page_title: Origami
section_title: Mathematics and practical applications
hierarchical_section_title: Origami / Mathematics and technical origami / Mathematics and practical applications
caption_attribution_description: Information/Description = Origami spring Source = Made by me, invented by Jeff Beynon Date = 9th February 2006 Author = Jason Ruck
context_page_description: Origami is the art of paper folding, which is often associated with Japanese culture. In modern usage, the word "origami" is used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word kirigami to refer to designs which use cuts.
  The small number of basic origami folds can be combined in a variety of ways to make intricate designs. The best-known origami model is the Japanese paper crane. In general, these designs begin with a square sheet of paper whose sides may be of different colors, prints, or patterns. Traditional Japanese origami, which has been practiced since the Edo period, has often been less strict about these conventions, sometimes cutting the paper or using nonsquare shapes to start with. The principles of origami are also used in stents, packaging, and other engineering applications.*
context_section_description: The practice and study of origami encapsulates several subjects of mathematical interest. For instance, the problem of flat-foldability (whether a crease pattern can be folded into a 2-dimensional model) has been a topic of considerable mathematical study.
  A number of technological advances have come from insights obtained through paper folding. For example, techniques have been developed for the deployment of car airbags and stent implants from a folded position.
  The problem of rigid origami ("if we replaced the paper with sheet metal and had hinges in place of the crease lines, could we still fold the model?") has great practical importance. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.
  Origami can be used to construct various geometrical designs not possible with compass and straightedge constructions. For instance paper folding may be used for angle trisection and doubling the cube.
caption: Spring Into Action, designed by Jeff Beynon, made from a single rectangular piece of paper[16]
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