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Folding fractions: https://wild.maths.org/folding-fractions

There's a standard compass-and-straightedge construction for dividing a line segment evenly into a given number of smaller segments, and origami folding constructions are (depending on the model of what is allowed) at least as powerful, so it shouldn't be surprising that you can fold arbitrary even subdivisions of the side of an origami square. But this construction of $\frac{1}{n+1}$ from $\frac{1}{n}$ by Kazuo Haga is particularly elegant.