I'm writing a paper on origami in maths and currently looking at approximating rational fractions using various methods: crossing diagonals, Fujimoto, Haga, Noma methods.
Reading Origami and Geometric Constructions by Robert J. Lang page 14:
I would be very grateful if someone could explain why the bottom edge is divided into fractions $y=w/(w+x)$ and $z=x/(w+x)$
(assuming the $w$ on the right side of the pic is meant to be an $x$)
By similar triangles, and assuming $y+z=1$, we have $y=\dfrac{h}{x}$ and $z=\dfrac{h}{w}$. This means that $$\dfrac{h}{x}+\dfrac{h}{w}=1$$ and rearranging gives $$h=\frac{wx}{w+x}$$