Kawasaki's theorem governs this process by showing that alternating angles around a vertex must sum to 180 degrees, and it also determines when the outcome of this process can be  attened.
Haga's theorem shows how to use this process to generate an arbitrary rational number. Maekawa's theorem relates the number of  mountains  and  valleys  obtained through this process. The Huzita-Hatori axioms formalize what can be done using this process, which can solve third-degree equations and therefore is capable of doubling the cube and trisecting the angle.   Kawasaki's theorem governs this process by showing that alternating angles around a vertex must sum to 180 degrees, and it also determines when the outcome of this process can be  attened. For ten points, identify this Japanese practice which can be used for geometric construction as well as for art to create things like paper cranes.
Haga's theorem shows how to use this process to generate an arbitrary rational number.
origami [accept descriptive answers like paper folding, prompt on folding]