Metric paper which always has the same ratio of dimensions when folded in half that being 1/sqrt(2). How was the logic behind this derived?
In: Mathematics
Everyone who have been doing a bit of mathematics have noticed this quirk. It can be a bit odd to work with fractions of strange numbers so we often end up normalizing a fraction when solving equations. With 1/sqrt(2) we can multiply with sqrt(2)/sqrt(2) as this is just 1 and you can multiply any number with 1. So you end up with sqrt(2)/sqrt(2)^2 which is just sqrt(2)/2. This is so common that you tend to do this automatically when solving equations.
But this is also the basis behind the metric papers, and were actually used before metrics were invented. We do not know exactly who came up with this first or even if it was just one idea. We have some letters from 1786 between two German scientists which mentions 1/sqrt(2) paper but they probably did not invent it. We also find mentions of it in a 1798 French tax law which shows that it was a common ratio.
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