Origami as an art is quite varied. Paper folding can be done with the intention of imitating particular animals, people, or objects. It can be a study of simple form and curves, like the one-fold origami discussed in the film. Or, paper can be used to explore movement, such as the spring-like action of folded paper.
Art requires ability and practice. It usually takes years of discipline to develop the skills to excel at an art form. This is just the case with origami. Creating something like this scaly dragon out of paper required time, patience, practice, and skill. Origami is a creative process in which an artist translates his or her ideas into the physical. Paper, like clay or painting, is versatile, moldable, and detailed. An artist uses their hands to tweak, mold, and perfect the paper into a figure with emotion, meaning, and interest. Origami is as much a result as it is a process. In this respect, any material is art once it is intentionally changed in the hands of the artist.
The mathematics of origami is intricate and very complex. The remarkable thing about it it that it encompasses all types of mathematics. Origami can be used to teach geometry and trigonometry for the obvious reason that it involves shapes, angles, and their properties. Paper folding even draws parallels to calculus, which is what makes it such a powerful tool. It is essentially a problem solving puzzle. How can you transform 2D paper into a specific 3D form? And what will that 3D form look like in 2D? Like art, the mathematics of origami requires abstract, multidimensional thinking.
I would have liked for the documentary to address more mathematics and science than it did. It would have been very interesting to know specifically how origami relates to calculus and engineering, and what principles of paper folding mathematicians and engineers might use in their work. Between the Folds also hinted that mathematics of origami may have the potential to explain the universe. To make such a grand statement as that, more explanation was needed.
The film still leaves the audience with some excitement about the potential of paper. If paper folding is such a powerful thing, what can we learn about the world around us from between the folds?
