查看“︁摺紙數學”︁的源代码

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'''折纸数学'''是指對'''[[摺紙]]'''[[藝術]]從[[數學]]的角度加以研究。比如，研究某個特定的紙模型的可展性（研究該模型是否可以攤平而無須把它弄破）以及使用摺紙來解[[方程|數學方程]]。

某些[[尺規作圖#古希腊三大名题|經典幾何作圖問題]]例如[[三等分角]]，或者將立方體的體積擴大一倍（[[倍立方]]）等問題都被證明為[[尺規作圖]]不可能解決的。但是它們可以通過幾個摺紙步驟加以解決。一般地，摺紙可以通過作圖求解不超過4次的[[代數方程]]。藤田—羽鸟公理集（Huzita-Hatori axioms，以日本数学家藤田文章和羽鸟公士郎<ref>{{Cite web|title=K's 折り紙|url=https://origami.ousaan.com/indexj.html|accessdate=2020-11-25|work=origami.ousaan.com|archive-date=2017-07-03|archive-url=https://web.archive.org/web/20170703053344/http://origami.ousaan.com/indexj.html|dead-url=no}}</ref>命名）是這一領域的重要研究成果。

作爲利用幾何概念對摺紙進行研究的結果，Haga定理可以用來把紙的一邊精確地三等分、五等分、七等分和九等分。其他定理則允許我們從正方形摺出其它圖型，例如等邊[[三角形]]、[[正六邊形]]、[[正八邊形]]以及特定的矩形比如[[黃金矩形]]和[[白銀矩形]]等。

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The problem of [[Rigid Origami|rigid origami]], treating the folds as hinges joining two flat, rigid surfaces such as [[sheet metal]], 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.-->
從帶有摺痕的平紙重新摺出原來的形狀這一問題已被Marshall Bern和Barry Hayes證明為[[NP完全]]問題<ref>{{Cite web |url=http://citeseer.ist.psu.edu/bern96complexity.html |title=The Complexity of Flat Origami (Extended Abstract) (1996) |access-date=2007-08-27 |archive-date=2007-10-17 |archive-url=https://web.archive.org/web/20071017190816/http://citeseer.ist.psu.edu/bern96complexity.html |dead-url=no }}</ref>。其它技術上的結果在《幾何摺紙算法》一書第二部分有更詳細的介紹。<ref name="GFALOP">{{Citation
  | last1 = Demaine
  | first1 = Erik
  | last2 = O'Rourke
  | first2 = Joseph
  | title = Geometric Folding Algorithms: Linkages, Origami, Polyhedra
  | publisher = 劍橋大學出版社
  | date = 2007年7月
  | location = 
  | pages = 
  | url = http://www.gfalop.org
  | doi = 
  | id = 
  | isbn = 978-0-521-85757-4
  | accessdate = 2021-12-19
  | archive-date = 2021-02-27
  | archive-url = https://web.archive.org/web/20210227030557/http://www.gfalop.org/
  | dead-url = no
  }}</ref>

對一張紙不斷對摺，其[[損失函數]]為<math>L = \frac{\pi t}{6} (2^n + 4)(2^n - 1)</math>，這裡 L 代表紙張的最小長度，t 代表紙張厚度，n 代表摺疊次數。這個函數是Britney Gallivan在2001年（那時候他還是個高中學生）提出的，他能把一張紙對摺12次。之前人們一直以爲不管多大的紙最多只能對摺8次。

==參考==
<references/>

==外部連結==
*[https://web.archive.org/web/20070418030541/http://www.merrimack.edu/~thull/OrigamiMath.html Origami Mathematics Page] by [https://web.archive.org/web/20070812051233/http://www.merrimack.edu/~thull/ Dr. Tom Hull]
*[https://web.archive.org/web/20070814033424/http://www.merrimack.edu/~thull/rigid/rigid.html Rigid Origami] by [https://web.archive.org/web/20070812051233/http://www.merrimack.edu/~thull/ Dr. Tom Hull]
*[http://www.paperfolding.com/math/ Origami & Math] {{Wayback|url=http://www.paperfolding.com/math/ |date=20080119172749 }} by [https://web.archive.org/web/20070824012645/http://www.paperfolding.com/email/ Eric M. Andersen]
*[https://web.archive.org/web/20170520133146/http://www.cut-the-knot.org/pythagoras/PaperFolding/index.shtml Paper Folding Geometry] at [[cut-the-knot]]
*[https://web.archive.org/web/20170410134814/http://www.cut-the-knot.org/pythagoras/PaperFolding/SegmentDivision.shtml Dividing a Segment into Equal Parts by Paper Folding] at [[cut-the-knot]]
*[https://web.archive.org/web/20051102085038/http://pomonahistorical.org/12times.htm Britney Gallivan has solved the Paper Folding Problem]
*[http://www.abc.net.au/science/k2/moments/s1523497.htm Folding Paper - Great Moments in Science - ABC] {{Wayback|url=http://www.abc.net.au/science/k2/moments/s1523497.htm |date=20080726155603 }}
*[http://www.technologyreview.com/blog/arxiv/25591/ Origami Crease Pattern Design Proved NP-Hard] {{Wayback|url=http://www.technologyreview.com/blog/arxiv/25591/ |date=20110418024702 }}

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[[Category:摺紙|Z]]
[[Category:趣味数学]]

[[es:Matemáticas del origami]]