Origami

Origami is the art of folding objects out of paper to create both two-dimensional and three-dimensional subjects. The term derives from the Japanese oru, meaning to fold, and kami, meaning paper, and it has become the generic description of this art form. Most origami is folded from a single square sheet, although rectangles and other nonsquare sheets are used in the modular and composite styles.

The folding of paper in Japan goes back centuries, arising probably within religious ceremonies and among court nobles as a pastime. The origins of origata are traced to the Heian period between 794 and 1185, when styles of wrapping were developed for poetry, money and fans, and the techniques were taught exclusively through oral transmission in schools such as the Ogasawara School. By the 17th century much of the Japanese population was folding birds, animals and boxes.

Paper folding was also practised in Europe and had become well established there by the 19th century. Lister argues that the word origami was coined in Japan as long ago as the Western middle ages, while Hatori Koshiro suggests the late 12th Century. In Japan the term origami came into use in place of the older word orikata by 1880.

Among the earliest books of origami instructions are Tsutsumi-no Ki by Sadatake Ise, a 1764 book of 13 ceremonial folds dealing with ceremonial folding and knotting rather than recreation, and Sembazuru Orikata by Akisato Rito, with 49 linked cranes. Sembazuru Orikata instructs the folder to make multiple cranes from a single sheet of strong paper cut into smaller squares connected at the corners. The basic design of the classic crane had been known as a single fold long before 1797 and so predates the Sembazuru Orikata. Hiden senbazuru orikata was published in Japan in 1797. The related Chushingura Orikata, two printed sheets issued in the same year as the Senbazuru Orikata, shows figures from a famous play.

The Kayara-gusa is a private manuscript compilation in 233 volumes, never printed or published, with volumes 27 and 28 on paperfolding. The only copy is held by the Asahi newspaper library in Osaka. The name Kan no mado is widely used in the West but appears to come from a misreading of characters on the back of the Library of Congress facsimile, where the correct reading would be Fuyuno Mado, meaning Winter Window. Because the paperfolding occupies volumes 27 and 28 of the second section, called the Kayara-gusa, Lister says the preferred name is Kayara-gusa rather than Kan no mado. A facsimile was hand-copied around 1920 for Professor Frederick Starr of Chicago University, passed with his papers into the Library of Congress, and was found there in March 1960 after a search prompted by Gershon Legman and the Brossmans.

Sadako Sasaki was two years old when she was exposed to the atomic bomb, and she showed no apparent injuries as she grew up. Nine years later, in the sixth grade, she fell ill and was diagnosed with leukemia at the Hiroshima Red Cross Hospital. Classmates of Sadako Sasaki launched a nationwide fundraising campaign for a memorial to her and the other children killed by the bomb, and 1958 saw the statue installed in Hiroshima Peace Memorial Park.

Washi is the traditional paper of Japanese origami, tougher than ordinary wood-pulp paper and made from gampi, mitsumata or paper mulberry fibres. Washi craftsmanship is the traditional practice of making paper by hand from the fibres of the paper mulberry plant, which are separated and soaked in clear river water before being filtered through a bamboo screen. Hand-made washi is used for letter writing, books and documents, and for home interiors such as paper screens, room dividers and sliding doors.

Most inhabitants of the practising washi communities take part in the process, from cultivating and harvesting the mulberry plant to creating new washi products that promote the craft at home and abroad. Washi knowledge and skills are transmitted within craftspeople's families, through preservation associations and by local municipalities, with practising families and their employees learning under washi masters who inherited the techniques from their parents.

In 2025 UNESCO inscribed Japan's washi craftsmanship of traditional hand-made paper on the Representative List of the Intangible Cultural Heritage of Humanity.

Cutting was traditionally part of origami, though most modern folders avoid it; the practice survives in the Rokoan style of connected cranes. Wet folding, a technique invented by Akira Yoshizawa, uses paper carrying a water-soluble glue that is dampened before folding and hardens as it dries. In unit origami, squares are folded into identical modules that interlock to build symmetric solids, tessellations and boxes. Tomoko Fuse popularized modular origami, which brought mathematical attention to the art of folding paper.

Origami construction is governed by the seven Huzita-Justin axioms, which set out what can be built from single creases that align points and lines. At the first international meeting on origami science, Humiaki Huzita and Benedetto Scimemi described six fundamentally different ways to make a single crease.

Any graph of straight line segments drawn in the plane can be produced by folding a sheet and making one straight cut, a result originally developed by Erik Demaine, Martin Demaine and Anna Lubiw.

Origami methods have been borrowed for the folding of automobile air bags and of large space telescopes, and related principles may govern the folding of proteins. Because manufacturers often prefer to build a product from a single piece of material, determining whether and how a shape can be folded becomes a problem of optimization. Origami accordingly raises research questions in algorithm complexity and optimization, and it finds uses that range from work at the molecular scale to manufacturing and space applications. Its principles now reach into furniture making, architecture, robotics design, engineering and medical solutions. Optical systems that combine multiple mirror reflections, meanwhile, demand tedious graphic layout work to size the mirrors correctly and to keep ray bundles unobstructed.

NASA has pursued starshade technology through a focused activity known as S5, an effort to bring the technology to Technical Readiness Level 5 (TRL5). An occulter placed inside a telescope is known as a coronagraph, whereas an occulter placed outside the telescope is called a starshade. A starshade deployment animation depicts the change from the stowed configuration to the deployed configuration, including the eventual jettison of the Petal Launch and Unfurl Subsystem. A simulation video shows the translation of out-of-band starlight, known as the Arago spot, in the telescope camera used for lateral sensing and formation flying maneuvers.

MIT researchers presented a printable origami robot that begins as a flat sheet of plastic, folds itself up when heated, and measures roughly a centimeter from front to back. The tiny robot weighs about a third of a gram, can swim, climb an incline, cross rough terrain and carry twice its own weight, and apart from the self-folding sheet its only component is a permanent magnet on its back. The design was motivated by a hypothetical medical scenario in which tiny material sheets injected into the body would travel to an intervention site, fold themselves up and later dissolve. For outside control, the researchers placed the robot on a rectangular stage with an electromagnet at each of its four corners and varied the fields rapidly enough that the robot moved nearly four body lengths a second.

At Harvard's John A. Paulson School of Engineering and Applied Sciences, researchers showed they can tune the rigidity and floppiness of an origami structure by changing how densely extra folds are added and how they are patterned across the material. The findings appeared in the Proceedings of the National Academy of Sciences. Mahadevan, the senior author, said the study probes the percolation of rigidity, meaning how floppiness changes with the density of redundant folds in a system. Siheng Chen said folding a structure in a particular pattern can encode information into the material, and that rearranging the spatial organization of folds allows that information to be stored and erased, laying the ground for origami memory usable in mechanical computation.

Akira Yoshizawa introduced the diagramming notation known as the Yoshizawa-Randlett system, and his early career unfolded through a series of modest and then prominent displays: a small exhibition at the Utsunomiya Education Hall in 1950, held in connection with a teachers' conference, was followed by his first major exhibition in the Ginza in 1955 with sponsorship from Tokyo Electric Power. Gershon Legman, an American on the point of moving to France, discovered Yoshizawa for the West in 1953 and arranged for an exhibition of his models at the Stedelijk Museum in Amsterdam in the autumn of 1955, drawing on models from the Ginza display. Robert Harbin's book Paper Magic, which quoted a letter from Gershon Legman, carried news of Yoshizawa's folding through the English-speaking world from 1956 onward, and Western enthusiasts quickly took up his new way of folding. Lillian Oppenheimer of New York, founder of the Origami Center, made Yoshizawa a vice-president of that organization and in April 1959 travelled to Japan to visit him. A school photograph from 1925 shows Yoshizawa at the age of fourteen, shortly after he left home for Tokyo, where he could afford only one year of high school and continued his education at evening classes.

Origami was relatively unknown in the United States until Lillian Oppenheimer discovered the flapping bird at a family gathering in the late 1940s, an encounter that triggered a fascination dominating the rest of her long life. She sought out and taught folders in the New York area and began corresponding with paperfolders around the world, gradually gathering a small group of dedicated people through the 1950s and 1960s. Michael Shall, a young teacher from Pennsylvania, founded The Friends of The Origami Center of America with Alice Gray, Robert Neale, Florence Temko and other folders, and in 1980 the organization was incorporated as a volunteer-run, tax-exempt educational and cultural arts body. The Friends bought Lillian Oppenheimer's supplies business in 1987 and became OrigamiUSA on the first of July in 1994, after its founder died in 1992 at the end of a long life devoted to origami.

OrigamiUSA reports over 1600 members in 49 states and 19 countries and has local-area groups in cities across the United States and Canada. It is based at the American Museum of Natural History in New York City, where it operates autonomously thanks to the generosity of the museum's trustees. It runs classes, workshops and an annual convention, and publishes a quarterly magazine, instruction booklets and an annual collection of original models that runs to some 300 pages. Lang is recognized as one of the world's leading masters of origami, having studied the art for more than fifty years and catalogued and diagrammed over 800 designs. Lang pioneered the cross-disciplinary marriage of origami with mathematics, has consulted on engineering uses ranging from air-bag design to expandable space telescopes, and in 2011 was elected an Honorary Member of the British Origami Society.

In Japan the first kindergarten was established in 1875 and origami was promoted for early childhood education, with origami subjects listed among the activities in the kindergarten's 1877 regulations. Origami was not regarded as art until the middle of the 20th century, when folders around the world began experimenting with different styles, techniques and materials, and it is now a sophisticated international art form worthy of museum exhibition and scholarship. Folding Paper: The Infinite Possibilities of Origami was the first museum exhibition devoted to the history of paper folding, the work of leading origami artists, and the links between origami and mathematics, science and design. The exhibition examined the relationship between origami and art, science and mathematics, and demonstrated its impact in areas as diverse as space exploration, medical research and fashion design.

• First–second centuries CE
  Paperfolding begins
  Paperfolding originated in the region of modern-day China and Korea as paper manufacturing processes were refined.^{14Origami: History & Traditional Patterns · United States Air Force Academy Library ↗}
• Fourteenth–fifteenth centuries
  Samurai culture
  Origami spread through samurai culture.^{14Origami: History & Traditional Patterns · United States Air Force Academy Library ↗}
• Seventeenth–eighteenth centuries
  Wider society
  Origami reached wider society.^{14Origami: History & Traditional Patterns · United States Air Force Academy Library ↗}
• 1920
  Starr facsimile
  A facsimile was hand-copied for Professor Frederick Starr of Chicago University.^{6Kayaragusa, alias "Kan no mado" · British Origami Society (David Lister collection) ↗}
• March 1960
  Facsimile found
  The facsimile was found at the Library of Congress after a search prompted by Gershon Legman and the Brossmans.^{6Kayaragusa, alias "Kan no mado" · British Origami Society (David Lister collection) ↗}