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Topic: Computational origami

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	computational origami - a definition from Whatis.com
		Computational origami is a type of computer-assisted design (CAD) program used to model the ways in which various materials, including paper, can be folded.
		In one of a myriad of future applications, computational origami could help biologists learn how to create properly folded artificial proteins (proper folding is necessary to their functioning because only the unfolded surfaces of natural proteins interact with their environment).
		Computational origami has been used to create complex paper objects, such as insects, that were once thought to be beyond the medium's capacities.
	whatis.techtarget.com /definition/0,,sid9_gci943046,00.html (372 words)

	AT&T News Release, 1990-07-24, "Computational origami" patent (Site not responding. Last check: 2007-10-15)
		With computational origami, just as the visible small rectangle can be unfolded to return the paper to its flat, unfolded size, so can a small arrangement of processors that is organized like the small rectangle be "unfolded" and made to emulate an arrangement of many more processors that are organized like the unfolded paper.
		Putting the two concepts together, with computational origami, complex computations (the folded paper airplane) can be "mapped" to a large, regular array of interconnected processors (the unfolded piece of paper), and the large regular array can in turn be "mapped" to a small array of interconnected processors (the paper folded into small squares).
		Computational origami would organize a kitchen full of cooks like a roomful of jugglers, with each cook tossing and receiving recipe ingredients at just the right time," he said.
	www.att.com /news/0790/900724.bla.html (628 words)

	Computational Origami
		Origami was purely a hobby for Lang until he decided to apply the kind of mathematical modeling he used in laser physics to paper folding.
		He says computational origami helped him automate the process by which he determined how to make the precise kinds of folds needed to produce a multilegged insect and its antennae.
		Lang sees a definite future for computational origami in engineering and design work, but he acknowledges that the field is relatively esoteric and requires artistic as well as computational, mathematical and engineering skills.
	www.computerworld.com /printthis/2004/0,4814,92956,00.html (915 words)

	Computational Origami Project
		My interest in origami is revitalized by many interesting research results by mathematicians and computer scientists around the end of 1980s.
		Computational origami is to create origami by means of computation.
		We are interested in both aspects of origami, but as a research strategy, we separate them and pursue two different goals.
	www.score.is.tsukuba.ac.jp /~ida/Ida2004/CompOrigami.htm (321 words)

	Extreme Origami: ScienCentral Video News
		Origami is the ancient art of paper folding, and the most common style is folding a single uncut piece of paper.
		While he says that many origami artists have no mathematical background, his work in computational origami and origami mathematics has ratcheted up the competition in the field.
		He says that origami's principles can be used for anything that folds, from better packaging to expandable medical implants, like stents that prop open clogged arteries.
	www.sciencentral.com /articles/view.php3?type=article&article_id=218392855 (792 words)

	Origami & Math
		So, you're interested in origami and mathematics...perhaps you are a high school or K-8 math teacher, or a math student doing a report on the subject, or maybe you've always been interested in both and never made the connection, or maybe you're just curious.
		But back to origami construction...origami construction is defined as those geometric operations that can be formed by folding a piece of paper, using the raw edges and points of the paper, as well as any subsequent crease lines and points created while folding.
		Origami and Geometric Construction, which provides great descriptions and exercises for the 5th and 6th axioms, as well as descriptions of how to trisect the angle and double a cube via folding
	www.paperfolding.com /math (2393 words)

	Science
		Origami technology, which is the application of origami (and folding in general) to the solution of problems arising in engineering, industrial design, and technology in general.
		Origami math defines the "ground rules" for computational origami's goal of solving origami design problems (and quantifying their difficulty).
		Continuing this series, Origami USA, the American national origami society, is pleased to announce The Fourth International Conference on Origami in Science, Mathematics, and Education (4OSME), to be held September 8-10, 2006, at the California Institute of Technology, Pasadena, California, USA.
	www.langorigami.com /science/science.php4 (259 words)

	House 8 Weblog \| Surface Deep (Site not responding. Last check: 2007-10-15)
		The construction is one of an astonishing collection of paper objects folded by Dr. David Huffman, a former professor of computer science at the University of California, Santa Cruz, and a pioneer in computational origami, an emerging field with an improbable name but surprisingly practical applications.
		Computational origami, also known as technical folding, or origami sekkei, draws on fields that include computational geometry, number theory, coding theory and linear algebra.
		Most computational origamists are driven by sheer curiosity and the aesthetic pleasure of these structures, but their work is also finding application in fields like astronomy and protein folding, and even automobile safety.
	www.house8.com /weblog/archives/004789.php (1227 words)

	ReferenceFinder
		The idea of the simulator was that one could manipulate a sheet of paper on-screen using mouse and keyboard, and we'd try to have the screen image of the paper display what the paper would be doing if we performed the analogous actions on a real sheet of paper.
		Origami Simulation is a program that simulates the folding of a sheet of paper on-screen.
		Origami Simulation was written in Object Pascal for the Mac OS, using Lightspeed's THINK Pascal and the THINK Class Library.
	www.langorigami.com /science/origamisim/origamisim.php4 (600 words)

	BBC NEWS \| Technology \| Origami help for tech design
		Origami - the Japanese art of folding paper to make models - is being put to a new use - to help engineers design, amongst other things, new telescopes and cars.
		Exploiting the study of the way that paper folds, known as computational origami, can reveal both better ways to construct objects and also predict how they will respond to certain pressures.
		But computational origami is a relatively new study, and is helping to solve problems in many surprising areas.
	news.bbc.co.uk /1/low/technology/3301947.stm (552 words)

	Robotic origami folding (Site not responding. Last check: 2007-10-15)
		Origami is a fresh challenge for the field of robotic manipulation.
		Pureland origami is the most basic, allowing only mountain and valley folds.
		We are currently working on understanding more complicated origami skills (like reverse folding, squash folding, the rabbit ear, and prayer folding) that require the simultaneous manipulation of multiple non-colinear creases.
	www.cs.dartmouth.edu /~robotics/origami.html (328 words)

	Tech Tidbit -- July 2004
		Simply put, it is the application of computers and mathematics to the traditional Japanese art of paper folding.
		Computational origami is being applied in these and many other areas.
		News Release from ATandT, July 24, 1990, announcing that Alan Huang, head of the Optical Computing Research department at ATandT Bell Laboratories, was granted a U.S. patent for a technique he calls "computational origami," which reformats computations and then folds them to fit into various computers.
	www.alteich.com /tidbits/t070104.htm (589 words)

	Unfolding the field of computational origami @ workopolis.com (Site not responding. Last check: 2007-10-15)
		To create the animal, he first drew in a computer a stick image to indicate general design properties such as how many legs his lobster should have and where the legs were to connect to the body.
		Similarly, the computer has allowed origami artists to create what was once viewed as the summa of their art form: folded paper insects.
		An original impetus for computational origami was the belief that the mathematics it unveiled might allow computer processors to be folded in the most efficient way.
	workopolis.com /servlet/Content/fasttrack/20031011/FOLD11?... (840 words)

	arts@MIT Press Release 10/29/2004: Origami Master Robert Lang to Visit MIT
		Robert Lang has been an avid student of origami for over 30 years and is now recognized as one of the world's leading masters of the art, with over 400 designs catalogued and diagrammed.
		His work combines aspects of the Western school of mathematical origami design with the Eastern emphasis upon line and form to yield models that are at once distinctive, elegant, and challenging to fold.
		A pioneer of the cross disciplinary marriage of origami with mathematics, Lang has presented several refereed technical papers on 'origami-math' at mathematical and computer science professional meetings.
	web.mit.edu /arts/announcements/prs/2004/1029_lang.html (495 words)

	[No title]
		By using N-dimensional networks, an Origami machine can be built which has the same latency but much higher throughput than a randomly interconnected circuit for the same purpose.
		We demonstrate the practical application of origami to the design and construction of a working test-bed computer, using off the shelf components and interconnection technology.
		A small three-function processor is designed which cna be time-multiplexed using {\em computational origami\/} to produce the desired output stream, as well as reset itself to receive additional inputs.
	www.mit.edu /afs/sipb/user/rfrench/texbib/origami.bib (445 words)

	Computational Origami
		My interest in origami is revitalized by many interesting resarch results by mathematicians and and computer scientists around the end of 1980s.
		The talk of Corado Boehm, at IFIP 1.6 WG meeting in Utrecht, 2001, who suggested to implement and analyze his set of origami axioms was the start of my actual involvement of computational rigami.
		We are interested in both aspects of origami, but as a resarch strategy, we separate them and pursue two different goals.
	www.score.is.tsukuba.ac.jp /~ida/Ida2004/OldCompOrigami.htm (207 words)

	IT Conversations: Robert Lang
		The last decade of the twentieth century saw a revolution in the development and application of mathematical techniques to origami.
		Robert J. Lang describes how geometric concepts have led to the computer solution of a broad class of origami folding challenges and, as a consequence, enabled origami designs of astonishing complexity and realism to be developed.
		He is the author or co-author of eight books and numerous articles on origami and is a regular lecturer on the connections between origami, mathematics, science, and technology.
	www.itconversations.com /shows/detail660.html (388 words)

	The Ultimate Mathematics of origami - American History Information Guide and Reference (Site not responding. Last check: 2007-10-15)
		Fields of interest include a given origami model's flat-foldability (whether the model can be flattened without damaging it) and the use of origami folds to solve mathematical equations.
		Origami folds can be constructed to solve square roots and cube roots; fourth-degree polynomial equations can also be solved by origami folds.
		The problem of rigid origami, treating the folds as hinges joining two flat, rigid surfaces such as sheet metal, has great practical importance.
	www.historymania.com /american_history/Computational_origami (215 words)

	Origami master Lang will visit MIT - MIT News Office
		His work combines aspects of the Western school of mathematical origami design with the Eastern emphasis on line and form to yield models that are at once distinctive, elegant and challenging to fold.
		A pioneer of the cross-disciplinary marriage of origami with mathematics, Lang has presented several refereed technical papers on origami-math at mathematical and computer science trade meetings.
		He is currently studying protein folding and hopes that computational origami--the geometry of paper folding--could eventually lead to the design of custom-made proteins to help fight disease.
	web.mit.edu /newsoffice/2004/arts-lang-1110.html (700 words)

	Mathematics of origami biography .ms (Site not responding. Last check: 2007-10-15)
		The art of origami has received a considerable amount of mathematical study.
		Questions regarding an origami model's flat-foldability (whether the model can be flattened without damaging it) are considered.
		The capability of origami to solve mathematical equations is of interest as well.
	www.biography.ms /Computational_origami.html (183 words)

	O'Reilly Network: OSCON 2005: Know When to Fold 'Em (Site not responding. Last check: 2007-10-15)
		If you haven't seen examples of more modern origami and what is possible with a single piece or paper, follow the links to Lang's website for a look at a more realistic-looking frog than you are familiar with.
		Whether origami is being applied to scientific challenges, presented in its classical form, or used to create challenging, authentic representations, we admire and respect the work being presented.
		Both origami and open source software are accomplished with sets of symbols, tools, methods, and parts.
	www.oreillynet.com /pub/a/network/2005/08/08/origami.html (1157 words)

	The Institute For Figuring // Online Exhibit: Mathematical Paper Folding
		Traditional origami models, painstakingly developed by hand, have mostly been simple structures – stylistic sketches of animals and flowers, and pretty decorative boxes.
		This new “technical folding,” also known as origami sekkei, vastly expands the traditional repertoire, enabling construction of immensely complex forms that could not have been achieved by the old methods.
		In line with the practical evolution of ever more intricate forms, these new approaches have also given rise to a new breed of “computational origami” theorists who bring to bear on the blank sheet a raft of formal techniques, analyzing the potentialities inherent in this infinitely fecund form.
	www.theiff.org /oexhibits/paper01.html (241 words)

	Intro (Site not responding. Last check: 2007-10-15)
		When I took the Computational Geometry course, an occasion presented itself to me: Explore origami with a perspective I had never thought of before, mathematics and computer science.
		Origami, because of its more manual approach, does not depend on visual skills as much as Euclid's Edge & Compass constructions on a sheet of paper.
		Origami is the framework that studies good and bad foldings, and understands how to prevent bad ones.
	cgm.cs.mcgill.ca /~athens/cs507/Projects/2002/ChristianLavoie/intro.html (453 words)

	The Geomblog: Computational Origami OR How to eat sugary cereal that's good for you
		Computational geometry draws its parentage both from geometry, and from the theory of computation.
		Robert Lang, credited with being one of the pioneers of the field of computational origami, has a program called TreeMaker that you can use to design origami designs from scratch.
		Alas, the question we asked earlier has an answer, but like most questions in theoretical computer scieince, it is an answer we may not like: Determining whether a given sequence of creases can be achieved by flat folding is NP-hard.
	geomblog.blogspot.com /2004/03/computational-origami-or-how-to-eat.html (357 words)

	abstracts.html
		An origami crease pattern is the analog of the genome.
		Origami models with similar, but not identical, crease patterns and folding sequences can be compared to closely related species with similar, but not identical, genomes and developmental sequences.
		Origami, the art of paper-folding, and other types of hands-on activities increase students' ability to communicate mathematically and increase students' understanding of mathematical concepts (Fuys and Lievov, 1997; Hartshorn and Boren, 1990; Salend and Hofstetter,1996; Wohlhuter, 1998).
	www.merrimack.edu /~thull/osm/abstracts.html (7613 words)

	Ivars Peterson's MathTrek -Folding Maps
		Now, Erik D. Demaine of the computer science department at the University of Waterloo in Ontario and his coworkers have developed an efficient method for recognizing when a creased sheet indeed is foldable into a flat package.
		Mathematicians and others have been studying ways to systematize origami design by developing rules that would enable a computer to calculate what sequence of creases in a square a paper will produce a desired figure.
		Beyond the mathematics of origami, "our study is motivated by applications in sheet metal and paper product manufacturing, where one is interested in determining if a given structure can be manufactured using a specified creasing machine, which is typically restricted to performing simple folds," the researchers note.
	www.maa.org /mathland/mathtrek_1_15_01.html (795 words)

	Origami solves road map riddle
		Unlike a computer model, real paper has thickness - an A4 sheet is nearly impossible to fold in half more than six times.
		Computational origami is attacking other seemingly intractable paper-folding challenges.
		Computational origami also creates new designs for the Japanese art.
	www.innovations-report.com /html/reports/logistics/report-7812.html (297 words)

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