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
Suppose I have a piece of paper that is 1m x 2m. How do I get the same 1:2 ratio but with the 1m as the long side? I take a ¼ of the paper.
Suppose I have a piece of paper that is 1m x 3m. How do I get the same 1:3 ratio but with the 1m as the long side? I take a ⅑ of the paper.
So if I have a piece of paper that is 1 by X in ratio, if I take 1 / X² of the paper, I will preserve the ratio.
If X is 1.414 or √2 then I will preserve the ratio when I take ½ of the paper.
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