From constructing a midpoint on a line to observing specific divisions of a plane, the art form of Origami borrows many mathematical tools in order to create complex, and often symmetrical, patterns in a paper medium known as a fold. For this project, the traditional fold known as the Origami Crane/Swan will be thoroughly examined as it contains the unique property to lie completely flat when complete. This phenomenon occurs because the vertices holding the fold together are not all considered to be flat folds. The different types of vertices interacting with each other create a natural locking mechanism within the medium and make it impossible for the medium to unravel. Using established geometrical and origami theorems, this project intends to deconstruct these locks and investigate the mathematics behind how the construction works.
Davis, Zachary, "Folding Mathematics: A Mathematical Approach to Origami" (2019). Mathematics Senior Capstone Papers. 11.