The Public Paperfolding History Project

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A Brief History of Educational and Recreational Paperfolding in Europe and the Americas after Cross-Fertilisation
 

I have used 1867 as a starting point for this section because it is the date at which Japanese recreational paperfolding designs first begin to appear in the West, initially in France. However, this date does not mark an abrupt watershed. It took time for the few Japanese designs that reached the West to become well-known and even longer for them to exert an influence on the creation of new designs through the realisation that the base forms of the Paper Crane and the Blow-up Frog, what we now call the bird base and frog base respectively, could be developed into many other designs as well.

It is difficult to evaluate the extent to which recreational paperfolding permeated popular Western culture during this period. Most probably, the situation was much as it still is today. Most people perhaps knew one or two simple paperfolds off by heart (though which ones these were would probably have changed over the years) and may also have folded paper as an occasional pastime as and when a newspaper or magazine article, or a book caught threir attention. A much smaller number of people may well, as they do today, have folded paper rather more regularly, as a hobby, or as therapy, and learned a rather wider repertoire of folds. Of these, some few may have developed an enthusiasm that went beyond a mere hobby, and may, perhaps, also have discovered a facility for creating their own designs. Throughout much of this period these enthusiasts largely seem to have folded in isolation, until the formation of the origami societies provided a way for them to develop contacts with each other.

Taken broadly, this seems to have been true in all areas of Western Europe and the Americas, but, in detail, the development of recreational paperfolding after 1867 was substantially different in the French-speaking, Spanish-speaking, German-speaking, Dutch-speaking, Portuguese-speaking and English-speaking cultures.

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A: Well known paperfolds first appearing in Froebelian manuals after 1867

The Pig

'Die Praxis Des Kindergartens' by Auguste Koehler, which was published in 1873 states that in Froebel's time only one method of developing a square was known, that of folding the corners inwards (ie blintzing the square). The author says that he developed a second method, that of folding the edges inwards, (ie bookfolding the square) which was published in his earlier work relating to paperfolding. (The footnote identifies this as 'Kindergarten and Elementarklasse. II Jahrang. Weimar. Bohlau 1861', but I have not been able to trace a copy of this work.) To modern folders this may seem an unimportant distinction, but this discovery seems to have led Auguste Koehler to design the Pig, which is first published in this work (or, perhaps, in the earlier work which I cannot find). Modern folders are not generally over-impressed with the Pig design, yet it was revolutionary in its time. In their book 'Froebel's Occupations', published in 1896, Kate Douglas Wiggin and Nora Archibald Smith call it ‘the crowning glory of the sequence, a star of the purest ray and the first magnitude.' And so it was.

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The Lotus

The Lotus first appears as a napkin fold in 'Des Kindes Erste Beschaftigungsbuch' by E Barth and W Niederley, which was published in Bielefeld and Leipzig in 1876.

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B: Paperfolding in France

i. Paperfolding as an aid to manual training

In 1849 the French publication 'Bulletin de la Societe D'Encouragement Pour L'Industrie Nationale' published a report by the mathematician Theodore Olivier, titled 'Enseignement Industriel - Geometrie Pratique', which explained a new method, discovered by Martin Chatelain, of teaching practical geometry using paperfolding. The report recommends its use in the teaching of apprentices. Full details of the method are, unfortunately, not given.

On 27th July 1882 the French government minister, Jules Ferry, issued a decree regulating the pedagogical organisation and the study plan of public primary schools (Arrêté du 27 juillet 1882 réglant l’organisation pédagogique et le plan d’études des écoles primaires publiques) which made it mandatory for French primary schools to include manual work (activities designed to aid the development of manual skills, which would then be useful in an industrial and economic context) in their curricula. There is no specific mention of paperfolding in this decree (although it does mention cardboard modelling /cartonnage) but a second decree issued a day later (Arrete reglant l'organisation pedagogique des maternelles publique et les programmes d'enseignement) did mention ‘pliage’ (paperfolding) several times. Many primary schools subsequently began to include paperfolding as part of their manual training syllabus and, as had happened with Froebelian kindergarten education, publishers then began issuing manual work textbooks to assist teachers in incorporating this element in their lessons. Many of these textbooks included paperfolding elements.

For instance, 'Cours de Travail Manuel (Pour les Garcons) - Premiere Partie - Cours Elementaire' by A Planty, which was published in Paris in 1887, explains how to fold a Chapeau du Gendarme (a version of the Newspaper Hat), a simple wallet, the Table, The Windmill, the Cocotte, some strip folded letters of the alphabet and various decorations that in a Froebelian context we would call Forms of Beauty.

In a more formal context, the 'Bulletin de la Société de Protection des Apprentis', an official document issued by the Société de Protection des Apprentis et des Enfants Employes par les Manufactures in Paris in 1891, sets out educational syllabuses which make use of paperfolding. It includes, among other folds, the Waterbomb, the Patisserie Box and ‘La Grenouille Japonaise’ (otherwise known as the Blow-Up Frog).

Initially, these textbooks are all published in French, but magazine articles and books about manual work, including paperfolding, begin to appear in Spanish from 1903 onwards. 'La Ensenanza del Trabajo Manuel' by Pedro de Alcántara García and Teodosio Leal y Quiroga, was published in Madrid in 1903, closely followed by ‘Guia Practica del Trabajo Manual Educativo' by Ezequiel Solana, which was published in 1904. I do not know if these Spanish publications were also produced in response to a change in educational law, or whether manual work became popular in Spanish schools for some other reason.

It seems obvious that the result of teaching paperfolding in schools as a means of increasing manual dexterity must also, surely, have acted to increase the recreational use of paperfolding as children’s play.

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ii. Japonisme, the Paper Crane, the Flapping Bird and the Blow-up Frog

After Japan came out of her self-imposed period of isolation in 1853, Japanese design, particularly in the form of prints and ceramics (the one often arriving weapped inthe other), began to have a huge influence in Western Europe, particularly in France, and it became very fashionable to own Japanese objects and mimic Japanese forms and customs.

The influence of Japanese design in the West was reinforced by Japan’s participation in the Expositions Universelle held in Paris in 1867 (where there were two Japanese pavilions, one official and one private, funded by the Satsuma family), 1878, 1889 and 1900.

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The Paper Crane

We do not know how the Paper Crane became known in the West. It is possible that either it was shown or demonstrated at the 1867 Exposition or that some knowledge of it was gleaned from a woodblock print.

However it became known, it was featured on a membership card for a private drinking club in Paris called the Société de Jing-lar that had been formed in 1868 (or possibly 1869) by a small number of enthusiasts for all things Japanese. Three of these membership cards have survived. Unfortunately, we have no idea how the founders of Société de Jing-lar came to know about the Paper Crane or even whether or not they knew how to fold it.

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The Flapping Bird

The origin of the Flapping Bird is a mystery. It is, effectively, a simplification of the Paper Crane, which appears if the head and tail (or feet) are not thinned. It is thus easily possible that the basic form of the design could be arrived at by accident when trying to fold the Paper Crane while not being exactly sure how it should be made. It is also possible that, once having arrived at the basic form, the flapping action could be discovered in a similarly accidental way, though not necessarily by the same person at the same time.

The basic form of the design first appears in a pictorial story by the Catalan illustrator Apeles Mestres which is clearly dated 2nd August 1883.  The words below the illustration read, in translation, 'This story was told to me by a swallow that came flying from paper country'. There is no indication that Apeles Mestres knew that the wings would flap if the tail were pulled.

Detail from a pictorial story by Apeles Mestres dated 1883

The design next appears in an anonymous article in Issue 621 of the French magazine La Nature of 25th April 1885, headed 'Recreations Scientifique' and subheaded 'Un Oiseau Mecanigue En Papier' ( a mechanical paper bird). The article includes a wood cut print showing how the bird was to be held in order to make it flap and the information that it originated with 'les prestidigitateurs japonais' (Japanese conjurors).

The statement that the Flapping Bird originated with 'les prestidigitateurs japonais', seems suspect to me. If this statement were true it would be very odd that there should be no record of the design in Japan until 1957. Consequently it seems likely that this is an example of the practice, common in the 19th century, of attributing a Chinese or Japanese origin to some novelty or entertainment to enhance it with an air of oriental mystery.

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The Blow-up Frog

Japan’s participation in the 1889 Exposition (the event for which the Eiffel Tower was constructed) was particularly important from the point of view of paperfolding history. The magazine La Nature Issue 852 of 28th September 1889 contained an article headed 'Recreation scientifiques' and subheaded 'La grenouille japonaise en papier' (The Japanese Paper Frog) which explains how to make the Blow-up Frog (though the author does not appear to be aware that the frog can be inflated).

The article is interesting not only for the diagrams it contains, but also for the incidental information it provides. In his introductory paragraphs the author, Dr Z…, states, roughly, 'The Ministry of Public Education of Japan has sent to the Exhibition an interesting series of industrial and artistic designs ... made by children of both sexes in the country's school rooms ... but one can notice others which are not less curious. These are the recreational works done by the small children of the Azabu private school in Tokyo. The series of displays showing cut out and coloured papers combined to make flowers, butterflies or marquetry designs are quite attractive and our children would probably be happy to know how to make such pretty things. In France, it is true, we also know the charming game of folding paper. The classic Cocotte, the box and the galiote etc., are popular here but we must agree that the Japanese have more ingenious models. The Frog that we put in front of our young readers is an example’, and, ‘We also noticed in the exhibition other designs among which were the crab from red paper, the junk and the hat of Daimios, the parrot etc., The way these designs are made has many points of resemblance to the Frog.'

Itis difficult to identify the 'crab from red paper', but the' junk' is probably the Takarabune, the 'hat of Daimos' the Kabuto, and the 'parrot' the Paper Crane.

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iii. Scientific and mathematical paperfolding

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iv. Le Prestidigitateur Alber

Between 1899 and 1903 'Le Prestidigitateur Alber', otherwise known as the magician Alber Graves (real name Jean Jacques Édouard Graves), published a series of articles in the French children's magazine 'Mon Journal' which included some traditional Japanese designs, Alber claimed that his source for these designs was a Japanese friend variously named as Mlle Kawala, Mlle Kawada or Madame Kawada, though whether this lady actually existed or was invented as part of his magician's patter is hard to say.

Some of the designs, such as the Paper Crane and the Blow-up Frog were, as we have seen, already known in the West. Others, such as the Lily, the Palanquin (a version of the Kago), the Crab and the Kabuto had not appeared in the West before. One, Le Kiosque Japonais, is assigned a Japanese origin, but is not evidenced from Japan.

His book ‘Les petits secret amusant’, published in 1908, later brought many of the same designs to a wider audience, and many subsequently become established in the Western European repertoire.

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v. 20th Century books

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C: Paperfolding in the Spanish speaking world

i. The paperfolding of Miguel de Unamuno

Miguel de Unamuno, born in 1864 and died in 1936, was a Spanish academic, author and thinker who was also influential in the development of paperfolding in Spain and beyond.

In 1888 he published an account, 'Historia de Unas Pajaritas de Papel', of how, when he was 10 years old, he and his cousin folded and played with paper Pajaritas and other toys during the bombing of Bilbao during the Third Carlist War.

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1n 1902 the Argentinean magazine ‘Caras y Caretas’ published a letter from Unamuno which was illustrated by a picture of what he called the 'most perfect paper pajarita known', 'although, to be sure, starting out from other figures'. The design is developed from a bird base and appears to be an early version of his Avechucho, made with a simpler head and beak than later versions. We do not know with certainty what the 'other figures' it was derived from were, but, the obvious candidates are either the Paper Crane or the Flapping Bird.

Unamuno amd his 'most perfect paper pajarita known'

In April of the same year Unamuno’s second novel 'Amor y pedagogía' was published. The original manuscript for this novel was shorter than the publisher required so it was lengthened by the addition of a foreword, an epilogue and a treatise on the Cocotte / Pajarita design titled 'Apuntes para un tratado de cocotología'. This treatise was attributed to Don Fulgencio, one of the main characters in the story. Much of it seems to be deliberately obscure.

(This treatise may have been inspired by the article 'Pajaritologia', by Senesio Delgado, which had been published in 1894. It is possible that Unamuno called his paperfolding ‘cocotologia’ because the more obvious, more Spanish, term, ‘pajaritalogia’ had already been used.)

Unamuno went on to devise a number of other designs from the bird base, including several other birds, a seal, a teapot and an Empire style table.

Photograph from Estampa showing a few of Unamuno's designs

He remained a passionate recreational paperfolder until his death in 1936 and his design work and love of folding paper inspired the Spanish / Argentinean paperfolding tradition.

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ii. After Unamuno

Information about his topic will be added in due course

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iii. Vincente Solorzano Sagredo

Information about his topic will be added in due course

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iv. Ligia Montoya

Information about his topic will be added in due course

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D: Paperfolding in Germany

Information about his topic will be added in due course

The Magazine Cover Box

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E: Paperfolding in the English speaking world

i. Articles in magazines

In children's magazines

By the 1880s paperfolding designs began to appear in magazines aimed at children.

In the USA in 1881 St Nicholas magazine published a reader’s letter explaining and illustrating the Newspaper Ladder and, in the same issue, diagrams for the Fold and One Cut Latin and Maltese Crosses and showed how to arrange all the pieces released by cutting out the Latin Cross to form an Altar.

In England in 1886 the Boy’s Own Paper published diagrams for the Flapping Bird and a written description of how to make the Chinese Junk.

In the USA in 1887 St Nicholas magazine published another reader’s letter explaining how to make a Japanese design, the Sanbo on Legs, under the somewhat surprising name of 'Nantucket Sinks'.

In magazines for adults

Paper Planes

A design for 'A Model Paper Monoplane that can be Steered' (now better known as 'The Swallow') was published in the November 1917 issue of Popular Mechanics magazine.

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Strangely, another design for a 'Paper Glider' (now better known as 'The Cut and Fold Aeroplane) was published by in 'The Magic of Science' by A Frederick Collins in the same year.

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ii. The decline of Falten / The rise of Paper Sloyd

During the early part of the 20th century interest in Froebel's classic paperfolding based occupations began to decline, though at a different rate in different countries. It had, of course, never been particularly influential in France, where, as we have seen, paperfolding was seen as a way of promoting manual dexterity rather than creativity. In England and the USA, Froebelian-style paperfolding began to be replaced in the kindergarten and primary school syllabuses by Paper Sloyd, which was a type of cardboard modelling where simple, useful, objects, such as boxes, were made from templates, the process being to cut out the basic shape from the template, fold it up and glue it together. This type of handicraft was much more easily accessible for pupils, but equally of much less educational value.

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iii. Paper Magic and other books

Many of the recreational paperfolding designs which Le Prestidigitateur Alber had published in 'Mon Journal' and '‘Les petits secret amusant’ were republished in the early 1930s in 'La Nature'.

There seems to have been something of a trend around this time, which lasted until the 1960s, for conjurors to both include paperfolding effects in their magic acts and for them to be personally, as well as professionally, interested in the subject, perhaps because the act of folding something out of a piece of smooth, flat paper has the same appeal as, for instance, making a rabbit appear from an empty hat. Paperfolding is not trickery, but it can appear to be magical.

Conjurors have long supplemented their earnings from performances by writing books explaining how magical effects are achieved, and irt is but a small jump from this to writing books about paperfolding. English and American authors, in particular, seized this opportunity for expanding their earning power. 1919 saw the publication of ‘Paper Tricks’ by Will Goldston, 1920 of ‘Paper Magic’ by Will Blyth, 1922 ‘Houdini’s Paper Magic’ by Harry Houdini (though possibly ghost written by Walter B Gibson), and 1923 ‘More Paper Magic’, again by Will Blyth. The most influential of all these books, ‘Fun with Paper Folding’ by William D Murray and Francis J Rigney, followed five years later in 1928. R M Abraham published two books containing paperfolding material, 'Winter Nights Entertainments' in 1932 and followed this up with ''Diversions and Pastimes' in 1933. Joseph Leeming also included paperfolding material in some of his many books, particularly in 'Fun with Paper', which was published in 1939.

Another influential English language book published during this period was 'Paper Toy Making' by Margaret Campbell. It is undated but probably published in 1937. This book is credited with awakening an interest in contemporary recreational paperfolding in Robert Harbin, the leading stage illusionist of his day.

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iv. Flexagons

Information about his topic will be added in due course

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v. Josef Albers and the Bauhaus

Information about his topic will be added in due course

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vi. Paperfolding in the Rupert Annuals

Information about his topic will be added in due course

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vii. The Increasing influence of Japanese paperfolding

1957 saw the beginning of a new trend for the publication of books about Japanese paperfolding, or origami (as paperfolding was now frequently known), by Japanese authors, but in English, in the West, and particularly in the USA. The first of these were 'Origami: Japanese Paperfolding' by Isao Honda and 'Origami: Book 1' by Florence Sakade, both of which were published in 1957. Other books by the same authors followed in the next few years and they were joined, from 1962 onwards, by books by Tatsuo Miyawaki, and from 1965 on by books by Chiyo Araki. These colourful books, which mostly explained a fairly small number of quite simple designs, sold well and established the idea in the consciousness of the general public in the West that paperfolding (now widely known as origami) was an oriental, and mostly a Japanese, art form. The words 'the Japanese art of origami' became a cliche in the publishing world, and many Americans of Japanese heritage, or Japanese nationals living in the USA, became involved in teaching or demonstrating traditional Japanese designs (even if some of these were originally Western European in origin). Even the conceptual artist Yoko Ono, who was later to marry John Lennon, once made part of her living as an origami demonstrator.

Yoko Ono demonstrating origami in Abraham & Strauss bookshop New York in 1961

This idea, that origami was a peculiarly Japanese artform, was encouraged by the Japanese government, who were looking to find ways to rehabilitate Japan's international reputation after the damage done to it by the Second World War, and were actively promoting Japanese arts and crafts in overseas countries as a way of achieving this. In 1966, for instance, the Japanese Ministry of Foreign Affairs arranged for Akira Yoshizawa to visit Oceania and eight European countries to exhibit and teach his designs, and, in the same year, made a propaganda film titled 'Origami: The Folding Papers of Japan' featuring Akira Yoshizawa and many of his designs, which was, presumably, disseminated more widely.

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viii. Robert Harbin

In 1955 his hands appeared, folding paper, as ‘Mr Left and Mr Right’, in a short segment of the BBC children’s programme ‘Jigsaw’. ‘Mr Left and Mr Right’ first aired on 2nd January 1955 and ran for six bi-weekly shows during in prime time on Saturday evenings.

Harbin collected as many paperfolds as he could and, in 1956, published them in a book, also called, perhaps rather unimaginatively, 'Paper Magic'. As well as traditional Western European, Japanese and Chinese designs, it also included designs by Harbin himself and by Miguel Unamuno, Natividad Sánchez Ferrero, Solorzano and others. Not all these designs were correctly attributed, but Harbin's efforts to do so, even if not always successfully, marks the beginning of the modern practice of acknowledging the source of recreational paperfolds by naming the original designer. (In the case of 'traditional' paperfolds, of course, the original designer is not known.) This book was to be very influential in its turn.

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ix. Gershon Legman

This is the back ground for the most significant exchange of ideas and designs between Japanese and Western European / American recreational paperfolders, which has eventually led to an almost complete merger of the two traditions, began in the early 1950s, when Gershon Legman, an American folklore researcher and writer, who had moved to France to escape being caught up in the persecution of left-wing leaning intellectuals by Senator McCarthy, began to gather information about recreational paperfolding, a subject in which he had become deeply interested. By 1952 he had gathered sufficient material to be able to publish a short bibliography on the subject. By 1957 He was in touch with recreational paperfolders from across the globe, including Akira Yoshizawa, Ligia Montoya (from Argentina), George Rhoads (from the USA), Lillian Oppenheimer (also from the USA) and Robert Harbin (from England). As a result, a global network of people interested in recreational origami began to be formed, with the result that ideas and designs originating with paperfolders in one part of the world could now quickly become known to paperfolders in another.

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x. Lillian Oppenheimer

In June 1958 the New York Times carried an article that featured Lillian Oppenheimer and her love of recreational paperfolding, and in October of the same year the inaugural meeting took place of what she called 'The Origami Center', not yet a formal organisation, but essentially a useful umbrella name under which she and her friend Frieda Lourie could promote paperfolding classes and bring people who were already interested in recreational paperfolding together. Lillian Oppenheimer also began to publish a magazine, 'The Origamian', which shared news and ideas, and later folding diagrams, to which paperfolders across the world could subscribe.

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xi. Influential paperfolders associated with The Origami Center

Jack J Skillman

Information about his topic will be added in due course

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Frederick G Rohm

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Neal Elias

Information about his topic will be added in due course

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Giuseppe Baggi

Information about his topic will be added in due course

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Robert E Neale

Information about his topic will be added in due course

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Sam Randlett

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Adolpho Cerceda

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Philip Shen

Information about his topic will be added in due course

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xii. Books and TV appearances by Western authors

As a result of all this, recreational paperfolding began to become a much more popular form of self-entertainment in the West than it probably ever had been before, and this in turn provided a market for further books and television programmes. During the early 1960s the plethora of books about origami from Japanese authors were joined by books written by Western authors, notably Samuel Randlett's 'The Art of Origami', published in 1961 and 'The Best of Origami', published in 1963, and Robert Harbin's 'Secrets of Origami', published in 1963, each of which featured many contemporary rather than 'traditional' designs and carefully credited the new designs to their individual creators. Another Harbin book, ‘Teach Yourself Origami’ first published in 1968, became a best-seller when it was republished in paperback as ‘Origami: The Art of Paper-Folding’, and, later as 'Origami 1'. Between 1968 and 1971 Harbin also appeared in thirty-two fifteen-minute-long episodes of a series made by Yorkshire Television, called, simply, ‘Origami’, in which he demonstrated how to fold objects such as birds, animals, and flowers. These programmes were accompanied by a series of articles published in ITV’s "Look-In" magazine. Harbin’s 1975 book ‘Have Fun with Origami’ was a collection of designs sent in by viewers and readers during the course of this series.

xiii. The influence of Akira Yoshizawa

In July 1970 the rather obscure 'Beacon Magazine of Hawaii' published an article by Leland Stowe, a Pullitzer prize winning journalist, about the design work of Akira Yoshizawa. The article was subsequently republished in the magazine 'Reader's Digest', which claimed to have a worldwide circulation of over 29 million copies in 13 languages, first in the USA edition and then in other national editions around the world. (This is not so unlikely as it seems. Leland Stowe worked as an editor for 'Reader's Digest' and the article may therefore have been 'planted' in Hawaii in order to be picked up for republication later on.) This article brought Yoshizawa to the attenion of a whole new audience and is probably the platform on which much of his subsequent fame and influence on recreational paperfolding design was built.

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F: National paperfolding organisations in Western Europe and the Americas

The Winter 1965 issue of 'The Origamian' contained a column which advised that an Argentine version of the Origami Center, the Centro Argentina Para Origami, had been formed, but did not include the name of the correspondent.

By October 1967, there was sufficient interest among enthusiasts in Great Britain to support the formation of a formal recreational paperfolding organisation, the British Origami Society, which was established as an educational charity. Robert Harbin became the first President of this society.

France: The Mouvement français des plieurs de papier (MFPP) was founded by Jean-Claude Correia in 1978.

Italy: The Centro Diffusione Origami (CDO) was founded by Roberto Morassi and Giovanni Maltagliati in 1979.

Germany: Origami Deutschland was founded by Paulo Mulatinho and 7 other origami enthusiasts in 1979.

Spain: The Asociación Española de Papiroflexia (AEP) was founded in 1980.

USA: The Friends of the Origami Center of America was founded by Michael Shall, Alice Gray, Gay Gross, Natalie Epstein, Alan Kaplan, Robert Neale, Florence Temko, Gwen Williams, and others, in 1980, as a formal successor to Lillian Oppenheimer's informal Origami Center organisation. In 1994, after her death in 1992, the organisation changed its name to OrigamiUSA.

The Netherlands: The Origami Sociëteit Nederland (OSN) was founded in 1983.

There are many more such societies founded after this date.

These national societies promoted, and continue to promote, interest in recreational paperfolding, organise meetings, conventions and exhibitions, publish perodicals enabling the sharing of news, ideas, and diagrams for new designs, and act as sources of information for the media.

Somewhat bizzarely, however, some forms of recreational paperfolding, such as Golden Venture / 3D modular origami are not usually included in the activities of the majority of these societies.

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G: Paperfolding ethics

Getting rid of the cuts / The idea of pure origami

Information about his topic will be added in due course

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H: The development of original paperfolding techniques

Paper Sculpture

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Pop-ups and Origami Architecture

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Modular origami

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Corrugations and Tessellations

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Box-pleating

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Wet-folding

Information about his topic will be added in due course

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Circle packing and grafting

Information about his topic will be added in due course

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The use of curved creases

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I: The impact of the internet and social media

The internet has made it much easier for recreational paperfolders to keep in touch with each other and information about new designs and design ideas now spreads with lightning speed, so that it is now probably impossible to distinguish between paperfolding styles and techniques on a geographical basis.

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