Origami

Origami is the art of paper folding, which is often associated with Japanese culture. In modern usage, the word “origami” is used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word kirigami to refer to designs which use cuts, although cutting is more characteristic of Chinese papercrafts.

Origami (origami, origami) is Japanese traditional play that folds paper to make shapes such as animals and plants and living tools. It also refers to the work itself that was folded up, a square special paper made for origami, Chiyogami. A senior samurai was used for wrapping things with Japanese paper, the folding form, the rework part has disappeared from the reworking method, widely developed and popularized for the players to the common people, it is a representative culture of Japan.

The artistic aspects of origami are evaluated, and complicated and excellent works that were not in the past were created, and in addition to the folding method to pass on to each country, new folding methods are also being invented (various folding forms, folding methods See the list of traditional origami).

In addition to being studied as a field of mathematics from the geometrical nature of origami, it is being utilized as a means of storage and deployment of structures in engineering fields as well.

The small number of basic origami folds can be combined in a variety of ways to make intricate designs. The best-known origami model is the Japanese paper crane. In general, these designs begin with a square sheet of paper whose sides may be of different colors, prints, or patterns. 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 or using nonsquare shapes to start with. The principles of origami are also used in stents, packaging and other engineering applications.

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. Additional bases are the preliminary base (square base), fish base, waterbomb base, and the frog base.

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.

Origami has several basic shapes. For example, the basic form of a crane has four pointed “cados”, and if folding animals it is easier to create by hitting them on their heads and feet. The representative ones are described below.

In general, we use square paper only for origami. However, depending on the work, there are cases in which other paper is used as a rectangle (mainly with edge ratio 1: √ 2). Works using newspaper etc. (hat, mitt, paper gun etc) are also available. Even attempts have been made to make banknotes as origami material and to incorporate figures such as people into parts of the completed work. There are works using special papers such as pentagons, hexagons and octagons, but in such cases you can cut them out of square paper as needed.

Origami, which is the most commonly sold in shops, is 15 cm square, but less than that · Origami of more than that (5 cm square, 7.5 cm square, 24 cm square, 35 cm square etc.) are also on the market. Also, rare but circular origami etc. exist. Regarding coloring, there are also two-sided color ones, transparent ones, with special patterns such as gradations and polka dots, ones whose surface is divided into two equal parts or four equal parts, etc. Currently more than 1000 kinds of origami It is said that paper is available.

When folding complicated works, use your own paper that backed with foil paper using metal foil or metal foil (eg aluminum foil, shape will not easily collapse) on the back of light Japanese paper (hard to break) There are many.

For exhibition work, we often cut paper and washi selected for good appearance into squares (or shapes according to the work) in many cases. A technique called wet folding is also used, where thick paper (such as Western paper) is occasionally moistened and then folded. With this technique, thick paper can be easily folded and wrinkles can be drastically reduced. You can also fix the bent shape, or “fold” (distort) and fold the paper.

Even if there is no square paper around, if you devise a document that you do not need in front of you for example to make it square, you can enjoy origami sufficiently without preparing paper in advance.

Normal copy paper with weights of 70–90 g/m2 can be used for simple folds, such as the crane and waterbomb. Heavier weight papers of (19–24&nb 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 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, 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.

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. Many folders believe that no tool should be used when folding. 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 they keep their shape better, and a spray is needed when wet folding.

In order to tell people how to fold origami, there is a fold chart showing the process with a picture (often a photograph). In folding charts, it is customary to represent mountain folding lines with one-dot chain lines (“- – – – – – – -“) and valley folding lines with broken lines (“- – – – -“) in many cases. Also, sentences are often added to make understanding easier.

Origami not only covers still-life, there are also moving objects; Origami can move in clever ways. 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 consists of putting a number of identical pieces together to form a complete model. Normally the individual pieces are simple but the final assembly may be tricky. Many of the modular origami models are decorative balls like kusudama, the technique differs though in that kusudama allows the pieces to be put together using thread or glue.

Chinese paper folding includes a style called Golden Venture Folding where large numbers of pieces are put together to make elaborate models. It 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”. Sometimes paper money is used for the modules. 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.

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 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 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, and the first instruction book on tessellation folding patterns was published by Eric Gjerde in 2008. 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 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.

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.

A number of technological advances have come from insights obtained through paper folding. For example, techniques have been developed for the deployment of car airbags and stent implants from a folded position.

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.

Origami can be used to construct various geometrical designs not possible with compass and straightedge constructions. For instance paper folding may be used for angle trisection and doubling the cube.

Application of origami, or research involves several mathematical tasks. For example, flat-foldability is one of such mathematical tasks as to whether a development map can be folded flat to a two-dimensional work.

Gaussian curvature of flat paper is 0 at any point on the surface. Therefore, the fold line is a straight line with the original curvature of 0. But this curvature condition no longer holds for flat paper, such as wet paper or wrinkled paper with fingernail.

The problem of rigid origami (ie whether it is possible to fold a work like a piece of paper using a hinged sheet metal at the fold position) is an important practical matter. For example, Miura folding can be folded even with a rigid body, and it is used to fold a solar cell panel of a satellite.

Besides that, origami is also applied to the folding of airbags and the folding of medical stent grafts (new type artificial blood vessels using stents and artificial cloths).

Technical origami, known in Japanese as origami sekkei, is an origami design approach in which the model is conceived as an engineered crease pattern, rather than developed through trial-and-error. With advances in origami mathematics, 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 developed 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 crease pattern is a layout of the creases required to form the structure of the model. 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 model. 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. By opening up a folded model, you can observe the structures that comprise it; the study of these structures led to a number of crease-pattern-oriented design approaches

The pattern of allocations is referred to as the ‘circle-packing’ or ‘polygon-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.

As a circle encloses the maximum amount of area for a given perimeter, circle packing allows for maximum efficiency in terms of paper usage. However, other polygonal shapes can be used to solve the packing problem as well. The use of polygonal shapes other than circles is often motivated by the desire to find easily locatable creases (such as multiples of 22.5 degrees) and hence an easier folding sequence as well. One popular offshoot of the circle packing method is box-pleating, where squares are used instead of circles. As a result, the crease pattern that arises from this method contains only 45 and 90 degree angles, which often makes for a more direct folding sequence.

A number of computer aids to origami such as TreeMaker and Oripa, have been devised. Treemaker allows new origami bases to be designed for special purposes and Oripa tries to calculate the folded shape from the crease pattern.

Copyright in origami designs and the use of models has become an increasingly important issue in the origami community, as the internet has made the sale and distribution of pirated designs very easy. It is considered good ettiquette to always credit the original artist and the folder when displaying origami models. It has been claimed that all commercial rights to designs and models are typically reserved by origami artists; however, the degree to which this can be enforced has been disputed. Under such a view, a person who folds a model using a legally obtained design could publicly display the model unless such rights were specifically reserved, whereas folding a design for money or commercial use of a photo for instance would require consent. The Origami Authors and Creators group was set up to represent the copyright interests of origami artists and facilitate permissions requests.

However, a court in Japan has asserted that the folding method of an origami model “comprises an idea and not a creative expression, and thus is not protected under the copyright law”. Further, the court stated that “the method to folding origami is in the public domain; one cannot avoid using the same folding creases or the same arrows to show the direction in which to fold the paper”. Therefore, it is legal to redraw the folding instructions of a model of another author even if the redrawn instructions share similarities to the original ones, as long as those similarities are “functional in nature”. The redrawn instructions may be published (and even sold) without necessity of any permission from the original author. The Japanese decision is arguably in agreement with the U.S. Copyright Office, which asserts that “copyright does not protect ideas, concepts, systems, or methods of doing something.”