How to fold it: The mathematics of linkages, origami, and polyhedra

How to Fold it: The Mathematics of Linkages, Origami, and Polyhedra

Volumn , Issue , 2011, Pages 1-177

  O'Rourke, Joseph ^a  

^a SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924143240     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511975028     Document Type: Book

References (30)

1. Erik D. Demaine and Joseph O’Rourke. Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press, July 2007. http://www.gfalop.org.
2. Joseph O’Rourke. Computational Geometry in C. Cambridge University Press, 2nd edition, 1998.
3. Thomas H. Cormen, Charles E. Leiserson, Ron L. Rivest, and Cliff Stein. Introduction to Algorithms. MIT Press, Cambridge, MA, 3rd edition, 2009.
4. Alfred Bray Kempe. How to Draw a Straight Line: a Lecture on Linkages. Macmillan & Co., 1877.
5. John Bryant and Chris Sangwin. How Round Is Your Circle?: Where Engineering and Mathematics Meet. Princeton Univ. Press, 2008.
6. Tom Standage. The Turk: The Life and Times of the Famous Eighteenth-Century Chess Playing Machine. Walker & Co., 2002.
7. “reconfigurable mechanisms and robots.” The Folding@Homeweb site is at http://folding.stanford.edu/.
8. Nadia Benbernou. Fixed-angle polygonal chains: Locked chains and the maximum span. Undergraduate thesis, Smith College, 2006.
9. Nadia Benbernou and Joseph O’Rourke. On the maximum span of fixed-angle chains. In Proceedings of the 18th Canadian Conference Computational Geometry, pages 93-96, 2006.
10. Ciprian S. Borcea and Ileana Streinu. Extremal configurations of manipulators with revolute joints. In Reconfigurable Mechanisms and Robots, pages 279-284. American Society of Mechanical Engineers, 2009.
11. Thomas Hull. Project Origami: Activities for Exploring Mathematics. A K Peters, 2006.
12. Erik D. Demaine and Martin L. Demaine. Recent results in computational origami. In Origami3: Proceedings of the 3rd International Meeting of Origami Science, Mathematics, and Education, pages 3-16. A K Peters, 2002.
13. Marshall Bern and Barry Hayes. The complexity of flat origami. In Proceedings of the 7th ACM-SIAM Symposium Discrete Algorithms, pages 175-183, 1996.
14. Erik D. Demaine, Martin L. Demaine, and Anna Lubiw. Folding and one straight cut suffice. In Proceedings of the 10th Annual ACM-SIAM Symposium Discrete Algorithms, pages 891-892, January 1999.
15. Marshall Bern, Erik D. Demaine, David Eppstein, and Barry Hayes. A disk-packing algorithm for an origami magic trick. In Origami3: Proceedings of the 3rd International Meeting of Origami Science, Mathematics, and Education, pages 17-28. A K Peters, 2002.
16. Marshall Bern and Barry Hayes. Origami embedding of piecewise-linear two- manifolds. In Proceedings of the 8th International Latin American Symposium Theoretical Informatics, pages 617-629. Springer LNCS 4957, 2009.
17. Koryo Muira called what is now known to us as the Muira Map Fold the “Developable Double Corrugation Surface” in Origami3.
18. Koryo Miura. The application of origami science to map and atlas design. In Origami3: Proceedings of the 3rd International Meeting of Origami Science, Mathematics, and Education, pages 137-145. A K Peters, 2002.
19. Devin J. Balkcom, Erik D. Demaine, Martin L. Demaine, John A. Ochsendorf, and Zhong You. Folding paper shopping bags. In Origami4: Proceedings of the 4th International Meeting of Origami Science, Mathematics, and Education, pages 315-334. A K Peters, 2006.
20. Greg N. Frederickson. Hinged Dissections: Swinging & Twisting. Cambridge University Press, 2002.
21. Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott D. Kominers. Hinged dissections exist. In Proceedings of the 24th Annual ACM Symposium on Computational Geometry, pages 110-119, 2008.
22. To appear in the journal Discrete & Computational Geometry, 2011.
23. Geoffrey C. Shephard. Convex polytopes with convex nets. Mathematical Proceedings of the Cambridge Philosophical Society, 78:389-403, 1975.
24. Joseph Malkevitch. Milestones in the history of polyhedra. In Marjorie Senechal and George Fleck, editors, Shaping Space: A Polyhedral Approach, pages 80-92. Birkhauser, Boston, 1988.
25. Joseph O’Rourke. Unfolding orthogonalpolyhedra. In Jacob E. Goodman, Janos Pach, and Richard Pollack, editors, Proceedings Snowbird Conference Discrete and Computational Geometry: Twenty Years Later, pages 307-317. American Mathematical Society, 2008.
26. Mirela Damian, Robin Flatland, and Joseph O’Rourke. Epsilon-unfolding orthogonal polyhedra. Graphs and Combinatorics, 23 [Suppl]:179-194, 2007. Akiyama-Chvatal Festschrift.
27. Mirela Damian, Robin Flatland, and Joseph O’Rourke. Unfolding Manhattan towers. Computational Geometry: Theory & Applications, 40(2):102-114, 2008.
28. Joseph O’Rourke. Folding polygons to convex polyhedra. In Timothy V. Craine and Rheta Rubenstein, editors, Understanding Geometry for a Changing World: National Council of Teachers of Mathematics, 71st Yearbook, pages 77-87. National Council of Teachers of Mathematics, 2009.
29. Yuri D. Burago and Viktor A. Zalgaller. Isometric piecewise linear immersions of two-dimensional manifolds with polyhedral metrics into R3. St. Petersburg Mathematical Journal, 7(3):369-385, 1996. Translated by Sergei G. Ivanov.
30. Joseph O’Rourke. On folding a polygon to a polyhedron. ar Xiv:1007.3181v1 [cs.CG]. http://arxiv.org/abs/1007.3181