Origami

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The traditional crane and papers of the same size used to fold it
A paper pegasus designed by F. Kawahata

Origami (Japanese: 折り紙; ori, to fold, and kami, paper; "folding paper") is the Japanese art of paper folding. The goal of this art is to create three-dimensional paper figures using geometric folds and crease patterns. Today, origami refers to all types of paper folding, even those of non-Japanese origin.

Origami only uses a small number of different folds, but they can be combined in a variety of ways to make intricate designs. In general, these designs begin with a square sheet of paper, whose sides may be different colors, and usually proceed without cutting the paper. Contrary to most popular belief, traditional Japanese origami, which has been practiced since the Edo period (1603–1867), has often been less strict about these conventions, sometimes cutting the paper during the creation of the design (Kirigami, 切り紙) or starting with rectangular, circular, triangular or other non-square sheets of paper.

Today origami is a popular hobby and art form all over the world. Modern practitioners have developed new techniques, including wet-folding, which allow them greater freedom of design. The mathematical principles of origami are used in engineering technology.

Contents

History

The origins of origami are disputed, but origami certainly farther in Japan than anywhere else. Origami was mostly a traditional art until Akira Yoshizawa spurred an artistic renaissance of origami with his new advancements, including wet-folding and the Yoshizawa-Randlett system of diagramming. In the 1960s the art of origami began to become popular worldwide and new styles, such as modular origami, and movements, including the kirikomi, purist and pureland, developed.

Origins and Traditional Designs

The "invention" of folding paper probably followed soon after the invention of paper itself. Paper was first invented and popularized in China, and many Chinese speculate that origami originated from Chinese paper folding. The earliest known traditions of Japanese paper folding were of ceremonial origin, such as the Japanese noshi (white paper folded with a strip of dried abalone or meat, attached to gifts and considered a token of good fortune), first recorded during the Muromachi period (1392–1573). Origami was initially used only for religious purposes due to the high cost of paper. When new production techniques made paper cheaper and more available, origami became popular as a form of entertainment and traditional paper figures such as the crane were developed; during this period, the first two origami books were published.

A type of European origami evolved independently; the folded baptismal certificate of the sixteenth century representing a little bird (pajarita in Spanish or cocotte in French) was one of the only models developed outside of Japan.

The Japanese word "origami" itself is a compound of two smaller Japanese words: oru, meaning fold, and kami, meaning paper. It is only recently that all forms of paper folding were grouped under the word origami. Before that, paper folding for play was known by a variety of names, including orikata, "orisue, orimono, tatamigami and tsutsumi (a kind of gift wrapping used for formal occasions). It is not clear when the word "origami" came into use; it has been suggested that the word was adopted in the kindergartens because the written characters were easier for young children to write. Another theory is that the word "origami" was a direct translation of the German word Papierfalten, brought into Japan with the Kindergarten Movement around 1880.

Modern Designs and Innovations

An example of Modular Origami (Geometric shapes formed from Sonobe units)

Complex origami models normally require thin, strong paper or tissue foil for successful folding; these lightweight materials allow for more layers before the model becomes impractically thick. Modern origami has broken free from the traditional linear construction techniques of the past, and models are now frequently wet-folded or constructed from materials other than paper and foil. A new generation of origami creators has experimented with crinkling techniques and smooth-flowing designs used in creating realistic masks, animals, and other traditionally artistic themes.

Joseph Albers, the father of modern color theory and minimalistic art, taught origami and paper folding in the 1920s and 1930s. His methods, which involved sheets of round paper that were folded into spirals and curved shapes, have influenced modern Japanese origami artists like Kunihiko Kasahara. Friedrich Fröbel, founder of the kindergartens, recognized paper binding, weaving, folding, and cutting as teaching aids for child development during the early 1800s.

The work of Akira Yoshizawa of Japan, a prolific creator of origami designs and writer of books on origami, inspired a modern renaissance of the craft. He invented the process and techniques of wet-folding and created an initial set of symbols, the standard Yoshizawa-Randlett system (later improved on by Robert Harbin and Samuel Randlett) for writing down origami instructions. His work was promoted through the studies of Gershon Legman, published in the seminal books of Robert Harbin, Paper Magic and Secrets of the Origami Masters, which introduced the wide world of paper folding to the West in the mid 1960s. Modern origami has attracted a worldwide following, with ever more intricate designs and new techniques such as 'wet-folding,' the practice of dampening the paper somewhat during folding to allow the finished product to hold shape better, and variations such as modular origami (also known as unit origami), where many origami units are assembled to form a decorative whole.

Sadako and the Thousand Cranes

Sadako Sasaki memorial in Hiroshima, surrounded by paper cranes

One of the most famous origami designs is the Japanese crane (orizuru, 折鶴). The crane is auspicious in Japanese culture; legend says that anyone who folds one thousand paper cranes will have their heart's desire come true. Many Japanese prepare a garland of one thousand paper cranes (senbazuru) when a friend or family member is ill, as a form of prayer for their recovery.

A famous story has turned the origami crane into a symbol of peace. In 1955, a twelve-year-old Japanese girl named Sadako Sasaki, who had been exposed to the radiation of the atomic bombing of Hiroshima as an infant, was dying of leukemia. She decided to fold one thousand cranes in hopes of becoming cured. When she realized that she would not survive, she wished instead for world peace and an end to suffering. Sadako folded more than 1,300 cranes before her death and was buried with a wreath of one thousand cranes to honor her dream. While her effort could not extend her life, it moved her friends to make a granite statue of Sadako in the Hiroshima Peace Park: a young girl standing with her hand outstretched, a paper crane flying from her fingertips. The tale of Sadako has been dramatized in many books and movies. In one version, Sadako wrote a haiku that translates into English as: "I shall write peace upon your wings, and you shall fly around the world so that children will no longer have to die this way."

Paper and Other Materials

Smallcrane.jpg
Some people fold miniature origami models as a challenge

Although almost any laminar material can be used for folding, the choice of material used greatly affects the folding and final look of the model.

Normal copy paper with weights of 70–90 grams/meter² can be used for simple folds, such as the crane and water bomb. Heavier weight papers of 100 grams/meter² or more can be wet-folded. This technique allows for a more rounded sculpting of the model, which becomes rigid and sturdy when dry.

An example of a paper art star on a window, which does not meet the typical requirements of origami as it is constructed from multiple pieces of paper

Special origami paper, often also referred to as kami, is sold in prepackaged squares of various sizes ranging from 2.5 to 25 centimeters or more. It is commonly colored on one side and white on the other; however, dual colored and patterned versions exist and can be used effectively for multi-colored models. Origami paper weighs slightly less than copy paper, making it suitable for a wider range of models.

Foil-backed paper, just as its name implies, is a sheet of thin foil glued to a sheet of thin paper. Related to this is tissue foil, which can be made by gluing a thin piece of tissue to kitchen aluminum 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. Both types of foil materials are suitable for complex models.

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

Mathematics of Origami

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 two-dimensional model) has been a topic of considerable mathematical study. Folding a flat model from a crease pattern has been proven by Marshall Bern and Barry Hayes to be NP complete.

Paper exhibits zero Gaussian curvature at all points on its surface, and only folds naturally along lines of zero curvature. But the curvature along the surface of a non-folded crease in the paper, as is easily done with wet paper or a fingernail, no longer exhibits this constraint.

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 significant practical application. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.

Technical Origami

Origami Chinese dragon

The field of technical origami, also known as origami sekkei, has developed almost hand-in-hand with mathematical origami. In the early days of origami, development of new designs was largely a mix of trial-and-error, luck and serendipity. With advances in origami mathematics however, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding occurs. This method of origami design was pioneered by Robert J. Lang, Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes and human figures with fingers and toes.

The main starting point for such technical designs is the crease pattern (often abbreviated as 'CP'), which is essentially the layout of the creases required to form the final model. Although not intended as a substitute for instructional diagrams, folding from crease patterns is becoming popular, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams.

Paradoxically, when origami designers come up with a crease pattern for a new design, the majority of the smaller creases are relatively unimportant and added only towards the completion of the crease pattern. What is more important is the allocation of regions of the paper and how these are mapped to the structure of the object being designed. For a specific class of origami bases known as “uniaxial bases,” the pattern of allocations is referred to as the “circle-packing.” Using optimization algorithms, a circle-packing figure can be computed for any uniaxial base of arbitrary complexity. Once this figure is computed, the creases which are then used to obtain the base structure can be added. This is not a unique mathematical process, hence it is possible for two designs to have the same circle-packing, and yet different crease pattern structures.

Origami as a Hobby

Origami is a popular hobby in Japan for both children and adults. Before the advent of television and video games, origami was a common form of indoor entertainment for Japanese children. Stationery shops carry many varieties of origami paper. In addition to traditional papers, new designs are frequently released, printed with popular cartoon characters, exciting patterns and colors, and thermal inks which change color according to the temperature. Some origami designs produce toys such as paper samurai helmets, balls, boxes, water bombs, hopping frogs, ninja stars, paper airplanes and animated faces.

Origami is used for a number of ceremonial and religious purposes, such as the ornamentation of temples and ancestral shrines, presentation of gifts and temple offerings, preparations for New Year celebrations, and the decoration of plaques commemorating special occasions. Origami is sometimes used as a means of practicing Zen Buddhism, with special attention to ritual, concentration, the internal attitude of the artist, and the meaning of the designs. Adults sometimes attend classes with origami “Masters” to learn how to fold intricate figures.

Origami and Child Development

Paper folding is recognized as an excellent means of developing hand-eye coordination and mental concentration in young children. It has been shown that the use of the hands directly stimulates certain areas of the brain. Since successful origami requires making precise geometric folds, it also teaches children to pay attention to detail and to take the time to make the folds correctly. Origami is frequently used as an activity in kindergartens and elementary schools. Working with colors and three-dimensional objects also heightens awareness of perspective and artistic sensitivity.

Origami is also used for therapeutic purposes, such as art therapy and rehabilitation after an injury or stroke. British paper folder John Smith invented Pureland Origami, which uses only mountain and valley folds, to make origami easier for inexperienced folders and those who have impaired motor skills. Since many of the more complicated processes common in regular origami are impossible for these people, alternative manipulations have been developed to create similar effects.


References

  • Fuse, Tomoko. Unit Origami: Multidimensional Transformations. Tokyo: Japan Publications, 1990. ISBN 0870408526
  • Ishii, Takayuki. One Thousand Paper Cranes: The Story of Sadako and the Children's Peace Statue. ISBN 0440228433
  • Kasahara, Kunihiko. Origami Omnibus: Paper Folding for Everybody. Tokyo: Japan Publications, Inc. ISBN 4817090014
  • Kasahara, Kuniko and Toshie Takahama. Origami for the Connoisseur. Tokyo: Japan Publications, Inc., 1987. ISBN 0870406701
  • Harbin, Robert. Teach Yourself Origami. NTC/Contemporary Publishing Company, 1992.
  • Kasahara, Kunihiko. Extreme Origami. Sterling, 2003. ISBN 0806988533
  • Lang, Robert J. Origami Design Secrets: Mathematical Methods for an Ancient Art. A. K. Peters, Ltd., 2003.
  • Lang, Robert J. The Complete Book of Origami: Step-by-Step Instructions in Over 1000 Diagrams. Mineola, NY: Dover Publications, 1988. ISBN 0486258378

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