Origami

Last updated

Origami cranes Cranes made by Origami paper.jpg
Origami cranes
The folding of an Origami crane
A group of Japanese schoolchildren dedicate their contribution of Thousand origami cranes at the Sadako Sasaki memorial in Hiroshima. Hiroshima senzaburu.jpg
A group of Japanese schoolchildren dedicate their contribution of Thousand origami cranes at the Sadako Sasaki memorial in Hiroshima.

Origami ( 折り紙 , Japanese pronunciation:  [oɾiɡami] or [oɾiꜜɡami] , from ori meaning "folding", and kami meaning "paper" (kami changes to gami due to rendaku)) 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.

Contents

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. [1] [2]

History

The folding of two origami cranes linked together, from the first known book on origami, Hiden senbazuru orikata, published in Japan in 1797 Hiden Senbazuru Orikata.jpg
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 Froebel'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 "parajita," 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 Froebel'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 Origami-Basisfaltungen.png
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

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

A crane and papers of the same size used to fold it Orizuru.jpg
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 Bonefolders.jpg
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

In addition to the more common still-life origami, there are also moving object designs; 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

A stellated icosahedron made from custom papers OrigamiStar-BlackPen.png
A stellated icosahedron made from custom papers

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

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

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

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 Tea bag folding (3229463907).jpg
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 ]

Mathematics and technical origami

Mathematics and practical applications

Spring Into Action, designed by Jeff Beynon, made from a single rectangular piece of paper Origami spring.jpg
Spring Into Action, designed by Jeff Beynon, made from a single rectangular piece of paper

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. [20]

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.

Technical origami

Technical origami, known in Japanese as origami sekkei (折り紙設計), 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. [21] 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. [22] TreeMaker allows new origami bases to be designed for special purposes [23] and Oripa tries to calculate the folded shape from the crease pattern. [24]

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. [25] It is considered good etiquette 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. [26] 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". [27] 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." [28]

These pictures show examples of various types of origami.

See also

Related Research Articles

Yoshizawa–Randlett system

The Yoshizawa–Randlett system is a diagramming system used to describe the folds of origami models. Many origami books begin with a description of basic origami techniques which are used to construct the models. There are also a number of standard bases which are commonly used as a first step in construction. Models are typically classified as requiring low, intermediate or high skill depending on the complexity of the techniques involved in the construction.

Mathematics of paper folding Overview of the mathematics of paper folding

The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability, and the use of paper folds to solve up-to cubic mathematical equations. The discipline is often pursued by the use of washi paper.

Modular origami

Modular origami or unit origami is a paperfolding technique which uses two or more sheets of paper to create a larger and more complex structure than would be possible using single-piece origami techniques. Each individual sheet of paper is folded into a module, or unit, and then modules are assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. These insertions create tension or friction that holds the model together.

Robert J. Lang American physicist (born 1961)

Robert J. Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. He is known for his complex and elegant designs, most notably of insects and animals. He has studied the mathematics of origami and used computers to study the theories behind origami. He has made great advances in making real-world applications of origami to engineering problems.

Paper craft

Paper craft is a collection of crafts using paper or card as the primary artistic medium for the creation of two or three-dimensional objects. Paper and card stock lend themselves to a wide range of techniques and can be folded, curved, bent, cut, glued, molded, stitched, or layered. Papermaking by hand is also a paper craft.

Miura fold Origami folding pattern

The Miura fold is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Koryo Miura.

Wet-folding

Wet-folding is an origami technique developed by Akira Yoshizawa that employs water to dampen the paper so that it can be manipulated more easily. This process adds an element of sculpture to origami, which is otherwise purely geometric. Wet-folding is used very often by professional folders for non-geometric origami, such as animals. Wet-folders usually employ thicker paper than what would usually be used for normal origami, to ensure that the paper does not tear.

Satoshi Kamiya is a Japanese origami artist. Known internationally to be a master of the craft, he began folding at age two. Kamiya began designing origami models in 1995, and has since published hundreds of his creations. Perhaps his most famous design is Ryu-Zin 3.5, an elaborate dragon covered with scales and having feelers, claws, and horns. The work can take up to one month to fold properly. Kamiya has drawn inspiration for his designs from Manga, nature, and both eastern and western mythologies.

History of origami

The history of origami followed after the invention of paper and was a result of paper's use in society. Independent paper folding traditions exist in East Asia, and it is unclear whether they evolved separately or had a common source.

Toshikazu Kawasaki

Toshikazu Kawasaki is a Japanese paperfolder and origami theorist who is known for his geometrically innovative models. He is particularly famous for his series of fourfold symmetry "roses", all based on a twisting maneuver that allows the petals to seem to curl out from the center of the flower. Kawasaki also teaches Mathematics at Sasebo Technical Junior College.

Crease pattern

A crease pattern is an origami diagram that consists of all or most of the creases in the final model, rendered into one image. This is useful for diagramming complex and super-complex models, where the model is often not simple enough to diagram efficiently.

Origami paper

Origami paper is used to fold origami, the art of paper folding. The only real requirement of the folding medium is that it must be able to hold a crease, but should ideally also be thinner than regular paper for convenience when multiple folds over the same small paper area are required.

Kawasakis theorem Result about crease patterns with a single vertex that may be folded to form a flat figure

Kawasaki's theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero. Crease patterns with more than one vertex do not obey such a simple criterion, and are NP-hard to fold.

The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring to Vladimir Arnold and the folding of a Russian ruble bank note. Some versions of the problem were solved by Robert J. Lang, Svetlana Krat, Alexey S. Tarasov, and Ivan Yaschenko. One form of the problem remains open.

Paper toys are toys made of paper. They are constructed in several ways, by folding, as in paper airplanes, paper fortune tellers or Origami, or by cutting, decorating or assembling pieces of paper with glue or tape to create a paper doll or paper model.

Ligia Montoya was an Argentinian paper-folding artist, who played an important role in all aspects of the 'golden age' of the international origami movement from the 1950s, from which developed modern artistic origami—that is, innovative paper-folding exploring a variety of different approaches, rather than repeating limited traditional figures.

Yoshimura buckling

In mechanical engineering, Yoshimura buckling is a triangular mesh buckling pattern found in thin-walled cylinders under compression along the axis of the cylinder, producing a corrugated shape resembling the Schwarz lantern. The same pattern can be seen on the sleeves of Mona Lisa.

Jeannine Mosely holds a Ph.D. in EECS from the Massachusetts Institute of Technology, and is known for her work as an origami artist. She is best known for her modular origami designs, especially her work using business cards. She has organized several crowd-sourced origami projects built from tens of thousands of business cards involving hundred of volunteers for each project. She is also known for her minimalist origami designs, curved crease models, and her invention of "or-egg-ami" models made from egg cartons.

Origami Polyhedra Design is a book on origami designs for constructing polyhedra. It was written by origami artist and mathematician John Montroll, and published in 2009 by A K Peters.

References

  1. Merali, Zeeya (June 17, 2011), "'Origami Engineer' Flexes to Create Stronger, More Agile Materials", Science, 332 (6036): 1376–1377, Bibcode:2011Sci...332.1376M, doi:10.1126/science.332.6036.1376, PMID   21680824 .
  2. "See a NASA Physicist's Incredible Origami" (video). Southwest Daily News. March 16, 2019.
  3. Laing, Ellen Johnston (2004). Up In Flames. Stanford University Press. ISBN   978-0-8047-3455-4.
  4. Hatori Koshiro. "History of Origami". K's Origami. Retrieved January 1, 2010.
  5. Joan Sallas. "Gefaltete Schönheit." 2010.
  6. Lister, David. "David Lister on The Pajarita". The Lister List. Retrieved December 7, 2019.
  7. "History of Origami in the East and West before Interfusion", by Koshiro Hatori. From Origami^5, ed. Patsy Wang Iverson et al. CRC Press 2011.
  8. Margalit Fox (April 2, 2005). "Akira Yoshizawa, 94, Modern Origami Master". The New York Times .
  9. Lang, Robert J. "Origami Design Secrets" Dover Publications, 2003.
  10. Gould, Vanessa. "Between the Folds, a documentary film".
  11. McArthur, Meher (2012). Folding Paper: The Infinite Possibilities of Origami. Tuttle Publishing. ISBN   978-0804843386.
  12. McArthur, Meher (2020). New Expressions in Origami Art. Tuttle Publishing. ISBN   978-0804853453.
  13. Rick Beech (2009). The Practical Illustrated Encyclopaedia of Origami. Lorenz Books. ISBN   978-0-7548-1982-0.
  14. Jeremy Shafer (2001). Origami to Astonish and Amuse. St. Martin's Griffin. ISBN   0-312-25404-0.
  15. Bettens, Christiane. "First origami tessellation convention". Flickr. Retrieved July 20, 2015.
  16. Gjerde, Eric (2008). Origami Tessellations. Taylor & Francis. ISBN   9781568814513.
  17. Lang, Robert J. (2003). Origami Design Secrets. A K Peters. ISBN   1-56881-194-2.
  18. 1 2 "Strip folding". Origami Resource Center. 2018. Retrieved February 19, 2018.
  19. The World of Geometric Toy, Origami Spring , August, 2007.
  20. Cheong Chew and Hiromasa Suziki, Geometrical Properties of Paper Spring, reported in Mamoru Mitsuishi, Kanji Ueda, Fumihiko Kimura, Manufacturing Systems and Technologies for the New Frontier (2008), p. 159.
  21. "TreeMaker".
  22. Patsy Wang-Iverson; Robert James Lang; Mark Yim, eds. (2010). Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education. CRC Press. pp. 335–370. ISBN   978-1-56881-714-9.
  23. Lang, Robert. "TreeMaker" . Retrieved April 9, 2013.
  24. Mitani, Jun. "ORIPA: Origami Pattern Editor" . Retrieved April 9, 2013.
  25. Robinson, Nick (2008). Origami Kit for Dummies. Wiley. pp. 36–38. ISBN   978-0-470-75857-1.
  26. "Origami Copyright Analysis+FAQ" (PDF). OrigamiUSA. 2008. p. 9.
  27. "Japanese Origami Artist Loses Copyright Battle With Japanese Television Station". Keissen Associates. Retrieved September 3, 2015.
  28. "What Does Copyright Protect?". Copyright.gov. United States Copyright Office. Retrieved September 4, 2015.
  29. "House of Cards: Chapter 6". AV Club.
  30. "House of Cards: Chapter 7". AV Club.
  31. Greenwald, Ted. "Q&A: Ridley Scott Has Finally Created the Blade Runner He Always Imagined". Wired. Retrieved March 14, 2015.
  32. Molly Brown, "King Arthur and the Knights of the Postmodern Fable"; in: The Middle Ages in Popular Culture: Medievalism and Genre – Student Edition, 2015, p. 163
  33. "Interview: Yoon Ha Lee, Author of Conservation of Shadows, on Writing and Her Attraction to Space Opera". SF Signal. May 30, 2013. Retrieved March 27, 2017.
  34. Guide, British Comedy. "QI Series O, Episode 10 - Origins And Openings". British Comedy Guide. Retrieved January 13, 2019. The art of folding paper into shapes without cutting it comes from Germany. Origami uses white paper, which can be folded and cut. German kindergartens use paper that is uncut and is coloured on one side, and this came into Japan when the country opened its borders in 1860. Thus what we generally consider origami today in fact has German roots.

Further reading