Why is 1:√2 the only aspect ratio that remains the same when it is ‘folded in half’ (hence the usage in paper dimensions)

Question

1:2 becomes 1:1 or 1:4 depending on folding axis, etc

In: 10

Answer 1

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.