Geometric Folding Algorithms
{{Short description|2007 mathematics book by Demaine and O'Rourke}}
{{italic title}}
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press ({{ISBN|978-0-521-85757-4}}).{{r|maa|ejor|ems|acm}}
A Japanese-language translation by Ryuhei Uehara was published in 2009 by the Modern Science Company ({{ISBN|978-4-7649-0377-7}}).{{r|trans}}
Audience
Although aimed at computer science and mathematics students,{{r|ems|acm}} much of the book is accessible to a broader audience of mathematically-sophisticated readers with some background in high-school level geometry.{{r|ejor|acm}}
Mathematical origami expert Tom Hull has called it "a must-read for anyone interested in the field of computational origami".{{r|hull}}
It is a monograph rather than a textbook, and in particular does not include sets of exercises.{{r|acm}}
The Basic Library List Committee of the Mathematical Association of America has recommended this book for inclusion in undergraduate mathematics libraries.{{r|maa}}
Topics and organization
The book is organized into three sections, on linkages, origami, and polyhedra.{{r|maa|ejor}}
Topics in the section on linkages include
the Peaucellier–Lipkin linkage for converting rotary motion into linear motion,{{r|acm}}
Kempe's universality theorem that any algebraic curve can be traced out by a linkage,{{r|maa|acm}}
the existence of linkages for angle trisection,{{r|maa}}
and the carpenter's rule problem on straightening two-dimensional polygonal chains.{{r|acm}}
This part of the book also includes applications to motion planning for robotic arms, and to protein folding.{{r|maa|ejor}}
The second section of the book concerns the mathematics of paper folding, and mathematical origami. It includes the NP-completeness of testing flat foldability,{{r|ejor}}
the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat),{{r|ejor|acm}}
the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns,{{r|ejor|acm}}
the fold-and-cut theorem according to which any polygon can be constructed by folding a piece of paper and then making a single straight cut,{{r|ejor|acm}}
origami-based angle trisection,{{r|acm}}
rigid origami,{{r|ejor}}
and the work of David A. Huffman on curved folds.{{r|acm}}
In the third section, on polyhedra, the topics include polyhedral nets and Dürer's conjecture on their existence for convex polyhedra, the sets of polyhedra that have a given polygon as their net, Steinitz's theorem characterizing the graphs of polyhedra, Cauchy's theorem that every polyhedron, considered as a linkage of flat polygons, is rigid, and Alexandrov's uniqueness theorem stating that the three-dimensional shape of a convex polyhedron is uniquely determined by the metric space of geodesics on its surface.{{r|acm}}
The book concludes with a more speculative chapter on higher-dimensional generalizations of the problems it discusses.{{r|acm}}
References
{{reflist|refs=
| last = Carbno | first = Collin
| date = May 2009
| journal = MAA Reviews
| publisher = Mathematical Association of America
| title = Review of Geometric Folding Algorithms
| url = https://www.maa.org/press/maa-reviews/geometric-folding-algorithms-linkages-origami-polyhedra}}
| last = Paquete | first = Luís
| date = November 2009
| doi = 10.1016/j.ejor.2008.06.009
| issue = 1
| journal = European Journal of Operational Research
| pages = 311–313
| title = Review of Geometric Folding Algorithms
| volume = 199}}
| last = mbec
| journal = EMS Reviews
| publisher = European Mathematical Society
| title = Review of Geometric Folding Algorithms
| url = https://euro-math-soc.eu/review/geometric-folding-algorithms-linkages-origami-polyhedra
| year = 2011}}
| last1 = Fasy | first1 = Brittany Terese
| last2 = Millman | first2 = David L.
| date = March 2011
| doi = 10.1145/1959045.1959056
| issue = 1
| journal = SIGACT News
| pages = 43–46
| publisher = Association for Computing Machinery
| title = Review of Geometric Folding Algorithms
| volume = 42| s2cid = 6514501
}}
}}
External links
- [http://www.gfalop.org/ Authors' web site for Geometric Folding Algorithms] including contents, errata, and advances on open problems
{{Authority control}}
Category:Linkages (mechanical)
Category:Computational geometry
Category:2007 non-fiction books
Category:2009 non-fiction books
{{Mathematics of paper folding}}