(Non)Existence of Pleated Folds: How Paper Folds Between Creases

Graphs and Combinatorics

Volumn 27, Issue 3, 2011, Pages 377-397

  Demaine, Erik D ^a   Demaine, Martin L ^a   Hart, Vi ^b   Price, Gregory N ^a   Tachi, Tomohiro ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b The University of Tokyo ^*

Author keywords

Developable surface; Folding; Hypar; Hyperbolic paraboloid; Origami

Indexed keywords

EID: 79954631615     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00373-011-1025-2     Document Type: Article

References (25)

1. Adler, E. D.: A new unity! The art and pedagogy of Josef Albers. PhD thesis, University of Maryland (2004).
2. Alefeld G., Herzberger J.: Introduction to Interval Computations. Academic Press, New York (1983).
3. Alexandrov, A. D.: Convex Polyhedra. Springer, New York (2005). Translation of Russian edition (1950).
4. Barequet G., Dickerson M., Eppstein D.: On triangulating three-dimensional polygons. Comput. Geometry: Theory Appl. 10(3), 155-170 (1998).
5. Chen L.-L., Woo T. C.: Computational geometry on the sphere with application to automated machining. J. Mech. Des. 114(2), 288-295 (1992).
6. Demaine, E. D., Demaine, M. L.: History of curved origami sculpture. http://erikdemaine. org/curved/history/ (2008).
7. Demaine, E. D., Demaine, M. L., Lubiw, A.: Polyhedral sculptures with hyperbolic paraboloids. In: Proceedings of the 2nd Annual Conference of BRIDGES: Mathematical Connections in Art, Music, and Science (BRIDGES'99), pp. 91-100, Winfield, Kansas, July 30-August 1 1999.
8. Donoso, M., O'Rourke, J.: Nonorthogonal polyhedra built from rectangles. arXiv: cs/0110059v2 [cs. CG], May 2002. http://www. arXiv. org/abs/cs. CG/011005. In: Proceedings of the 14th Canadian Conference on Computational Geometry, Lethbridge, Canada, August 2002, pp. 101-104 (Abstract).
9. Demaine E. D., O'Rourke J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press, New York (2007).
10. Fuchs D., Tabachnikov S.: More on paperfolding. Am. Math. Mon. 106(1), 27-35 (1999).
11. Gauss, C. F.: General Investigations of Curved Surfaces. Princeton University Library, 1902. Translated by J. C. Morehead and A. M. Hiltebeitel from 1827 original. Republished by Dover (2005).
12. Halsted, G. B.: Elements of Geometry. Wiley (1885). http://books. google. com/books?id=HCdoFvAcHyIC.
13. Hayes B.: A lucid interval. Am. Scientist 91(6), 484-488 (2003).
14. Huffman D. A.: Curvature and creases: a primer on paper. IEEE Trans. Comput. C25(10), 1010-1019 (1976).
15. 3: Proceedings of the 3rd International Meeting of Origami Science, Math, and Education, pp. 29-38, Monterey, California, March 2001.
16. Justin, J.: Mathematics of origami, part 9. British Origami, pp. 28-30, June 1986.
17. Koschitz, D., Demaine, E. D., Demaine, M. L.: Curved crease origami. In: Abstracts from Advances in Architectural Geometry (AAG 2008), pp. 29-32, Vienna, Austria, September 13-16, 2008.
18. Kasahara K., Takahama T.: Origami for the Connoisseur. Japan Publications, Inc., Tokyo (1987).
19. Moore R. E., Baker Kearfott R., Cloud M. J.: Introduction to Interval Analysis. SIAM Press, Philadelphia (2009).
20. Belcastro S.-M., Hull T. C.: Modelling the folding of paper into three dimensions using affine transformations. Linear Algebra Appl. 348, 273-282 (2002).
21. Spivak, M.: A Comprehensive Introduction to Differential Geometry, 2nd edn. Publish or Perish (1979).
22. Streinu, I., Whiteley, W.: Single-vertex origami and spherical expansive motions. In: Revised Selected Papers from the Japan Conference on Discrete and Computational Geometry. Lecture Notes in Computer Science, vol. 3742, pp. 161-173, Tokyo, Japan, October 2004.
23. Wertheim, M.: Origami as the shape of things to come. The New York Times, February 15, 2005. http://www. nytimes. com/2005/02/15/science/15origami. html.
24. Wikipedia.: Trilateration. http://en. wikipedia. org/wiki/Trilateration (2008).
25. Wingler, H. M.: Bauhaus: Weimar, Dessau, Berlin, Chicago. MIT Press (1969).