61. Mathematical Origami: Geometrical Shapes By Paper Folding There are many books on geometric and modular origami, but Or try to look for Mathematical origami Geometrical Shapes by paper folding at Fetch Used http://mathematicsbooks.org/189961818X.html

Home Search High Volume Orders Links ... Philosophy of Mathematics Additional Subjects Caves of God: The Monastic Environment of Byzantine Cappadocia Godel's Proof Essential Lightwave 3d 7.5 The Art of Being You ... Origami Flowers Mathematical Origami: Geometrical Shapes by Paper Folding Written by David Mitchell Published by Tarquin Pubns (July 1997) ISBN 189961818X Price $17.00 Buy from amazon.co.uk Customer Reviews Although not as fascinating as his PAPER CRYSTALS (a stellar work of modular origami), MATHEMATICAL ORIGAMI is a very solid work on the topic. David Mitchell again gives clear instructions in text and diagrams for a very intriguing branch of paperfolding. There are many books on geometric and modular origami, but Mitchell's are more than just "look at this neat design." Instead, they are well thought out and very intelligently written. A must-have for fans of the art. My office generates lots of notices printed on brightly colored paper (usually printed on only one side). This is a great use for scrap paper. I think it is somewhat challenging (highschool level). I completed all but one. (the Decorative Rhombic Dodecahedron). Americans should note that A4 paper is not the American satandard 8.5" X 11" but it doesn't make any difference for most of the structures. When you get to the Skeletal Cube shave the 8.5 inch dimension to 7.78 inches. A concise and well-written book, with clear diagrams and straightforward instructions, suitable for any beginner in the field. Includes the most well-known mathematical representationof modular origami. Advanced users might prefer a higher-levelbook. Includes a list of references for further reading that might be helpful.

62. Paper Crafts Origami And the folding steps are full of wonder book display what s possible with good paper and some I recommend this book for an intermediate origamifolder because http://mathematicsbooks.org/Paper_Crafts_Origami.html

Home Search High Volume Orders Links ... Philosophy of Mathematics Additional Subjects Caves of God: The Monastic Environment of Byzantine Cappadocia Godel's Proof Essential Lightwave 3d 7.5 The Art of Being You ... Origami Flowers Featured Books Ultimate Origami Kit: The Complete Step-by-Step Guide to the Art of Paper Folding The tittle says "ultimate" but the contents are far from it. There's a modest selection of traditional models and several weak original models. The diagrams are clear and easy to follow. This book is geared to the beginner but is so limited in it's scope and quality of artistic expression that it does nothing to kindle an interest in origami. Try Easy Origami by Montrol for similar models, or better yet get The Joy of Origami or The World of Origami. Written by John Morin Jack Crane Published by Running Press (October 2000) ISBN 0762409142 Price $19.98 African Animals in Origami For all you John Montroll fans out there, buy this book. For everyone else, buy this book also! It is one of the best books for animals, with a wide variety of difficulty levels. From simple 'grass' to complex striped zebras, this book has it all. I enjoyed making some of the more unique models, like the bee-eater and rhinoceros. Another nice thing about this book in particular is that the models are much different than what are in many other books. Because the theme is Africa, a lot of the a... Written by John Montroll Published by Dover Pubns (December 1991)

63. Lukol Directory - Arts Crafts Origami of various completed models animals, masks, geometric shapes, oversized Boxes Gift boxes hand made by folding paper or fabric using origami techniques. http://www.lukol.com/Top/Arts/Crafts/Origami/

Lukol Directory - Arts Crafts Origami ... World Peace Project for Children The world's largest crane, diagram for the traditional crane, and other information relating to the story of Sadako and the Thousand Paper Cranes. http://www.sadako.org/ Anne's Origami Information on MIT's origami mailing list, with archives. Also a list of books she owns, some with pictures, table of contents and reviews. http://web.mit.edu/lavin/www/origami.html Fabric Origami Workshop Introduction, techniques, diagrams, and pictures of fabric origami. Includes book reviews and links as well as FAQs and related news on the topic. http://www.fabricorigami.com/ Jasper's Origami Menagerie A collection of diagrams and photos with a section dedicated to various types of animals. Includes a picture link index to diagrammed models on other websites. http://www.folds.net/ Online Origami Archive of the now defunct e-zine. Origami story, diagram, and links and information on organizations. http://members.aol.com/stamm/index.html Marc Kirschenbaum's Origami Original model diagrams in PDF format. Contains articles and resources and related links. http://marckrsh.home.pipeline.com/

64. Joseph Wu Origami architects, and mathematicians explore the geometry of origami Therapists and teachers use origami as a tool to Many people fold paper simply because it is fun http://www.origami.as/Info/intro.php

home articles What is origami? Origami , the Japanese name for the art of paper folding, comes from the Japanese verb oru (to fold) and the noun kami (paper). The word "origami" is now commonly used around the world. A finished origami figure is called a model , the method for folding a model is called a design , and drawn instructions for a model is called a set of diagrams . An origami artist is usually called a paperfolder The only requirement for origami is a piece of paper, making it one of the most accessible arts. Almost any paper may be used, but standard "origami paper" is thin, strong, and holds a crease very well. It is also usually white on one side and colored on the other side, and is cut into 15 cm squares (about 6 inches). Some origami artists also experiment with other materials, and have folded models out of cardboard, various types of cloth, wire mesh, sheet metal, and even sheets of pasta. The basic technique of origami is folding, and many complex folds have been developed. The simplest fold is the valley fold , where a flat piece of paper is folded towards the paperfolder. When this fold is unfolded, the crease line forms a valley shape. Closely related is the

65. Classic Cranes History To the mathematician, the beauty of origami is its simple geometry. Is there no wasted paper, awkward thickness, or arbitrary fold? http://www.origami-tsuru.com/crane7.htm

Introduction FOLDING: A COMPACT HISTORY From the book " Origami from Angelfish to Zen" by Peter Engel Paperfolding originated in China around the first or second century A.D. and reached Japan by the sixth century. The Japanese called this new art form origami (the name coined from ori, "to fold," and gami, "paper") and cultivated it as an art of understatement. Origami suggests; it implies without announcing outright, intimates with out brashness. It exists best in a kind of light the Japanese call ke, a soft, gentle light for intimate occasions. Why use a bright light when you can see in a dim one? Why shout when you can whisper? For that matter, why draw the entire bamboo tree when a few brush strokes suffice? Just as a three-line haiku evokes a setting or a season, the placement of a rock and a pond in a Japanese garden recalls the universe. It is a short imaginative leap from the rock to a mountain, from the pond to the sea. Origami is an art of economy. A few simple creases evoke an animal; modify the sequence slightly, and an entirely new beast appears. To the Japanese sensibility, the success of a completed origami figure depends on the creator's eye for form, structure, and proportion. Does it capture the creature's true form, the placement of its head and limbs, the shape of its shoulders and hips? Does it suggest the animal's motion, its stride, glide, or gallop? And finally, is the paper figure a mere likeness of the original, or does it delve deeper, into its essential character?

66. History The Moors used paper folding to create geometric figures. The first written set of origami appeared in 1797 AD with the publication of a How to Fold 1000 http://marian.creighton.edu/~marian-w/academics/english/japan/origami/History.ht

The History of Origami Paper making originated in China by Ts'ai Lun, a servant of the Chinese emperor. The art of paper folding began shortly after. The Chinese culture developed many simple forms, which many still are practiced today. The secret of paper was brought to Japan in the sixth century by Buddhists monks, it was quickly developed into their culture. Paper folding was used in every day life and also in the Shinto religion. Not only was paper folding developed in Japan, but the Moors, who were from Africa, brought it with them to Spain. The Moors used paper folding to create geometric figures. From Spain it spread to South America, then introduced to Europe and then to the United States. The art of Japanese paperfolding was passed from generation to generation, since nothing was ever written down. The first written set of origami appeared in 1797 AD with the publication of a How to Fold 1000 Cranes (Hiden Senbazuru Orikata). The crane was considered a sacred bird of Japan. It was said that if you fold 1000 cranes, one wish would be granted. The origami crane has become a global peace symbol. The word "origami" at first was not considered paperfolding, from which many think, but in actuality it meant paper certificates. "Origami Tsuki" means certified or gauranteed. In Japan, they would make and fold certificates for Tea Ceremony masters, or masters of swordsmanships, in order for them not to be duplicated. The paper folding word origami came about in 1880 from the old word oru (to fold) and kami (paper). Previously paper folding was called orikata, orisué, orimono and tatamgami.

67. Origami - Another Path/ Deafhomeschool.com one of the simplest of geometric shapes, and it ends introduction to Japanese art of paper folding has everything you need to practice origami an instructional http://www.deafhomeschool.com/study/crafts/origami.html

©2000-2004 Barbara L.M. Handley Another Path http://www.deafhomeschool.com What's New? Search Site Map Contact Origami Home Crafts Paper Airplanes Tools and resources for making paper airplanes. Paper Engineering An introduction to the art and science of building things with paper. Pop-Ups Learn to make your own pop-up books and cards. Sliceforms Links and resources for exploring these collapsible geometric paper models. Why origami? Origami is an essential tool in the exploration of mathematics and science. Origami demonstrates, in a very concrete way, the fact that simple shapes develop into complex patterns. You will see this over and over again in nature. Origami lets you bring it to your kitchen table. It begins with a square, one of the simplest of geometric shapes, and it ends...well, it doesn't. You can make anything with origami. Origami forms differ in complexity...young children can make the simplest forms. Complex constructions may require many years of practice and skill. We've only just begun our own explorations of origami, so I offer just a few resources for getting started. If you see a general ad for Amazon, please refresh this page and the proper book information, including price, should appear.

68. MATHEMATICS TOPCS What beautiful Geometric Facts! (ILOILO NEWS). How to find the center of a circle spinning top (ADDU). Space figures (Math 14). origami (paper folding activity2 http://www.addu.edu.ph/college/rstc/handouts/handouts_math.html

Reference for Mathematics lesson Sorry! We have not completed this page yet. As of now, only some of handouts are available. We are going to update this page step by step. Cognitive Reasoning and Problem Solving (Math 1) Whole Numbers (Math 1) 1=2? (ILOILO NEWS) Fractions and Decimals (Math 1) How to Find the Fractional Equivalent of a Repeating Decimal using Algebraic Method (ILOILO NEWS) How to classify a rational number and an irrational number? (ADDU) Integers and Rational Numbers (Math 1) Introduction to Algebra (Math 1) Why we use a variable in mathematics? (ADDU) Get used to a Calculator Chapter 2 (ILOILO NEWS) How old are they? (ILOILO NEWS) How you get the water (ILOILO NEWS) Mathematical Sentences and Expressions (Math 1,2) Ratio, Proportion, Percent and Variation (Math 1,3) Linear Equations and Inequalities (Math 2) How to change a repeating decimal into a fraction. (ADDU) Expornents (Math 3) Enjoy some puzzles (ILOILO NEWS) Enjoy some puzzle again? (ILOILO NEWS) Can you imagine the number? (ILOILO NEWS) Why is 10 ; equal to 1? (ILOILO NEWS) Radicals (Math 3) How to get square root? (ILOILO NEWS)

69. Origami Books Rojas, Hector origami Animals. Rosado, Raul HandsOn origami. Row, T. Sundara Geometric Exercises in paper folding. Sakata, Hideaki origami (Great Beginner book http://hem.passagen.se/dion/html/boklista.htm

Origami Books Origami Books by Title Origami Books by Author ORIGAMI BOOKS BY TITLE 3D Geometric Origami , by Rona Gurkewitz and Bennett Arnstein African Animals in Origami , J.Montroll Amazing Paper Planes , E.Hui Angelfish to Zen , Peter Engel Animal Origami for the Enthusiast , John Montroll The Art of Folding Money - Book 1 , B.Caruba The Art of Folding Money - Book 2 , B.Caruba Beautiful Origami , Z. Ayture-Scheele Best Jumbo Paper Aircraft , C.Morris Birds in Origami , John Montroll Book of Origami , An Usborne Book Brilliant Origami , David Brill The Buck Book , Anne Akers Johnson Classic Origami , P.D. Tuyen The Complete Book of Origami , Robert Lang Complete Origami , Eric Kenneway (Over 100 Projects!) Creating Origami , J.C.Nolan. Creative Origami , K.Kasahara Dinosaur Origami , Fumiaki Kawahata Don't Need Mommy for this Origami , V'Ann Cornelius Easy Origami , G.M.Gross and T. Weintraub The Encyclopedia of Origami and Papercraft Techniques , P.Jackson

70. ARTTalk - FREE Copy - Vol. 11, No. 11 - Paper Craft in the eighth century, they brought with them the practice of paper folding. This geometric style, the Moorish traditional school of origami, still exists in http://www.arttalk.com/artv1111-3.htm

.com ...the link between you, the visual artist, and the manufacturer of art materials. Established 1990 SIGN UP - FREE ARTtalk e-Newsletter Search all of ARTtalk!! Paper Craft OrigamiBeauty in Simplicity Although most people credit the Japanese with the origins of origami, paper folding actually originated in China around the first century. Sometime during the sixth century it arrived in Japan and was immediately embraced by the aristocracy. The Japanese named it "ori," meaning "to fold," and "gami," meaning "paper." Because paper had great value and was rare, its use was limited to the rich. But when the Japanese perfected inexpensive ways to produce paper, origami assumed a new role in the social structure of the country. Everyone could enjoy the simplicity, economy and "Zen" of folding. From the 1600's to the late 1800's there was a flourishing of Japanese arts and culture, and it was during this time that origami attained its most glorious stature. For generations, all patterns and directions for folding were handed down from one generation to the next. Historical documentation occurred when two texts, one written in 1797 ( How To Fold 1000 Cranes ) and one in 1845 ( Window on Midwinter ) documented the early Japanese "bases" or designs.

71. Folding Flat Silhouettes And Wrapping Polyhedral Packages New from a Cited by More Recognizing Simply Foldable origami Esther Arkin Michael (Correct) A Motion Planning Approach to folding From paper Craft to.. http://citeseer.ist.psu.edu/demaine99folding.html

72. The Evolution Of Origami origami emerging as an Art form, attempts to enrich by wet folding, careful selection of paper, and modules. Geometric folding attracts a considerable following http://www.users.waitrose.com/~pureland/the_evolution_of_origami.htm

The Evolution of Origami I divide up the evolution of Origami into four categories. Classical Neo classical Modern Hyper-Modern. Classical (In the sense of long established or traditional as defined by Chambers Dictionary) The characteristics of what I have called classical Origami are that it uses symmetry both in the paper and in the actual folding. Thus Square or hexagonal paper is used and the bases all have a deep symmetry. We do not know of any creators of the models which seem to be handed down within families as an ephemeral folk craft. There seems little or no innovation thus the balloon, or waterbomb, has been known in the West for some four hundred years. The models result from folding which employs landmarks derived from previous folds or the boundaries of the paper. The models are in the main toys or tricks usually 3 D , but in the case of Japan they also had decorative or symbolic folding. In Japan in an attempt to enhance the richness of the medium cutting was employed. This does not seem to be the case in the West. I have excluded Noshi and folds associated with Shinto as these do not seem to me to be in the mainstream of origami development. Neo Classical In the 1940's we see the emergence of creative folders notably Yoshizawa and Uchiyama. They still, however, used the classical bases and employed symmetry in the folding. In an attempt to increase the resources offered by folding, Yoshizawa used two piece models. We also saw the introduction of the blintzed bird base which added to the number of points available for models. In the neo- classical Origami thus we still see symmetry in both the paper and the folding of the Classical era, but there is a new concentration on the final outcome and Origami begins to emerge as a potential art form. Towards the end of the new classical period we see the publication of individual folders creations, notably Yoshizawa's in Japanese women's magazines. This was a vital step in the evolution of modern paper folding since Yoshizawa introduced his symbols at this time which have since become an international standard. Thus communication of folding innovation was enormously enhanced.

73. Wet Folding far in excess of any other method; wetfolded origami can safely the sizing and colouring within the paper is chemically neutral, the fold will also http://www.origami.vancouver.bc.ca/BOS/wetfold.html

74. Devin Balkcom Robotic origami folding. Joseph O Rourke s papers on computational origami. The WAFR paper (below, 3) presented some of our early work, and also describes an http://www.cs.cmu.edu/~devin/

Devin Balkcom I'm a Ph. D. student at the Carnegie Mellon Robotics Institute and the assistant coach for the CMU swim team . I expect to graduate in August, 2004, and have accepted a faculty position with the Dartmouth Department of Computer Science . My e-mail address is devin [at] ri.cmu.edu. Research I'm interested in fundamental models of robot, animal, and human locomotion and manipulation. How should models of the environment inform robot action? Contents of this page include my research on: Robotic origami folding Rigid-body dynamics Time-optimal mobile robots Mobile manipulation on the desktop I'm a member of the manipulation lab , and my research advisor is Matthew T. Mason . My research work has been primarily in three areas: robotic locomotion, the dynamics of frictional contact, and the kinematics of folding manipulation. My first work, with Matthew T. Mason, was the discovery of the fastest trajectories for vehicles with two driving wheels ( e.g. wheelchairs) the analytical time-optimal trajectories are only known for two other classes of mobile vehicles. My thesis work explores the problem of how to fold collapsible structures, using techniques inspired by human origami folders. Robotic origami folding The robot seems to be better-looking and more popular than I am.

75. Paper Folding Project Page 1 Of 4 Pages A paper folding Project. Paul Haeberli. Oct 1994. 1. To create this folded paper sculpture, start out with a piece of paper about 8.5 by 11.0 inches in size. 2. Fold the sheet in two and crease the http://www.sgi.com/grafica/fold/page001.html

A Paper Folding Project Paul Haeberli Oct 1994 1. To create this folded paper sculpture, start out with a piece of paper about 8.5 by 11.0 inches in size. 2. Fold the sheet in two and crease the edge. 3. Fold the sheet in two again in the same direction and crease the edge. Then fold it one more time and crease the edge really well. 4. Unfold the paper, then refold it so it looks like this zig-zag shape. You're about one third done already!

76. WannaLearn: Origami linked circles, more mountains, paper plane, pureland origami items, covering basic origami folds, aeroplanes and the mathematics of origami, including various http://www.wannalearn.com/Crafts_and_Hobbies/Origami/

More search options Crafts and Hobbies : Origami Home Crafts and Hobbies / Origami ] Free Instructional Sites: British Origami Society (Rating: 6.09 Votes: 269) Rate this site: Read Comments (4) How to Make an Origami Crane - a detailed, step-by-step illustrated guide to folding an origami crane, requiring only a square sheet of paper (Rating: 6.47 Votes: 66) Rate this site: Read Comments (5) Instructions for some Origami models - step-by-step instructional diagrams from a variety of authors on simple origami projects, including instructions on how to fold an aardvark, arrow, cool squid, crane, duck, elephant's head, flower form, linked circles, more mountains, paper plane, pureland mountains, pyramid, rota coaster, shining heart, simple fish, simple whale, square dance, star box, tessellating fish, the honeycomb, toad, traditional banger, tropical fish, wallet and more (Rating: 5.88 Votes: 67) Rate this site: Read Comments (3) Origami Help for Beginners - a short tutorial for beginners to origami that teaches the requisite skills to make almost any well-diagrammed model in any book or Website through explaining common folding symbols and written instructions (Rating: 6.44 Votes: 306)

77. Angle Trisection Since we re working with origami, the angle is in a piece of paper So what we want is to find how to fold along these dotted lines http://hverrill.net/pages~helena/origami/trisect/

http://hverrill.net/pages~helena/origami/trisect/ Origami Trisection of an angle How can you trisect an angle? It can be shown it's impossible to do this with ruler and compass alone, (using Galois theory) - so don't try it!!! But you may be able to find some good approximations. However, in origami, you can get accurate trisection of an acute angle. You can read about this in several places, but since it's so neat, I thought I'd put instructions up here too - more people should be able to do this for a party trick! Jim Loy has informed me that this construction is due to to Hisashi Abe in 1980, (see "Geometric Constructions" by George E. Martin). See Jim Loy's page at http://www.jimloy.com/geometry/trisect.htm for a description of many other ways to trisec an angle. Since we're working with origami, the angle is in a piece of paper: So what we want is to find how to fold along these dotted lines: Note, if you don't start with a square, you can always make a square, here's the idea. We're going to trisect this angle by folding. I'm going to try and describe this in a way so that you'll remember what to do. Suppose we could put three congruent triangles in the picture as shown: These triangles trisect the angle. So we need to know how to get them there.

78. Origami Glossary Modular origami, Where many sheets of paper are folded into (often) identical units or modules. These are then slotted together to form larger geometric designs http://www.britishorigami.org.uk/theory/glossary.php

Origami Glossary a rectangle with has sides in the proportion of 1: root 2 - the diagonal of a square forms the long side of an A proportion rectangle. Action model A design which "does" something when finished, such as a banger or paper plane Adult origami Origami designs of a sexual nature AEP Associacion Espanol Pairoflexia - Spanish folding society Back-coating Gluing two different sheets (such as foil and tissue paper) together to form a single sheet. Base A combination of folds that can be used as a starting point for creating. Bird base A classic base formed by petal folding both sides of a preliminary base BOGS British Origami Gourmet Society - a group of paperfolders who practise folding during meals. (see poppadom) BOS British Origami Society Blintz to fold all four corners of a square into the centre Box- pleating a technique developed by American folder Neal Elias which pleats the paper and collapses into narrow points. Bronco sinkin A legendary origami figure CDO Centro Diffusione Origami - Italian origami Society Chapeaugraphy The folding of a felt ring into shapes representing hats Circular origami As the name suggests, the use of circular paper as the starting point for origami.

79. Arts, Crafts: Origami for various origami related materials paper, books, diagrams Including models folded by Ben Ball. origami Gallery by Sebastian Kirsch Photographs of various http://www.combose.com/Arts/Crafts/Origami/

Top Arts Crafts Origami ... Paper Airplanes Related links of interest: Kids and Teens:Sports and Hobbies:Crafts:Origami Regional:Asia:Japan:Arts and Entertainment:Traditional:Origami and Washi Shopping:Crafts:Paper Anne's Origami - Information on MIT's origami mailing list, with archives. Also a list of books she owns, some with pictures, table of contents and reviews. Anools-Origami - Overview of the art and a gallery of personally folded items, including some very small models. Origami tools and related links. Brooklyn Origami Center - Diagrams of original models and brief information about origami. Charles Esseltine's Origami - Non-traditional patterns. Creased.com - Origami Greeting Cards and Gifts - Origami products: greeting cards, jewelry, books, ornaments, artwork, and paper (origami, chiyogami, and washi). Contains a brief history, definitions, diagrams and pictures of completed models. Dave's Origami Emporium - Diagrams of traditional, modular, money, and original designs. Articles, book and software lists, and origami inspired ray-tracing. Doug Philips' Origami - Gallery of completed models and a review/listing of a few models found online and in books.

80. Activity Subject: The Alphabet of origami should be demonstrated before students start work asking questions regarding geometric terms revealed with each fold of the paper. http://www.scopeonarope.lsu.edu/classroom/lessonplans/ORIGAMI/georigami.html

A Tactile Geometric Experience SOARING at LSU SOAR Summer Workshop Grade Level Author's Name: Linda S. Bonnette Activity Subject: Geometry LA State Standards: G-4-E, G-6-E, G-2-M, G-4-M and Art: CE-1VA-E6, CE-1VA-M6 Summary of Exercise: Students will construct a three dimensional geometrical model known as the Sonobe Unit. Students will follow along while the teacher demonstrates using SOAR Set-Up 3 (1X Stand and View). This construction will promote geometric concepts and communication in verbal, visual, tactile, and written formats. The students will use their math journals to write a description of the Sonobe Unit and illustrate each fold. Students may then construct more elaborate units and/or teach another student or class how to fold the Sonobe Unit. Materials: SOAR , TV, VCR, videotape, recycled telephone book paper, gift wrap paper, or old magazines cut into 6 or 8 inch squares (6 sheets per student) to practice before using good origami paper, popsicle sticks (to "crisply crease" each fold), Origami paper (various colors), and waxed paper Procedure: Setup the SOAR with the 1X lens using the stand on a flat surface. Teacher uses a 6 or 8 inch square of paper (recycled, waxed, or origami) to demonstrate each fold of the Sonobe Unit. The "Alphabet" of origami should be demonstrated before students start work on the Sonobe Unit. The teacher should be asking questions regarding geometric terms revealed with each fold of the paper. These may include terms such as: parallel, perpendicular, congruent, right angle, triangle, square, rectangle, etc.

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