A first step

History

The folding of two origami cranes linked together, from the first known book on origami, Hiden senbazuru orikata, published in Japan in 1797

Distinct paperfolding traditions arose in Europe, China, and Japan which have been well-documented by historians. These seem to have been mostly separate traditions, until the 20th century.

In China, traditional funerals often include the burning of folded paper, most often representations of gold nuggets (yuanbao). The practice of burning paper representations instead of full-scale wood or clay replicas dates from the Song Dynasty (905–1125 CE), though it is not clear how much folding was involved.[3]

In Japan, the earliest unambiguous reference to a paper model is in a short poem by Ihara Saikaku in 1680 which mentions a traditional butterfly design used during Shinto weddings.[4] Folding filled some ceremonial functions in Edo period Japanese culture; noshi were attached to gifts, much like greeting cards are used today. This developed into a form of entertainment; the first two instructional books published in Japan are clearly recreational.

In Europe, there was a well-developed genre of napkin folding, which flourished during the 17th and 18th centuries. After this period, this genre declined and was mostly forgotten; historian Joan Sallas attributes this to the introduction of porcelain, which replaced complex napkin folds as a dinner-table status symbol among nobility.[5] However, some of the techniques and bases associated with this tradition continued to be a part of European culture; folding was a significant part of Friedrich Fröbel’s “Kindergarten” method, and the designs published in connection with his curriculum are stylistically similar to the napkin fold repertoire. Another example of early origami in Europe is the “pajarita,” a stylized bird whose origins date from at least the nineteenth century.[6]

When Japan opened its borders in the 1860s, as part of a modernization strategy, they imported Fröbel’s Kindergarten system—and with it, German ideas about paperfolding. This included the ban on cuts, and the starting shape of a bicolored square. These ideas, and some of the European folding repertoire, were integrated into the Japanese tradition. Before this, traditional Japanese sources use a variety of starting shapes, often had cuts; and if they had color or markings, these were added after the model was folded.[7]

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.[8] During the 1980s a number of folders started systematically studying the mathematical properties of folded forms, which led to a rapid increase in the complexity of origami models.[9]

Starting in the late 20th century, there has been a renewed interest in understanding the behavior of folding matter, both artistically and scientifically. The “new origami,” which distinguishes it from old craft practices, has had a rapid evolution due to the contribution of computational mathematics and the development of techniques such as box-pleating, tessellations and wet-folding. Artists like Robert J. Lang, Erik Demaine, Sipho Mabona, Giang Dinh, Paul Jackson, and others, are frequently cited for advancing new applications of the art. The computational facet and the interchanges through social networks, where new techniques and designs are introduced, have raised the profile of origami in the 21st century.[10][11][12] Techniques and materials Techniques A list of nine basic origami folds: the valley (or mountain), the pleat, the rabbit ear, the outside reverse, the inside reverse, the crimp, the squash, the sink and the petal Main article: Yoshizawa–Randlett system

Many origami books begin with a description of basic origami techniques which are used to construct the models. This includes simple diagrams of basic folds like valley and mountain folds, pleats, reverse folds, squash folds, and sinks. There are also standard named bases which are used in a wide variety of models, for instance the bird base is an intermediate stage in the construction of the flapping bird.[13] Additional bases are the preliminary base (square base), fish base, waterbomb base, and the frog base.[14] Origami paper Main article: Origami paper A crane and papers of the same size used to fold it

Almost any laminar (flat) material can be used for folding; the only requirement is that it should hold a crease.

Origami paper, often referred to as “kami” (Japanese for paper), is sold in prepackaged squares of various sizes ranging from 2.5 cm (1 in) to 25 cm (10 in) or more. It is commonly colored on one side and white on the other; however, dual coloured and patterned versions exist and can be used effectively for color-changed models. Origami paper weighs slightly less than copy paper, making it suitable for a wider range of models.

Normal copy paper with weights of 70–90 g/m2 (19–24 lb) can be used for simple folds, such as the crane and waterbomb. Heavier weight papers of 100 g/m2 (approx. 25 lb) or more can be wet-folded. This technique allows for a more rounded sculpting of the model, which becomes rigid and sturdy when it is dry.

Foil-backed paper, as its name implies, is a sheet of thin foil glued to a sheet of thin paper. Related to this is tissue foil, which is made by gluing a thin piece of tissue paper to kitchen aluminium foil. A second piece of tissue can be glued onto the reverse side to produce a tissue/foil/tissue sandwich. Foil-backed paper is available commercially, but not tissue foil; it must be handmade. Both types of foil materials are suitable for complex models.

Washi (和紙) is the traditional origami paper used in Japan. Washi is generally tougher than ordinary paper made from wood pulp, and is used in many traditional arts. Washi is commonly made using fibres from the bark of the gampi tree, the mitsumata shrub (Edgeworthia papyrifera), or the paper mulberry but can also be made using bamboo, hemp, rice, and wheat.

Artisan papers such as unryu, lokta, hanji[citation needed], gampi, kozo, saa, and abaca have long fibers and are often extremely strong. As these papers are floppy to start with, they are often backcoated or resized with methylcellulose or wheat paste before folding. Also, these papers are extremely thin and compressible, allowing for thin, narrowed limbs as in the case of insect models.

Paper money from various countries is also popular to create origami with; this is known variously as Dollar Origami, Orikane, and Money Origami. Tools Bone folders

It is common to fold using a flat surface, but some folders like doing it in the air with no tools, especially when displaying the folding.[citation needed] Some folders believe that no tool should be used when folding.[citation needed] However a couple of tools can help especially with the more complex models. For instance a bone folder allows sharp creases to be made in the paper easily, paper clips can act as extra pairs of fingers, and tweezers can be used to make small folds. When making complex models from origami crease patterns, it can help to use a ruler and ballpoint embosser to score the creases. Completed models can be sprayed so that they keep their shape better, and a spray is needed when wet folding. Types Action origami Main article: Action origami

In addition to the more common still-life origami, there are also moving object designs; origami can move. Action origami includes origami that flies, requires inflation to complete, or, when complete, uses the kinetic energy of a person’s hands, applied at a certain region on the model, to move another flap or limb. Some argue that, strictly speaking, only the latter is really “recognized” as action origami. Action origami, first appearing with the traditional Japanese flapping bird, is quite common. One example is Robert Lang’s instrumentalists; when the figures’ heads are pulled away from their bodies, their hands will move, resembling the playing of music. Modular origami A stellated icosahedron made from custom papers Main article: Modular origami

Modular origami consists of putting a number of identical pieces together to form a complete model. Often the individual pieces are simple, but the final assembly may be more difficult. Many modular origami models are decorative folding balls such as kusudama, which differ from classical origami in that the pieces may be held together using thread or glue.

Chinese paper folding, a cousin of origami, includes a similar style called golden venture folding where large numbers of pieces are put together to create elaborate models. This style is most commonly known as “3D origami”. However, that name did not appear until Joie Staff published a series of books titled 3D Origami, More 3D Origami, and More and More 3D Origami.[citation needed] This style originated from some Chinese refugees while they were detained in America and is also called Golden Venture folding from the ship they came on.[citation needed] Wet-folding Main article: Wet-folding

Wet-folding is an origami technique for producing models with gentle curves rather than geometric straight folds and flat surfaces. The paper is dampened so it can be moulded easily, the final model keeps its shape when it dries. It can be used, for instance, to produce very natural looking animal models. Size, an adhesive that is crisp and hard when dry, but dissolves in water when wet and becoming soft and flexible, is often applied to the paper either at the pulp stage while the paper is being formed, or on the surface of a ready sheet of paper. The latter method is called external sizing and most commonly uses Methylcellulose, or MC, paste, or various plant starches. Pureland origami Main article: Pureland origami

Pureland origami adds the restrictions that only simple mountain/valley folds may be used, and all folds must have straightforward locations. It was developed by John Smith in the 1970s to help inexperienced folders or those with limited motor skills. Some designers also like the challenge of creating within the very strict constraints. Origami tessellations

Origami tessellation is a branch that has grown in popularity after 2000. A tessellation is a collection of figures filling a plane with no gaps or overlaps. In origami tessellations, pleats are used to connect molecules such as twist folds together in a repeating fashion. During the 1960s, Shuzo Fujimoto was the first to explore twist fold tessellations in any systematic way, coming up with dozens of patterns and establishing the genre in the origami mainstream. Around the same time period, Ron Resch patented some tessellation patterns as part of his explorations into kinetic sculpture and developable surfaces, although his work was not known by the origami community until the 1980s. Chris Palmer is an artist who has extensively explored tessellations after seeing the Zilij patterns in the Alhambra, and has found ways to create detailed origami tessellations out of silk. Robert Lang and Alex Bateman are two designers who use computer programs to create origami tessellations. The first international convention devoted to origami tessellations was hosted in Brasília (Brazil) in 2006,[15] and the first instruction book on tessellation folding patterns was published by Eric Gjerde in 2008.[16] Since then, the field has grown very quickly. Tessellation artists include Polly Verity (Scotland); Joel Cooper, Christine Edison, Ray Schamp and Goran Konjevod from the USA; Roberto Gretter (Italy); Christiane Bettens (Switzerland); Carlos Natan López (Mexico); and Jorge C. Lucero (Brazil). Kirigami Main article: Kirigami

Kirigami is a Japanese term for paper cutting. Cutting was often used in traditional Japanese origami, but modern innovations in technique have made the use of cuts unnecessary. Most origami designers no longer consider models with cuts to be origami, instead using the term Kirigami to describe them. This change in attitude occurred during the 1960s and 70s, so early origami books often use cuts, but for the most part they have disappeared from the modern origami repertoire; most modern books don’t even mention cutting.[17] Strip folding

Strip folding is a combination of paper folding and paper weaving.[18] A common example of strip folding is called the Lucky Star, also called Chinese lucky star, dream star, wishing star, or simply origami star. Another common fold is the Moravian Star which is made by strip folding in 3-dimensional design to include 16 spikes.[18] Teabag folding Example of folded “tea bag” paper

Teabag folding is credited to Dutch artist Tiny van der Plas, who developed the technique in 1992 as a papercraft art for embellishing greeting cards. It uses small square pieces of paper (e.g., a tea bag wrapper) bearing symmetrical designs that are folded in such a way that they interlock and produce a three-dimensional version of the underlying design. The basic kite fold is used to produce rosettes that are a 3 dimensional version of the 2D design.

The basic rosette design requires eight matching squares to be folded into the ‘kite’ design. Mathematics teachers find the designs very useful as a practical way of demonstrating some basic properties of symmetry.[citation needed]