Celestial Weasel (celestialweasel) wrote,
Celestial Weasel
celestialweasel

Paper moon

As is often the case with these polls, when one sees the results one thinks of more questions. Mr zengineer may be disappointed that I don't have a profound point. I was just surprised that, once again, people at work looked at me as though I were mad when I said something about A[n] paper sizes.
So, anyway...
a) As presumably 5 of you know, the area of an A0 sheet of paper is a square metre. Size(A(n+1)) = 1/2 Size(A(n)). Therefore the size of an A4 sheet of paper is 1/16 of a square metre.
b) As mentioned in comments, the A series of paper sizes has the property that each size is got by halving the previous size along its long size. Therefore the ratio of the long side to the short side is sqrt(2) to 1.
c) Putting these facts together (viz the ratio and the fact that a sheet of A0 paper is a square metre) yields the sides of a sheet of A0 paper being 2^1/4 metres by 2^-1/4 metres (i.e. the square root of the square root of 2). Dividing these by 4 yields the size of an A4 sheet of paper.
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  • 2 comments
zengineer

zengineer

February 10 2015, 10:30:49 UTC 9 years ago

I was, of course, aware of this as it is of particular relevance to engineers. No one has ever told me how it came about though so I was prompted to google it.
"The advantages of basing a paper size upon an aspect ratio of \sqrt{2} were first noted in 1786 by the German scientist and philosopher Georg Christoph Lichtenberg.[2] Early in the 20th century, Dr Walter Porstmann turned Lichtenberg's idea into a proper system of different paper sizes. Porstmann's system was introduced as a DIN standard (DIN 476) in Germany in 1922"
So invented by a German Scientist/Philosopher - I was expecting it to be the paper industry.
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jackfirecat

jackfirecat

February 10 2015, 21:40:47 UTC 9 years ago

>the area of an A0 sheet of paper is a square metre.

I did not know that. I am pleased to now know that.
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