Origami (折り紙?, from ori meaning "folding", and kami meaning "paper" (kami changes to gami due to rendaku) is the traditional Japanese art of paper folding, which started in the 17th century AD at the latest and was popularized outside of Japan in the mid-1900s. It has since evolved into a modern art form. The goal of this art is to transform a flat sheet of paper into a finished sculpture through folding and sculpting techniques, and as such the use of cuts or glue are not considered to be origami. Paper cutting and gluing is usually considered kirigami.
The number of basic origami folds is small, but they can be combined in a variety of ways to make intricate designs. The best known origami model is probably the Japanese paper crane. In general, these designs begin with a square sheet of paper whose sides may be different colors or prints. Traditional Japanese origami, which has been practiced since the Edo era (1603–1867), 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 structures.
There is much speculation about the origin of Origami. While Japan seems to have had the most extensive tradition, there is evidence of an independent tradition of paperfolding in China, as well as in Germany, Italy and Spain, among other places. However, because of the problems associated with preserving origami, there is very little direct evidence of its age or origins, aside from references in published material.
In China, traditional funerals include burning folded paper, most often representations of gold nuggets (yuanbao). It is not known when this practice started, but it seems to have become popular during the Sung Dynasty (905–1125 CE). The paper folding has typically been of objects like dishes, hats or boats rather than animals or flowers.
The earliest evidence of paperfolding in Europe is a picture of a small paper boat in Tractatus de sphaera mundi, a textbook on astronomy, from 1490. There is also evidence of a cut and folded paper box from 1440. It is probable that paperfolding in the west originated with the Moors much earlier; it is not known if it was independently discovered or knowledge of origami came along the silk route.
In Japan, the earliest unambiguous reference to a paper model is in a short poem by Ihara Saikaku in 1680 which describes paper butterflies in a dream. Origami butterflies were used during the celebration of Shinto weddings to represent the bride and groom, so paperfolding had already become a significant aspect of Japanese ceremony by the Heian period (794–1185) of Japanese history, enough that the reference in this poem would be recognized. Samurai warriors would exchange gifts adorned with noshi, a sort of good luck token made of folded strips of paper.
In the early 1900s, Akira Yoshizawa, Kosho Uchiyama, and others began creating and recording original origami works. Akira Yoshizawa in particular was responsible for a number of innovations, such as wet-folding and the Yoshizawa–Randlett diagramming system, and his work inspired a renaissance of the art form. During the 1980s a number of folders started systematically studying the mathematical properties of folded forms, which led to a steady increase in the complexity of origami models, which continued well into the 1990s, after which some designers started returning to simpler forms.