The Origamics was invented and coined by its inventor a biologist Prof Kazuo Haga (Japan) in 1994.
Haga's First Theorem
Fold a square paper of size 1 unit x 1 unit: join the right-bottom vertex to the mid-point of the top edge.
This one fold creates respective edge points which mark out various ratios:
$latex \frac{1}{2}, \frac{1}{6}, \frac{1}{8}, \frac{3}{8}, \frac{\sqrt{5}}{2}, \frac{5}{24}, \dots $
Without ruler, this is the most accurate way to obtain length of $latex \frac{1}{3}, \sqrt{5} \dots $
As summarized in the diagram:
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