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Robert J. Lang (1988). The Complete Book of Origami: step-by-step instructions in over 1000 diagrams. Mineola, NY: Dover Publications. ISBN 0-486-25837-8; Peter Engel (1989). Origami from Angelfish to Zen. Mineola, NY: Dover Publications. ISBN 0-486-28138-8; Robert J. Lang (2003). Origami Design Secrets: mathematical methods for an ancient art ...
After a few years of this sort of use, designers such as Robert J. Lang, Meguro Toshiyuki, Jun Maekawa and Peter Engel began to design using crease patterns. This allowed them to create with increasing levels of complexity, and the art of origami reached unprecedented levels of realism. Now most higher-level models are accompanied by crease ...
Robert Lang folding an origami American flag, which includes 50 stars and 15 white and 13 red stripes, from a single uncut square. Lang was born in Dayton, Ohio, and grew up in Atlanta, Georgia. [1] Lang studied electrical engineering at the California Institute of Technology, where he met his wife-to-be, Diane. [2]
Koshiro Hatori and Robert J. Lang also found axiom 7. The axioms are as follows: Given two distinct points p 1 and p 2, there is a unique fold that passes through both of them. Given two distinct points p 1 and p 2, there is a unique fold that places p 1 onto p 2. Given two lines l 1 and l 2, there is a fold that places l 1 onto l 2.
Robert J. Lang showed in 1997 [2] that several classical origami constructions give rise to an easy solution. [ 6 ] [ 7 ] In fact, Lang showed that the perimeter can be made as large as desired by making the construction more complicated, while still resulting in a flat folded solution.
It includes the NP-completeness of testing flat foldability, [2] the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat), [2] [4] the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns, [2] [4] the fold-and ...
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Artists like Robert J. Lang, Erik Demaine, Sipho Mabona, Giang Dinh, Paul Jackson, and others, are frequently cited for advancing new applications of the art. The computational facet and the interchanges through social networks, where new techniques and designs are introduced, have raised the profile of origami in the 21st century.
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