of: 8.5 by 11 inches, or 216 mm x 279 mm. It has an aspect ratio of 1.291.
The origin of this format is pretty vague and mostly lost in history.
Wikipedia says:
The 11 inch length is about a quarter of “the average maximum stretch of an experienced vatman’s arm”....
Yeah... right, so basically US Letter is a standard because it is a standard, don’t ask questions, just deal with it.
ISO-216, the A-standard
This standard is mostly know for the European letter format: A4. It is 210 mm × 297 mm and has an aspect ratio of 1.414... which is the square root of 2. (woohooo math!) √2.
This square root of two isn’t a coincidence of course, it is credited to a German scientist called Georg Christoph Lichtenberg in 1786.... but this magic ratio was probably known a lot longer.
The square root of 2 has a "magic property" that makes ISO-216 far superior over US Letter!
The property A4 paper has is that is consists of exactly two A5 papers side-by-side. In turn, two of these A4 papers make up the larger A3 paper.
This makes it very easy for example to make a booklet in A5 format consisting of A4 papers turned sideways and folded.
If you scale up a documents in A5 they will exactly fit A4 paper. If you shrink an A3 image, it will exactly fit A4 and A5 paper.
If you want to use a copier and print two A5 pages on single sheet of A4 paper, go ahead! It all works out thanks to math!
This is impossible to do with US Letter, you’ll end up with unprinted white areas or stretched documents!
2/√2 = √2 MAGIC!
Just look at this table, there are some little rounding errors due to the millimeters, but overall it stays close to the square root of 2.
A4 210 mm × 297 mm ratio: 1.414
A5 148 mm × 210 mm ratio: 1.419
A6 105 mm × 148 mm ratio: 1.409
A7 74 mm × 105 mm ratio: 1.418
What happens when we do the same for US Letter?
The aspect ratio of US Letter is 1.291.
2/1.291 = 1.549...!
YUK!
And this happens when we keep folding US Letter:
216 mm x 279 mm ratio: 1.291
139 mm x 216 mm ratio: 1.554 - WTF?
108 mm x 139 mm ratio: 1.287 - back to normal...
69 mm x 108 mm ratio: 1.565 - OMG!
So dear mr. Trump, do you want to make America great again? Adopt ISO-216.
(and while you're at it, check out the metric system too!)
And Now You Know.
Music: Ben Sound
