Advertisement

Mathematics and Origami: The Art and Science of Folds

  • Natalija BudinskiEmail author
Living reference work entry

Latest version View entry history

Abstract

Origami is usually connected with fun and games, and the most common association with origami is a paper-folded crane, which has a special place in Japanese culture. The popularity of modern origami has grown in many aspects, including mathematical, scientific, artistic, or even as an enjoyable craft. This chapter describes the developmental path of origami from simple paper folding through to that of a serious scientific discipline. It might be said that it all started with the discovery of mathematical rules behind the folds, which led to the axiomatization of origami and the establishment of it as a mathematical discipline. Many unsolved problems, such as doubling the cube, became solvable thanks to origami. Interestingly, while developing as a scientific discipline, origami has also been establishing itself as a form of modern art and is a great inspiration to many contemporary artists in different creative disciplines, such as sculpture, fashion, or design. Examples of these contemporary art forms are shown in this chapter.

Keywords

Origami Mathematical Artistic Crane Scientific 

References

  1. Abel Z, Cantarella J, Demaine E, Eppstein D, Hull T, Jason K, Lang R, Tomohiro T (2016) Rigid origami vertices: conditions and forcing sets. J Comput Geom 7(1):171–184MathSciNetzbMATHGoogle Scholar
  2. Adler D (2004) A new unity, the art and pedagogy of Joseph Albers. Ph.D. thesis, University of MarylandGoogle Scholar
  3. Alperin R, Lang R (2006) One-, two-, and multi-fold origami axioms. In: Origami 4 fourth international meeting of origami science, mathematics and education. A K Peters Ltd, NatickGoogle Scholar
  4. Balkcom D (2002) Robotic origami folding. Ph.D. thesis, Carnegie Mellon UniversityGoogle Scholar
  5. Burton D (2006) The history of mathematics: an introduction. McGraw−Hill, New YorkGoogle Scholar
  6. Davis E, Demaine ED, Demaine ML, Ramseyer J, Tessellations O (2013) Reconstructing David Huffman’s origami tessellations 1. J Mech Des 135(11):111010.  https://doi.org/10.1115/1.4025428. ISSN 1050–0472. http://mechanicaldesign.asmedigitalcollection.asme.org/article.aspx?doi=10.111/1.4025428CrossRefGoogle Scholar
  7. Demaine E, Demaine M (2009) Mathematics is art. In: Proceedings of 12th annual conference of BRIDGES: mathematics, music, art, architecture, culture, Banff, pp 1–10Google Scholar
  8. Demaine E, Demaine M, Lubiw A (1999) Polyhedral sculptures with hyperbolic paraboloids. In: Proceedings of the 2nd annual conference of BRIDGES: mathematical connections in art, music, and science (BRIDGES’99), pp 91–100Google Scholar
  9. Demaine M, Hart V, Price G, Tachi T (2011) (Non)existence of pleated folds: how paper folds between creases. Graphs and Combinatorics 27(3):377–397MathSciNetCrossRefGoogle Scholar
  10. Dureisseix D (2012) An overview of mechanisms and patterns with origami. Int J Solids Struct 27(1):1–14MathSciNetGoogle Scholar
  11. Felton S, Tolley M, Demaine E, Rus D, Wood R (2014) A method for building self-folding machines. Science 345(6197):644–646CrossRefGoogle Scholar
  12. Fenyvesi K, Budinski N, Lavicza Z (2014) Two solutions to an unsolvable problem: connecting origami and GeoGebra in a Serbian high school. In: Greenfield G, Hart G, Sarhangi R (eds) Proceedings of bridges 2014: mathematics, music, art, architecture, culture. Tessellations Publishing, Phoenix, pp 95–102Google Scholar
  13. Fujimoto S (1976) Twist origami, Home printGoogle Scholar
  14. Harbin R (1956) Paper magic. Oldbourne Press, LondonGoogle Scholar
  15. Hull T (1994) On the mathematics of flat origamis. Congr Numer 100:215–224MathSciNetzbMATHGoogle Scholar
  16. Hull T (2002) The combinatorics of flat foldis survey. In: Proceedings of the third international meeting of origami science, mathematics, and education, pp 29–38zbMATHGoogle Scholar
  17. Hull T (2003) Counting mountain-valley assignments for flat folds. Ars Combin 67:175–188MathSciNetzbMATHGoogle Scholar
  18. Hull T (2006) Project origami: activities for exploring mathematics, Wellesley. AK PetersGoogle Scholar
  19. Huzita H (1989) Axiomatic development of origami geometry. In: Proceedings of the 1st international meeting of origami science and technology, pp 143–158Google Scholar
  20. Huzita H (1992) Understanding geometry through origami axioms. In: COET91: Proceedings of the first international conference on origami in education and therapy. British Origami Society, pp 37–70Google Scholar
  21. Jackson P (2011) Folding techniques for designers, from sheet to form. Laurence King Publishing, London, p 118Google Scholar
  22. Justin J (1986a) Mathematics of origami, Part 9. Br Origami Soc 118:28–30Google Scholar
  23. Justin J (1986b) Résolution par le pliage de l’équation du troisième degré et applications géométriques. L’Ouvert - Journal de l’APMEP d’Alsace et de l’IREM de Strasbourg (in French) 42:9–19Google Scholar
  24. Kasahara K (1973) Origami made easy. Japan Publications Inc, TokyoGoogle Scholar
  25. Kasahara K (2003) Extreme origami. Sterling, New YorkGoogle Scholar
  26. Konjevod G (2008) Origami science, mathematics and technology, poetry in paper, the first origami exhibition in Croatia with international origami masters. Open University Krapina, Krapina City GalleryGoogle Scholar
  27. Lakes RS, Witt R (2002) Making and characterizing negative Poisson’s ration materials. Int J Mech Eng Educ 30(1):50–58CrossRefGoogle Scholar
  28. Lalloo M (2014) Applied origami. Ingenia 61:33–37Google Scholar
  29. Lang R (1995) Origami insects and their kin. General Publishing Co., TorontoGoogle Scholar
  30. Lang R (2009) Mathematical methods in origami design. Bridges: mathematics, music, art, architecture, culture, pp 13–20, Banff Centre Banff, Alberta, CanadaGoogle Scholar
  31. Lebee A (2015) From folds to structures, a review. Int J Space Struct 30(2):55–74. Multi Science PublishingCrossRefGoogle Scholar
  32. Lister D (1997) Introduction to the third edition. In: Harbin R (ed) Secrets of origami: the Japanese art of paper folding. Dover Publications, Mineola, pp 1–3. (Originally published, 1964)Google Scholar
  33. Lv C, Krishnaraju D, Yu H, Jiang H (2014) Origami based mechanical metamaterials. Sci Report 4:5979CrossRefGoogle Scholar
  34. Maehara H (2010) Reversing a polyhedral surface by origami-deformation. Eur J Comb 31(4):1171–1180MathSciNetCrossRefGoogle Scholar
  35. Magrone P (2015) Form and art of closed crease origami. In: Proceedings of 14th conference of applied mathematics. Slovak University of Technology, BratislavaGoogle Scholar
  36. Mahadevan L, Rica S (2005) Self organized origami. Science 307:1740CrossRefGoogle Scholar
  37. Messer P (1986) Problem No. 1054. Crux Math 12:284–285Google Scholar
  38. Mitani J (2016) 3D origami art. A K Peters/CRC Press, NatickzbMATHGoogle Scholar
  39. Mukerji M (2007) Marvelous modular origami. A K Peters Ltd, NatickCrossRefGoogle Scholar
  40. Nishiyama Y (2012) Miura folding: applying origami to space exploration. Int J Pure Appl Math 79(2):269–279zbMATHGoogle Scholar
  41. Peraza-Hernandez E, Hartl D, Malak D Jr, Lagoudas D (2014) Origami-inspired active structures: a synthesis and review. Smart Mater Struct 23(9):1–50CrossRefGoogle Scholar
  42. Row S (1893) Geometrical exercises in paper folding. Addison & Co, Mountain RoadGoogle Scholar
  43. Schneider J (2004) Flat-foldability of origami crease patterns. http://www.sccs.swarthmore.edu/users/05/jschnei3/origami.pdf. http://www.britishorigami.info
  44. Smith J (1993) Some thoughts of minimal folding. British Origami. https://pdfs.semanticscholar.org
  45. Sorguç A, Hagiwara I, Selçuk S (2009) Origamics in architecture: a medium of inquiry or design in architecture. METU J Fac Archit 26(2):235–247CrossRefGoogle Scholar
  46. Tachi T (2011) Rigid-foldable thick origami. In: Origami5: fifth Int. meeting of origami science, mathematics, and education, pp 253–263CrossRefGoogle Scholar
  47. Turner N, Goodwine B, Sen M (2016) A review of origami application in mechanical engineering. Proc Inst Mech Eng C J Mech Eng Sci 230(14):2345–2362CrossRefGoogle Scholar
  48. Verrill H (1998) Origami tessellation. In: Bridges: mathematical connections in art, music, and science. Winfield, Kansas, pp 55–68Google Scholar
  49. Versnic P (2004) Folding for fun. Orihouse, p 36Google Scholar
  50. Wertheim M (2004) Cones, curves, shells, towers: he made paper Jump to life. NYork Times http://www.nytimes.com/2004/06/22/science/cones-curves-shells-towers-he-made-paper-jump-to-life.html
  51. Zhmud L (2006) The origin of the history of science in classical antiquity. Walter de Gruyter, BerlinzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Petro Kuzmjak SchoolRuski KrsturSerbia

Section editors and affiliations

  • Bharath Sriraman
    • 1
  • Kyeong-Hwa Lee
    • 2
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA
  2. 2.Department of Mathematics Education, College of EducationSeoul National UniversitySeoulSouth Korea

Personalised recommendations