摺紙

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摺紙（日語：折り紙；英語：paper folding或origami）是一種紙張摺疊的藝術，目的是要透過摺疊把紙張摺出各種指定的形狀和花樣。英語的「Origami」一詞源自日語，指所有種類的摺紙藝術，包括發源於日本以外的摺紙。

摺紙只需要少量的摺疊，但透過各種方法就可以組合出複雜精細的設計。一般而言，摺紙設計由正方形的紙張摺成，有時會配搭不同顏色，而剪紙通常是不需要的。有一說指，日本的傳統剪紙早見於江戶時代（1603年─1867年），但當時這門傳統手藝並不嚴謹，製作時間中甚至會運用到剪紙。另外，長方形、圓形、三角形以至其他形狀的紙張都會大派用場。

目录 1 歷史 2 紙張與其他材料 3 摺紙數學 4 工藝摺紙 5 摺紙書籍的作者 6 延伸閱讀 7 參見 8 外部連結

[编辑] 歷史

主条目：摺紙歷史

雖然一些歷史學家 [1] 指出，摺紙是發源自中國（因此摺紙的英語本應稱作「Zhe Zhi」），但是人們普遍認為摺紙在日本才得到真正的發展。在中國古代，摺紙主要是孩子用作消遣的一門傳統藝術，後來經日本人吉澤章加以改良，使之復興。他提出了濕折法，並與美國人Sam Randlett發明了吉澤章-Randlett系統（圖解摺紙術語）。1960年代，摺紙藝術開始發揚光大。組合式摺紙面世後，各項行動亦相繼推行，如開設切邊、純粹主義和淨土等摺紙思想的課程。

[编辑] 紙張與其他材料

雖然差不多所有薄片狀材料都可以摺疊，但材料的選用會直接影響摺疊的效果，以至模型的最終外型。

標準影印紙（70–90 g/m²）適用於簡單的摺疊，例如鶴和水彈。較重的紙（100 g/m²或以上）適用於濕摺。濕摺法可替模型塑造較圓的造形，因為濕水部分乾後會堅固。

特別的摺紙用紙（英語稱作「kami」，即日語「紙」的意思」）以預先包製的方格紙的形式售賣，各種尺寸由2.5至25厘米或更大不等。常見的摺紙用紙是一面彩色，一面白色的；不過，雙面彩色或有圖案的色紙亦見於市面，這些最適合變色模型。至於較輕的摺紙用紙，模型的適用範圍更廣。

有襯鋁箔紙，顧名思義，是一張與薄紙張膠合的金屬薄片。

在亞洲的台灣，某些摺紙愛好者也會自製所謂「合成紙」，就是將鋁箔與薄棉紙膠合起來使用。例如：[合成紙的摺紙飛馬] Related to this is tissue foil, which is made by gluing a thin piece of tissue 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. Both types of foil materials are suitable for complex models.

和紙 is the predominient 摺紙用紙 used in Japan. Washi is generally tougher than ordinary paper made from wood pulp, and is used in many traditional arts. Washi is commonly made using fibers from the bark of the gampi tree, the mitsumata shrub (Edgeworthia papyrifera), or the paper mulberry but also can be made using bamboo, hemp, rice, and wheat.

工藝紙，如雲龍紙、米紙、韓紙、雁皮紙、楮紙, saa have long fibres and are often extremely strong. As these papers are floppy to start with, they are often backcoated or resized with methylcellulose or wheat paste before folding. Also, these papers are extremely thin and compressible, allowing for thin, narrowed limbs as in the case of insect models.

[编辑] 摺紙數學

主条目：摺紙數學

摺紙的學習與研究涵蓋數學的不同範疇。譬如，平面可摺性的問題（一件起縐的形態能否摺成二維模型）是重要的數學研究主題。

值得注意的是，紙張面上的所有點展現零高斯曲率，而僅僅沿零曲率的線條自然地摺疊。但是，沿曲率不起摺痕的紙張面，可透過濕紙張或手指實現，並不展現這限制。

硬式摺紙的問題（「若用薄金屬板取代紙張，而摺線中有節點，我們能否仍舊摺出模型？」）有重大的實用價值。舉例，三浦公亮提出的硬式摺疊──三浦折疊（ミウラ折り）已應用於為太空人造衛星部署大型太陽電池板的陣列。

[编辑] 工藝摺紙

工藝摺紙，又稱「摺紙設計」, is a field of origami that has developed almost hand-in-hand with the field of mathematical origami. In the early days of origami, development of new designs was largely a mix of trial-and-error, luck and serendipity. With advances in origami mathematics however, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding even occurs. This method of origami design was pioneered by Robert Lang, Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes, human figures with full complement of fingers and toes, and the like.

The main starting point for such technical designs is the crease pattern (often abbreviated as 'CP'), which is essentially the layout of the creases required to form the final model. Although not intended as a substitute for diagrams, folding from crease patterns is starting to gain in popularity, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams.

Paradoxically enough, when origami designers come up with a crease pattern for a new design, the majority of the smaller creases are relatively unimportant and added only towards the completion of the crease pattern. What is more important is the allocation of regions of the paper and how these are mapped to the structure of the object being designed. For a specific class of origami bases known as 'uniaxial bases', the pattern of allocations is referred to as the 'circle-packing'. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial base of arbitrary complexity. Once this figure is computed, the creases which are then used to obtain the base structure can be added. This is not a unique mathematical process, hence it is possible for two designs to have the same circle-packing, and yet different crease pattern structures

[编辑] 摺紙書籍的作者

• 吉澤章 - 原創的現代摺紙，製作現代的摺紙圖解作品
• Robert J. Lang - 摺紙書作家，新著作為《摺紙設計祕密》
• Peter Engel - 影響深遠的摺紙藝術家、理論家
• Tomoko Fusé - 以盒式和組合式摺紙著名
• Robert Harbin - 英國的大眾化摺紙；also presented a series of short programmes entitled Origami, made by Thames Television for ITV
• Kunihiko Kasahara - devised a standardized method for creating any polyhedron
• John Montroll - probably the most prolific Western artist and author of over 16 books on origami
• Nick Robinson - origami artist and author of over a dozen books on origami
• Toshikazu Kawasaki - Japanese mathematician famous for his Iso-area folding theory and his many geometric folds, including Kawasaki's "Rose"
• Makoto Yamaguchi
• Satoshi Kamiya - One of the youngest geniuses of the origami field
• Norio Torimoto - Appointed Origami Master by the Nippon Origami Association in 2000. Gives lectures on mathematics using origami at The Royal Institute of Technology in Stockholm and other universites in Japan, Denmark and the UK.

[编辑] 延伸閱讀

• Robert J. Lang. The Complete Book of Origami: Step-by-Step Instructions in Over 1000 Diagrams. Dover Publications, Mineola, NY. Copyright 1988 by Robert J. Lang. ISBN 0-486-25837-8 (pbk.)

Pages 1-30 are an excellent introduction to most of these skills. Each of these 13 models is designed to let you practice one skill several times. Unfortunately, the remaining 24 models leave out lots of pre-creases.

• Tomoko Fuse. Unit Origami: Multidimensional Transformations. Japan Publications, inc. Tokyo. Copyright 1990 by Tomoko Fuse. ISBN 0-87040-852-6

This is an excellent book about modular origami, and serves as a great introduction to geometric models and designs.

• Kunihiko Kasahara. Origami Omnibus: Paper Folding for Everybody. Japan Publications, inc. Tokyo. Copyright 1988 by Kunihiko Kasahara. ISBN 4-8170-9001-4

A good book for a more advanced origamian, this book presents many more complicated ideas and theories, although the author tends to go off on long tangents about random topics. Still lots of good models though...

• Kunihiko Kasahara and Toshie Takahama. Origami for the Connoisseur. Japan Publications, inc. Tokyo. Copyright 1987 by Kunihiko Kasahara and Toshie Takahama. ISBN 0-87040-670-1

Another good book; same comments as the previous author.

• One Thousand Paper Cranes: The Story of Sadako and the Children's Peace Statue by Takayuki Ishii, ISBN 0-440-22843-3
• Sadako and the Thousand Paper Cranes by Eleanor Coerr, ISBN 0-698-11802-2
• Origami 1, Robert Harbin, 1969, ISBN 0-340-10902-5
• Origami 2, Robert Harbin, ISBN 0-340-15384-9
• Origami 3, Robert Harbin, 1972, ISBN 0-340-16655-X
• Origami 4, Robert Harbin, 1977, ISBN 0-340-21822-3 (rare)
• Origami Design Secrets, Robert J. Lang, 2003, ISBN 1-56881-194-2
• Extreme Origami, Kunihiko Kasahara, 2001, ISBN 0-8069-8853-3
• Ariomar Ferreira da Silva. Brincando com Origami Arquitetônico: 16 diagrams. Global Editora, São Paulo, Brazil. Copyright 1991 by Ariomar Ferreira da Silva and Leôncio de O. Carvalho. ISBN 85-260-0273-2

[编辑] 參見

• 組合式摺紙（Modular origami）
• 摺紙技巧（Origami techniques）
• 摺紙數學（Mathematics of paper folding）
• 中國摺紙（Chinese paper folding）
• 紙模型
• Noshi
• 紙飛機
• 藥玉（Kusudama）
• 摺紙建築（Origamic architecture）

[编辑] 外部連結

• [2] An extensive collection of links, with lots of organizations and topic-related pages sorted by an easy interface.
• The Lister List This is a collection of 115 essays by David Lister, one of origami's most eminent historians.
• 摺紙論壇 線上摺紙論壇
• Gilad的摺紙網頁 摺紙書書評（附圖）和摺疊模型的照片集
• ORILAND 由摺紙藝術家Yuri和Katrin Shumakov製作
• FOLDS.NET 初階至中階圖解
• 摺紙 大量圖解，適合初學者
• 愛因斯坦的摺紙 線上電子書，由Rick Nordal製作
• 摺紙片段 大量摺紙片段
• Works of Hsi-hua Liu 錫華的部落格，摺紙創作及討論。