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
We can set it up as a formula.
We want a piece of paper that has the same ratio of dimensions when it is folded in half. Lets say the short side has length 1 and we’ll call the long side we’re trying to find x. So the ratio of dimension is 1/x . If we fold it in half, the short side is now x/2 and the long side is 1. So the ratio of the folded piece of paper is (x/2) / 1, or just x/2. We want them equal to each other, so 1/x = x/2.
Multiply both sides by x, we get 1 = x^2 / 2.
Multiply both sides by 2, we get 2 = x^2
Take the squre root of both sides, we get sqrt(2) = x, and there’s your sqrt(2)
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