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Origami Paper Folding Geometry:     more detail

Mathematical Origami: Geometrical Shapes by Paper Folding by David Mitchell, 1997-07 Fun with figures, by Mae Blacker Freeman, 1946 Origamics: Mathematical Explorations Through Paper Folding by Kazuo Haga, Josefina C. Fonacier, et all 2008-09-11 Amazing Origami by Kunihiko Kasahara, 2002-03-28 Ornamental Origami: Exploring 3D Geometric Designs by Meenakshi Mukerji, 2008-12-01 Marvelous Modular Origami by Meenakshi Mukerji, 2007-04-24 Explore Folding of the Circle: Series Book 3 (Explore Folding of the Circle, Book 3) by Bradford Hansen-Smith, 2007 Geometric Origami by Robert Geretschlager, 2008-10-14

lists with details

21. Paper Folding - Models
    of five popout, glue, and fold-up polyhedra Patty paper geometry Student Workbook $3.95 This companion student origami paper $4.95 24 7 x 7 sheets of origami  
    http://www.mathartfun.com/shopsite_sc/store/html/OrigamiManips.html
    
    Extractions: Captured Worlds is a set of five pop-out, glue, and fold-up polyhedra. The five used in Captured Worlds are known as the Platonic Solids. They are decorated with fanciful scenes rendered in six-point perspective by internationally-known artist Dick Termes. This unique perspective system allows an entire three-dimensional surrounding to be projected onto the polyhedra. By Michael Serra. Patty Paper - the stuff that separates hamburger patties - can also be used for geometric investigations! These square of paper can be written on, they hold creases well, and they are semi-transparent like tracing paper. "Patty Paper Geometry" contains dozens of activities that motivate kids to read, write, and talk about geometry. This book is a blackline master book with 12 chapters of guided and open investigations. Grades 6-10. 272 pages, paperback.

22. Wauu.DE: Arts: Crafts: Origami: Geometry And Modulars
    index_en_sum.htm. origami Mathematics Mathematics of paper folding; includes a bibliography of articles and journals, Combinatorial geometry syllabus, and a  
    http://www.wauu.de/Arts/Crafts/Origami/Geometry_and_Modulars/

23. Wauu.DE: Arts: Crafts: Origami: Page 2
    geometry and Modulars (10). Money folding (4). origamic Architecture (16). paper Airplanes (27). Links URL hinzufügen. origami Gallery by Sebastian Kirsch  
    http://www.wauu.de/Arts/Crafts/Origami/more2.htm

24. Web Codes
    Read about the history of origami and view some origami designs. Learn how paper folding is related to geometry and read some folding tips.  
    http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefi

25. Focus On Learning Problems In Mathematics: A Survey Of Paper Cutting, Folding An
    origami or the art of paper folding receives Mathematics recommends that students use paper folding to perform symmetry and congruence in geometry (NCTM, 2000  
    http://articles.findarticles.com/p/articles/mi_m0NVC/is_1_25/ai_105477685
    
    Extractions: Origami or the art of paper folding receives substantial endorsement from current reform initiatives in mathematics education. Particularly, at the elementary school level, the National Council of Teachers of Mathematics in its Principles and Standards for School Mathematics recommends that students use paper folding to perform their initial investigations of symmetry and congruence in geometry (NCTM, 2000). Since prospective elementary school teachers need a solid foundation in the mathematical basis of these reform initiatives, textbooks for these future teachers should contain paper-folding applications. Although origami spans academic disciplines, paper folding has increasingly been applied to mathematical systems and structures (Hull, 1996; Auckly and Cleveland, 1995). Moreover, origami is a unique mathematical activity because one can take a sheet of paper and transform it into a three-dimensional object. This concrete experience in spatial reasoning can then be transformed into a lesson on symmetry or graph theory (Peterson, 1995). Educators have also applied paper folding to such diverse mathematical objects as logical structures (Cipra, 1998), axiomatic systems (Alperin, 2000), and tessellations with geometrical figures (Stewart, 1999).

26. Focus On Learning Problems In Mathematics: A Survey Of Paper Cutting, Folding An
    geometry, geometric constructions, and symmetry as opportunities for folding paper. Notable among the topics that received less attention in origami were  
    http://articles.findarticles.com/p/articles/mi_m0NVC/is_1_25/ai_105477685/pg_3
    
    Extractions: Three of the texts surveyed contained 20 or more paper-cutting opportunities. These texts were Long (24), Muster (24), and Masingila, (20). However, two texts (Bennett(a) and Billstein) also each contained 18 instances of paper cutting. Thus, the remaining five textbooks (Bassarear, Bennett(b), Miller, Q'Daffer, and Wheeler) contained about 12% of the total number of paper-cutting opportunities. Table XII illustrates this information for the five textbooks that contained the most paper-cutting/-tearing opportunities. Paper-tearing opportunities, of which there were 10 in the ten texts, accounted for the fewest number of classifications in the survey. Notably, the Bilistein textbook contained four of these ten opportunities. Four of the texts (Bennett(a), Masingila, Musser, and Wheeler) contained no instances of paper tearing.

27. Lukol Directory - Arts Crafts Origami Geometry And Modulars
    origami Mathematics Mathematics of paper folding; includes a bibliography of articles and journals, Combinatorial geometry syllabus, and a tutorial on  
    http://www.lukol.com/Top/Arts/Crafts/Origami/Geometry_and_Modulars/

28. American International School In Zagreb, Croatia General
    Information on the mathematics of paperfolding, including the geometry and origami axioms formulated by Italian-Japanese mathematician Humiaki Huzita.  
    http://www.asz.tel.hr/asz/libword.htm

29. Polyhedra And Paper Folding
    Hanson, Robert M.; Molecular origami Precision Scale Models Johnson, Donovan, paper folding for the Mathematics Class Space the art and geometry of polygons  
    http://www.stolaf.edu/people/cederj/Courses.dir/Geo.dir/bib-356/node4.html
    
    Extractions: Next: Transformation Geometry Up: Index of Topics Previous: Impossible Geometric Constructions Ball, Walter, Mathematical Recreations and Essays Baer, Steve, Zome Primer: elements of zonohedra geometry: two and three dimensional growths of stars with five fold symmetry QA491.B28 (oversize) Faulkner, J. Earl, ``Paper Folding as a Technique in Visualizing a Certain Class of Transformations,'' Mathematics Teacher 68, May `75, 376-77. Geretschlager, Robert, ``Euclidean Constructions and the Geometry of Origami,'' Mathematics Magazine , Dec '95 Hanson, Robert M.; Molecular Origami: Precision Scale Models from Paper, University Science Books, Sausalito, CA 1995. Hilton and Pederson, Approximating Any Regular Polygon by Folding Paper , Mathematics Magazine, May '83 Johnson, Donovan, Paper Folding for the Mathematics Class Miyazaki, Klji, An Adventure in Multidimensional Space: the art and geometry of polygons, polyhedra, and polytopes Olson, Alton, Mathematics Through Paper Folding , NCTM 1975.

30. Papiroflexia (origami)
    Tammy Yee s origami Page easy paper folding crafts for . Valerie Vann s Modular origami Page, The geometry Junkyard- origami.  
    http://origami.iespana.es/origami/links.html
    
    Extractions: Página oficial de la Asociacion Española de Papiroflexia R,M Página Oficial del Grupo Zaragozano de Papiroflexia R,M Netpark Origami Page (Spanish) R,M Asociación Vallecaucana de Origamistas R,M http://www.pobladores.com/territorios/aficiones/La_papiroflexia_mas_de_cerca Aviones de papel Marivi's Origamic Architecture Origami/Papiroflexia de Manuel Reina ... Origami - Entretenimientos - Contenidos.com En inglés http://members.aol.com/ukpetd/ Money Origami Joseph Wu's Origami Page Doug Philips' Origami Page ... Travel to Oriland Otros: Origami Origami Paper OPP AB Origami, le monde du pliage Origami-Montréal ... origami esperanto accueil

31. Origami Links From Debbie's Educational Link Page
    geometry Design origami folding Patterns **The Garden of origami GateSuper site Ori (to fold) + kami (paper) = origami, the art of paperfolding.  
    http://www.venus.net/~dschweit/edsites/origami/origami2.htm

32. Origami Links
    Maintainer Jorge Lucero Highlights mathematical aspects of origami. book paper folding which explains how to use paper folding to teach geometry in the  
    http://www.origami.as/link.php?category_id=002001&action=show_list&order_by=owne

33. Origami (reflection)
    To learn more about Buckminster Fuller s geometry, check out the Design Science Consortium, which was Since origami is the art of paper folding, I created  
    http://www.scottkim.com/inversions/gallery/origami.html
    
    Extractions: S TORY. In April 1988 I attended the 25th anniversary reunion of the Design Science program at Harvard University's Carpenter Center for the Visual Arts . Although I hadn't actually attended the program, let alone Harvard, I felt such kinship with this merry band of artist-mathematicians that I showed up anyway. The program, founded by Harvard professor Arthur Loeb, is a uniquely interdisciplinary of 3d polyhedral geometry and sculpture. Equal parts art, mathematics and engineering, the program has produced one of the most interesting collection of alumnae I've ever seen. Talks at the event included: Peggy Weil talking about her vision of the Weatherium: a multi-story inverted polyhedral globe that you view from a platform floating on the inside, with a live projected image of earth's surface as seen from weather satellites. Amy Edmundson, who wrote a most illuminating book about Buckminster Fuller's geometry called A Fuller Explanation, giving a hands-on workshop on building structures out of toothpicks and marshmallows. You quickly learn that in order to build anything stable you have to use triangulated structures like tetrahedra.

34. Articles: Folding, By Bryan Clair
    hasn t stopped hundreds of amateur geometry buffs from The myriad shapes an origami artist can create are a testament to the complexity of paper folding.  
    http://www.strangehorizons.com/2002/20020311/folding.shtml
    
    Extractions: S o, you like web magazines? You believe paper will become obsolete, resulting in acres of beautiful forest? Well, forget it. Go get a ream, and let's waste it with idle mathematical diversions. It's time to learn the ins and outs of paper folding. People have been folding paper for centuries. Not long after paper was invented in China, the Chinese were folding it. In Japan it became the art of origami, first practiced only by the elite, and then by the masses as paper became cheap and abundant. The patterns used to fold square sheets into representational figures propagated as oral traditions for centuries, though only a few simple designs survived to the earliest printed works. The best known origami design is the crane, and in fact the oldest surviving book on origami is the Hiden Senbazuru Orikata (How to Fold One Thousand Cranes). The book begins with basic instructions for folding the origami crane. With beautiful calligraphy and illustrations, it then shows dozens of ways to fold many cranes from one sheet of paper. In these multi-crane folds, the sheet is cut into small squares which remain joined by thin strips at the corners. Then the dexterous artist folds the individual cranes without tearing the strips.

35. The World's First Origami Folding Robot
    origami, the geometry of paper folding, looks simple when you re a kid. But it s actually quite challenging to design a robot to do it.  
    http://radio.weblogs.com/0105910/2004/05/14.html
    
    Extractions: vendredi 14 mai 2004 Devin Balkcom, a Carnegie Mellon graduate student in robotics, has built the world's first origami-folding robot as the subject of his thesis. Origami, the geometry of paper folding, looks simple when you're a kid. But it's actually quite challenging to design a robot to do it. Movements are quite complex, and paper, because it is flexible, is difficult to be manipulated by a robot. This news release says that the project uses kinematics, the study of mechanisms, to determine how folding is done and how paper can be treated as a flexible and rigid material. Here is what says the student about origami. "It's something we humans can do well, but we don't understand the mechanical details," said Balkcom. "Because a five-year-old child can learn to fold origami, we assume that it is a simple process, but the movements it requires are quite complex." Here is how he designed his robot. Balkcom built his origami robot with an industrial mechanical arm produced by Adept Technology , of Livermore, Calif. The robot uses a tiny suction cup attached to the arm to pick the paper up, rotate it and place it over a narrow gutter in the worktable. Then a ruler descends and presses the paper into the gutter to create a crease. This method is much less precise than a human and brings to light some interesting insights and questions about mechanisms.

36. InterMath | Investigations | Geometry
    Arnstein, Bennett, 3D Geometric origami Modular Polyhedra in Education and Therapy, origami USA, June 23 Alton T. Mathematics Through paper folding. Reston VA  
    http://www.intermath-uga.gatech.edu/topics/geometry/3dobjts/links.htm

37. ÁʶRºP¯Èª««~
    paper folding, paper folding which explains how to use paper folding to teach geometry in the classroom. origami Kaikan, ? .  
    http://origami.uhome.net/new_page_11.htm
    
    Extractions: FAX 03-5684-6080 A wide range of private publications, including booklets, BOS convention packs and a limited range of paper Japanese Paper and Origami Supplies(Australia) Retailers of origami papers and books and washi System GET'S Co., Ltd. Sasuga Japanese Bookstore Origami Videos, Books, Handmade Papers tel¡@048-654-1910¡@fax¡@048-654-1361 ¸Û¤å°ó·s¥úªÀ SEIBUNDO SHINKOSHA Publishers: Origami Books Fascinatings Folds Origamido §é¯È¹D Origami Videos, Books, Handmade Papers ¤p¬z©M¯È³Õª«À]OZU Washi Japanese paper shop Powell's Books A great place for used/out of print books. ¤é¥»¼Ö¤Ñºô¤W®Ñ©± Japanese Origami books Book Ends Many unusual and hard to find titles with possibly the widest range of origami books available in the UK.

38. CheatHouse.com - Origami And Geometric Constructions.
    look closely In high school geometry students examine way to do this with paper folding This list of the First International Conference on origami in Education  
    http://www.cheathouse.com/eview/15710-origami-and-geometric-constructions.html

39. MSN Encarta - Origami
    paper folding as a means of studying geometry. The Spanish tradition of folding paper became known as The widespread popularity of modern origami grew mainly  
    http://encarta.msn.com/encyclopedia_1741500677/Origami.html
    
    Extractions: MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Tasks Find in this article Print Preview Send us feedback Related Items Japan Paper more... Magazines Search the Encarta Magazine Center for magazine and news articles about this topic Further Reading Origami News Search MSNBC for news about Origami Internet Search Search Encarta about Origami Search MSN for Web sites about Origami Also on Encarta Encarta guide: The Reagan legacy Compare top online degrees Proud papas: Famous dads with famous kids Also on MSN Father's Day present ideas on MSN Shopping Breaking news on MSNBC Switch to MSN in 3 easy steps Our Partners Capella University: Online degrees LearnitToday: Computer courses CollegeBound Network: ReadySetGo Kaplan Test Prep and Admissions Encyclopedia Article from Encarta Advertisement Origami Multimedia 1 item Origami , art of folding paper to create three-dimensional figures of animals, people, objects, and abstract shapes. Origami is a Japanese word that combines the verb oru (to fold) and the noun kami (paper). The only material required for origami is a piece of paper. Almost any paper may be used, but folding is easiest if the paper is thin, strong, and able to hold a crease. Standard origami paper is usually cut into 15-cm (6-in) squares; it is generally plain white on one side, with a color or decorative pattern on the other. Some origami artists experiment with other materials, including cardboard, cloth, wire mesh, sheet metal, and even pasta.

40. Math On The Street: Where's The Math?
    Do any interesting mathematical questions arise from the process of folding paper? Can origami help someone learn arithmetic, algebra, geometry, and other  
    http://math.serenevy.net/?page=Origami-WhereMath&layout=framed

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