Rigid origami
From Wikipedia, the free encyclopedia
Rigid origami is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges. It is a part of the study of the mathematics of paper folding, it can be considered as a type of mechanical linkage, and has great practical utility. For instance it was used in the construction of large solar panel arrays that have to be folded before deployment. There is no requirement that the structure start as a flat sheet — for instance shopping bags with flat bottoms and airbags are studied as part of rigid origami.
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[edit] Mathematics
The number of standard origami bases that can be folded using rigid origami is restricted by its rules. [1] Rigid origami does not have to follow the Huzita–Hatori axioms, the fold lines can be calculated rather than having to be constructed from existing lines and points. However Kawasaki's Theorem and Maekawa's Theorem are still applicable.
The Bellows theorem says that a flexible polyhedron has constant volume when flexed. [2]
[edit] Applications
The Miura-fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.
Robert J. Lang has applied origami to the problem of folding airbags [3] and to folding a space telescope. [4]
Folding paper shopping bags is a problem where the rigidity requirement means the classic solution does not work. [5]
[edit] Recreational uses
Martin Gardner has popularised flexagons which are a form of rigid origami and the flexatube. [6]
[edit] References
- ^ Demaine, E. D (2001). Folding and Unfolding. Doctoral Thesis. University of Waterloo, Canada. http://etd.uwaterloo.ca/etd/eddemaine2001.pdf.
- ^ R. Connelly, I. Sabitov, A. Walz (1997). "The bellows conjecture". Beiträge zur Algebra und Geometrie 38 (1): 1–10.
- ^ Robert J. Lang. "Airbag folding". http://www.langorigami.com/science/airbag/airbag.php4.
- ^ "The Eyeglass Space Telescope". https://lasers.llnl.gov/programs/psa/pdfs/technologies/eyeglass_space_telescope.pdf.
- ^ Devin. J. Balkcom, Erik D. Demaine, Martin L. Demaine (November 2004). "Folding Paper Shopping Bags". Abstracts from the 14th Annual Fall Workshop on Computational Geometry (Cambridge, Massachusetts): 14–15. http://martindemaine.org/papers/PaperBag_CGW2004/.
- ^ Weistein, Eric W., "Flexatube" from MathWorld.
