Origami (Paper folding) (折り紙)

Origami is the traditional Japanese art of folding paper to make models of plants, animals, daily-use tools and amongst others. It also refers to a folded paper model itself or a piece of square paper used exclusively for origami. Recently, it has been recognized from its artistic aspect, and original, elaborate, designs of beauty have been created. In addition to the traditional way of folding paper in every country, new ways of folding paper are also being invented.
(See the list of traditional origami for respective ways of folding paper.)
Due to the geometric feature of origami, it has been studied as a field of mathematics.

Summary

In the past, colorful paper called chiyogami was used for origami. Therefore, origami paper can be called chiyogami. Recently, chiyogami has been sold as traditional art work.

In many cases, origami models are made of a sheet of paper without using scissors or glue, but scissors are used to cut paper for certain designs which require two sheets of paper, for example shuriken (a small throwing blade). A folding bone may be used if an intricate model is made or it is hard to make a crease in paper.

A model is made by folding paper carefully or tucking one end of the folded paper into a pocket. Because paper is folded continuously, a completed model can be much smaller than the unfolded paper.

Typical origami models include cranes (folded paper crane or connected cranes), balloons, paper airplanes, shuriken, kabuto (a samurai war helmet) and yakkosan (a samurai's attendant). A typical European origami model includes a small bird (or hen) called pajarito in Spanish and cocotte in French. In a broad sense, folded napkins for western dishes are also a type of origami.

Single square-paper folding without cutting

It is called 'fusetsu seihokei ichimaiori' in Japanese. Only a sheet of square paper is used for it without using scissors.

It is a fundamental type of origami, which many people seem to like.

Fukugo origami (Combined origami)

It consists of combining different models to make the end model. A traditional fukugo origami is a combined model of yakkosan and hakama (a pleated and divided skirt). Intricate models can be expressed relatively easily without cutting paper, and colorful designs can be achieved by using paper in different colors. When the models are put together, glue or wires may be used.

Kirikomi origami (Cut origami)

This involves facilitating the creation of intricate models by cutting paper to increase the corners of paper or cutting off a part of paper.
Many origami fans see it as an improper way of creating origami, but some say that, 'It is better than to be complicated by sticking to the fusetsu seihokei ichimaiori (single square-paper folding without cutting).'
The connected paper cranes seen in the "Hiden Senbazuru Origata (secret 1,000 paper cranes model)" are made by using scissors.

Unit origami (Modular origami)

A number of identical pieces are made by using multiple sheets of paper. It consists of putting those pieces together to make a complete model. It usually includes polyhedral objects with high symmetry such as a model generally called kusudama (decorative paper ball), and boxes. Two to dozens of, or at most, more than ten thousand pieces may be put together. When the unit pieces are put together, it is preferable to support the whole model only by the friction of paper, but they can also be glued together or sewn by threads. Kunihiko KASAHARA, Miyuki KAWAMURA and Tomoko FUSE are famous unit origami artists. Origamizaiku (origami work) is similar to the unit origami. The traditional model of shuriken is also a type of unit origami.

Shikake origami (Trick origami)

This is origami that is made as a movable toy in addition to the origami mentioned above. Traditionally, it includes a "camera (the shutter released)" and a "flying bird (the wings flapped by pulling the neck and the tail)." In recent years, intricate models have been created such as "kuroimori no majo (a witch in the black wood)" (the witch transformed into a dragon and vice versa) created by Satoshi KAMIYA.

Origami bases

There are some basic shapes in origami. For example, the crane base has four angular corners, which are applied to a head and legs to facilitate the creation of animal models. Typical origami bases are listed below.

Crane base

This is the intermediate stage of making a traditional paper crane model.

Iris base

This is the intermediate stage of making a traditional iris model. It is also called the frog base.

Fish base

This is the intermediate stage of making a fish.

Door base

It is the shape of a 'door' created by folding paper in half to be rectangle. This is used to make unit pieces for unit origami.

Origami paper

A square paper exclusively for origami is commonly used. Depending on the design, a rectangle (with a side-to-side ratio of one times the square root of two) or other papers can be used. Newspapers are used for some models (a hat, a mitt and a paper gun). There was even an attempt to use paper money as origami material and incorporate patterns like the portrait as a part of the design of the finished model. Some designs require special papers with polygonal shapes including the pentagon and hexagon, and in this case, it is better to cut out those papers of square papers as required.

15 cm-square origami paper is commonly sold in shops, but larger or smaller origami paper (5 cm, 7.5 cm, 24 cm, 35 cm square and etc.) is also available commercially. It is rare, but there is a circular origami paper as well. It is said that more than 1000 varieties of colorful origami paper are available with colors on both sides, transparent colors, gradational colors, special patterns such as dots, dual or quartered colors amongst others.

When intricate models are made, foil paper made of metal leaf or home-made paper made by lining (untearable) thin washi (Japanese paper) with metal leaf (for example, aluminum foil to avoid losing shape) is used.

In many cases, Western or Japanese paper selected for appearance is cut into a square (or an appropriate shape for them) for models destined for exhibition. Wet folding, a technique to dampen thick paper (such as Western paper) moderately as needed before folding, is used as well. If this technique is used, thick paper can be easily folded or creases can be considerably reduced. It allows curved shape to be fixed and paper to be folded with it stretched (or distorted).

Even if square paper is not available, origami can be fully enjoyed with paper made by shaping unwanted documents in hand into a square with a little ingenuity, and therefore it is not necessary to prepare origami paper in advance.

Folding diagrams

There is a folding diagram which shows the process with symbols (usually in pictures), allowing people to understand how to fold a piece of origami. Conventionally, in the diagram, dashed-dotted lines ('-・-・-・-・-') and broken lines ('- - - - -') show the mountain fold and the valley fold, respectively. In many cases, to facilitate understanding, instructions in writing are added to the diagram.

Major folds

In origami, there are basic folds as follows:

Mountain fold

Valley fold

Inside reverse fold

Outside reverse fold

There are other specific folds.

Bellows fold

Miura map fold

Origami tessellation

Spiral fold

History

The origin of origami has not been identified. Its possible origin includes China, Japan, Spain amongst others, but remains a matter of speculation. There is speculation that origami originated in China because paper originated in China, but as yet there is no strong evidence. Japanese origami seemed to have developed on its own, was not introduced by others as described below. In the 19th century, Europe had its own independent origami tradition, which was fused with Japanese origami when Japan opened up to the world. Now, the Japanese term 'origami' has become prevalent in the world and the "origami" is understood in many countries including Europe and America. Modern origami originated in Japan and Europe.

The Japanese origami can be split into two categories. Origami like the paper crane model commonly seen is called yugi origami (play paper folding), and other origami like noshi (folded red and white paper) is called girei origami (ceremonial paper folding).

Girei origami (ceremonial paper folding)

As far as is shown in literature, the earliest reference to the girei origami was ocho and mecho (male and female butterfly models) in the haiku, 'butterflies in a beggar's dream are origami' composed by Saikaku IHARA in the 'Ittyuya Dokugin onsenku (4000 Haikus Recited Alone All Day and Night)" in 1680. The ocho and mecho, which are attached to the mouth of a sake bottle, are stylized bottle wrappings. Furthermore, the current noshi is a stylized noshi awabi (a thin strip of dried abalone wrapped in folded red and white paper), and an example of the girei origami.

The girei origami is a part of a warrior family's manners and it would appear that it was developed mainly by the Ogasawara clan, the Ise clan and the Imagawa clan in the days of Yoshimitsu ASHIKAGA because "Tsutsumi no ki (record on wrapping)" written by Sadatake ISE in 1764 said that 'the folded paper models on the right were used during the time of the Kyoto shogun.'

Yugi origami (play paper folding)

The "Life of an Amorous Man" written by Saikaku IHARA in 1682 said that:

One day he folded origami and gave it to a female servant, saying "This is a model of male and female birds in one." After making an origami flower, he attached it to the treetop and said, "This is the branch of a conjoined tree and I will give it to you." He never forgot anything concerning amorous affairs.

The above-stated is the oldest record on the yugi origami.

The "Hiden Senbazuru Origata" (Secret Folding of Thousand Cranes) published in 1797 was clearly targeted towards adults, which proves that adults as well as children enjoyed origami in those days. This is considered to be the oldest origami book in existence.

The oldest origami in existence are origami models owned by the Moriwaki family. These models contain both the girei origami and the yugi origami, but the yugi origami was estimated to have been folded in the early 19th century.

European origami

Germanisches National Museum and Saxon Folk Art Museum in Germany possess origami models which are estimated to have been folded in the early 19th century.

The European origami was applied to childhood education by Friedrich Fröbel and introduced to Japan when Japan was opened up to the world.

Typical European traditional origami includes pajarita (cocotte), a sailboat (trick boat), a balloon and a paper airplane (arrow).

Modern and contemporary origami

International origami groups were formed mainly by Akira YOSHIZAWA and Toshie TAKAHAMA from Japan, Robert Harbin from the UK and Liliane Oppenheimer and Samuel Randlett from the US, after which, origami spread throughout the world.

Recently, intricate models have been made, starting with "Viva Origami" (created by Jun MEKAWA; authored by Kunihiko KASAHARA: ISBN 4387891165) published in 1983 and "Folding the Universe" (authored by Peter Engel) published in 1989. The technique of 'technical origami' developed by Jun MAEKAWA had a big influence on origami, and allowed for the rational designing of intricate models for the first time.

When the Nippon Origami Association and Japan Origami Academic Society were established in Japan, origami groups formed in countries including the US and the UK, allowing origami fans to deepen exchanges with each other. Thanks to the spread of the Internet, the speed of communication became faster and technical development has proceeded at an unprecedented speed.

Commercialized toys

The commercialization of traditional toys was applied to origami as well as marbles, kendama toy, and be-goma (spinning top) which were commercially developed into B-daman, DIGI-KEN, and characo badge (a badge doubled as a spinning top), respectively. TOMY Company, Ltd. and Konami Corporation have sold the Origami Wars and the Ori-glide: THE SUPER PAPER AIRPLANE, respectively. The cartoon called Origami senshi (origami warrior) was created in Taiwan and then turned into an anime.

Mathematics and practical applications

There are several mathematical challenges in the applications or study of origami. For example, flat-foldability, an issue as to whether or not a crease pattern can be folded into a two-dimensional model, is an example of a mathematical challenge.

If the paper is flat, the Gaussian curvature is zero at any point on the surface. Therefore, the crease line is fundamentally a straight line with a Gaussian curvature of zero. The condition of this curvature cannot be, however, applied anymore to warped paper such as wet paper or paper wrinkled by a finger nail.

The problem of rigid origami (whether or not a model can be folded like paper by using sheet metal with hinges in place of crease lines) is an important issue pertaining to practical use. For example, the Miura map fold allows a rigid body to be folded and has been used to fold large solar panels for space satellites.

In addition, origami has been applied to fold air bags and stent grafts for medical use.

List of people related to origami

There are some origami artists, but only a handful of artists working as professional. Many professional origami artists write origami books containing folding diagrams to make their living.