Origami

Origami (折り紙, origami) (from ori meaning "folding", and kami meaning "paper") is the ancient Japanese art of paper folding. The goal of this art is to create a given result using geometric folds and crease patterns preferably without the use of gluing or cutting the paper medium. "Origami" refers to all types of paper folding, even those of non-Asian origin.^{[citation needed]}

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. Contrary to most popular belief, 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 during the creation of the design.

History

Origami originated in China as "Zhe Zhi" (Simplified Chinese: 折纸, Traditional Chinese: 摺紙) in the first or second century AD, and it reached Japan in the sixth century. Origami had already become a significant aspect of Japanese ceremony by the Heian period of Japanese history. Samurai warriors would exchange gifts adorned with noshi, a sort of good luck token made of folded strips of paper. Origami butterflies were used during the celebration of Shinto weddings to represent the bride and groom.

In the 1960's the art of origami began to spread out, first with modular origami and then with various movements developing, including the kirikomi.

Paper and other materials

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 g/m² (19-24lb) can be used for simple folds, such as the crane and waterbomb. Heavier weight papers of 100 g/m² (approx. 25lb) 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.

Special origami paper, often also referred to as "kami" (Japanese for paper), is sold in prepackaged squares of various sizes ranging from 2.5 cm to 25 cm 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.

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 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 predominant 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 fibers from the bark of the gampi tree, the mitsumata shrub (Edgeworthia papyrifera), or the paper mulberry but also can be made using bamboo, hemp, rice, and wheat.

Artisan papers such as unryu, lokta, hanji, gampi, kozo, saa, and abaca have long fibres 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 are also popular to create origami with, called "Moneygami". It is common to create the figure depicted on the note itself.

Few other items other than paper and fingers are necessary to fold origami; however, some enthusiasts prefer to use a folding bone to sharpen creases while folding. Other folders grow certain nails long to aid with creasing instead of a folding bone.

Action Origami

Origami doesn't just cover still-lifes it covers real life objects; Origami can move in clever ways. Action origami includes origami that flies, requires inflation to complete, or, when complete, utilizes the kinetic energy of your hands applied at a certain region on the model and transfers it through an internal mechanism to move another flap or limb. Strictly speaking only the latter is really "recognized" as action origami. Action origami, first appearing with the traditional Japanese flapping bird, is quite common with Robert Lang's instrumentalists; when the figures' heads are pulled away from their bodies, their hands will move, resembling to play music.

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 2-dimensional model) has been a topic of considerable mathematical study.

Significantly, 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, is no longer subject to 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 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.

Technical origami

Technical origami, also known as origami sekkei (折り紙設計), is a field of origami that has developed almost hand-in-hand with the field of 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 even occurs. This method of origami design was pioneered by Robert Lang, Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes, human figures with a full complement of fingers and toes, and the like.

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 diagrams, folding from crease patterns is starting to gain in popularity, 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. Still, there are many cases in which designers wish to sequence the steps of their models but lack the means to design clear diagrams. Such origamists occasionally resort to the Sequenced Crease Pattern (abbreviated as SCP) which is a set of crease patterns showing the creases up to each respective fold. The SCP eliminates the need for diagramming programs or artistic ability while maintaining the step-by-step process for other folders to see. Another name for the Sequenced Crease Pattern is the Progressive Crease Pattern (PCP).

Paradoxically enough, 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.

Gallery

A paper Pegasus designed by F. Kawahata

A paper Pegasus designed by F. Kawahata

Authors of books about origami

Akira Yoshizawa - reinvented modern origami. Created the modern repertoire of folding symbols
Robert J. Lang - Author of many Origami books including the new benchmark Origami Design Secrets
Peter Engel - influential origami artist and theorist
Tomoko Fuse - famous for boxes and unit origami
Robert Harbin - popularised origami in Britain; also presented a series of short programmes entitled Origami, made by Thames Television for ITV
Eric Joisel - French wet-folder renowned for his life-like masks
Kunihiko Kasahara - devised a standardized method for creating many modular polyhedra
John Montroll - probably the most prolific Western artist and author of over 16 books on origami
Nick Robinson - origami artist and author of over a dozen books on origami
Toshikazu Kawasaki - Japanese mathematician famous for his Iso-area folding theory and his many geometric folds, including Kawasaki's "Rose"
Makoto Yamaguchi
Jeremy Shafer - California origamian entertainer who folds whimsical designs
Satoshi Kamiya - One of the youngest geniuses of the origami field
Nicolas Terry - French artist known for his unique, cartoonish style
Issei Yoshino - famed for his multimodular Tyrannosaurus and Triceratops skeletons
Marc Kirschenbaum - known for his instrumentalist designs
Didier Boursin
Duy Nguyen - known for his under the sea origami designs such as Dolphin, Walrus, and Angelfish, Nguyen belongs to a school of folders who regularly use cuts in their models, a controversial practice in origami circles.

Groups and Organizations

References

^ The World of Geometric Toy , Origami Spring, August, 2007.

External links

British Origami Society The U.K.'s central origami organization.
OrigamiUSA The biggest origami organization in the U.S.
BARF (Bay Area Rapid Folders) An origami group in California
Oxford Origami Society An origami group in Oxford, U.K.
Gilad's Origami Page Information and reviews for hundreds of origami books.
Origami.com Large collection of diagrams, suitable for beginners.
Animated Origami Animated diagrams for beginners.
[1] Large collection of diagrams, animated diagrams included, perfect for any skill level.

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[1] The World of Geometric Toy , Origami Spring, August, 2007.

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