1:2 becomes 1:1 or 1:4 depending on folding axis, etc
In: 10
Just simple Math: (Maybe not for a five years old)
Original sheet: Width: W and Height: H
Folded sheet: New width: w = H and new height: h = W/2
Requested: H/W = h/w
leads to: H/W = (W/2)/H
Multiply both side by (H/W): H/W * H/W = 1/2
Then: H/W = 1/√2
Take a piece of paper with an aspect ratio of 1:√2. If you fold it in half along the long axis, then its aspect ratio becomes 1:(√2)/2. Now, to see that this is the same aspect ratio, scale both sides up by √2. Then the aspect ratio would be √2:(√2*√2)/2. √2*√2 = 2, that’s what √2 means, so the aspect ratio is √2:2/2 = √2:1. This is the same aspect ratio as before, just the other way round.
The basic math excercise was already explained before in other comments, so i won’t repeat the steps.
I would like to add one thing: the math results at the end to this formula
>(a/b)^2 = constant
This equation always has *1 and only 1 positive solution*. This means that whatever folding proportion you choose, only 1 aspect ratio will ever work to satisfy the equation.
If you choose 1/2 (to fold in half) the number turns out to be 1/sqrt(2). The “cool mathy thing” is the fact that **only one aspect ratio** will ever work, given a folding pattern, and no one aspect ratio will ever work for more than one folding pattern.
1/sqrt(2) has nothing special “per se”, it just solves the equation.
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