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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.
Computational origami is a recent branch of computer science that is concerned with studying algorithms that solve paper-folding problems. The field of computational origami has also grown significantly since its inception in the 1990s with Robert Lang's TreeMaker algorithm to assist in the precise folding of bases. [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.
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 ...
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 ...
The Bug Wars were origami contests among members of the Origami Detectives (Tanteidan in Japanese) which started when one member made a bug, a horned beetle with outspread wings, from a single sheet of paper: this design provoked other members to design more complex origami in the shape of bugs, such as wasps and praying mantises.
Circle packing has become an essential tool in origami design, as each appendage on an origami figure requires a circle of paper. [12] Robert J. Lang has used the mathematics of circle packing to develop computer programs that aid in the design of complex origami figures.