41. Projects See MASU for folding applets. See Kim s Crane for origami paper purchases. folding geometry, Click HERE to go to the geometry seminar link to folding http://www.mtholyoke.edu/courses/jmorrow/projects.html

HOME ASSIGNMENTS Project List Below is a list of topics from which you may choose projects for the seminar. Each item on the list is really an umbrella topic that allows for lots of choices under the umbrella. You aren't restricted to using topics from the list, but you need to consult with me prior to doing the project. If nothing on the list so far looks interesting, please think about alternatives! I'm working on a resource list to go along with the project list. 1. Tilings of the plane (Tessellations) See Tessellations: The Secrets of Interlocking Patterns , Ginny Byer, Contemporary Books, 1999 and this web site, Science U: See also: Click above for an interactive example. 2. Tilings of 3-space Try http://spacebrick.com/geometry/index.html 3. Proofs of the Pythagorean Theorem: Thomas Jefferson did one - how about you? 4. Symmetry Below is a black and white photo of an origami quilt (interlocking folded squares of paper - no glue, no tape) made by Char Morrow. What are its symmetries? See Visions of Symmetry , Doris Schattschneider, Freeman, 1990;

42. Origami Links From Debbie's Educational Link Page origami is the Japanese name for the art of paper folding. Interactive origami in VRML geometry Sender, at Keio University presents Interactive origami http://www.venus.net/~dschweit/edsites/origami/origami2.htm

O r i g a m i L i n k s Functional Origami Origami designs, printable folding instructions and folding animations Netpark Origami Page (English) Welcome to the Multi-lingual Origami Page This page will show you how to create origami with aminations. Languages being planned: /English/Germany/Japanese/Russian and Spanish We are planning to put a new item every month starting form April. Origami Origami Index page with sub pages of origami diagrams, also includes links and brief history, etc. Jim Plank's Origami Page (Modular) Jim Plank's Origami Page (Modular) Instructions Directions for making polyhedrons with the penultimate module Directions for making the compound of 5 tetrahedrons (pictured above) Directions for making greater/lesser stellated dodecahedrons with... Site Map: Fly Over the Garden of ORIGAMI - SUPER SITE The Garden of ORIGAMI: GateSuper site Ori (to fold) + kami (paper) = origami, the art of paper-folding. The Garden of Origami offers a garland of information, from origins and aesthetics to folding diagrams and K-12 Alpenfalten - by Matthias Gutfeldt: Origami diagrams, pictures, and links

43. Key Curriculum Press | Unfolding Mathematics With Origami Boxes Unfolding Mathematics with origami Boxes combines the ancient art of paper folding mathematics to help students discover important concepts in geometry. http://www.keypress.com/catalog/products/supplementals/Prod_UnfoldOrigBoxes.html

Home Customer Service Ordering Information Contact Us ... Site Map State Resources Choose Your State... Alabama Alaska Arizona Arkansas Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Lousiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oregon Oklahoma Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Resource Centers The Geometer's Sketchpad Fathom Dynamic Data TinkerPlots Discovering Algebra ... Statistics in Action Professional Development In Partnership with You Summer Institutes Custom Workshops Implementation Workshops General Information Ordering Information Customer Service Contact Us Meet Our Authors ... Press Room Other Key Sites Key College Publishing KCP Technologies Keymath.com Supplementals Unfolding Mathematics with Origami Boxes Unfolding Mathematics with Origami Boxes Arnold Tubis and Crystal Mills Unfolding Mathematics with Origami Boxes combines the ancient art of paper folding with high school mathematics to help students discover important concepts in geometry. The Japanese masu, a box folded from a single uncut square, provides an engaging classroom activity and a tangible reference for students as they explore geometric figures. Blackline masters and a teacher-friendly design make the activities easy to implement.

44. GO.HRW.COM Lesson 1.4 geometry Using paper folding. Hexaflexagons Activity on page 42 of your text, you used paper folding, or origami, to construct a hexagon. http://go.hrw.com/ndNSAPI.nd/gohrw_rls1/pKeywordResults?MG1 Origami

45. Folding And Unfolding In Computational Geometry: Paper folding and Unfolding in Computational geometry. Part II paper OneDimensional origami. Equivalence of Folded States and Crimps; Connection to Linkages http://www.fucg.org/PartII/II.html

Folding and Unfolding in Computational Geometry Part II: Paper Last Update: Introduction History of Origami History of Origami Mathematics Defnitions Piece of paper Crease pattern Folded state Overlap order Continuous folding process Formalism: Infnitesimals? Geometric Construction Huzita's Axioms and the Resulting Characterization of Foldability Regular Polygons Generalizing the Axioms to Solve All Polynomials Foldability Single-Vertex Foldability Flat Foldings 3D Foldings Continuous Single-Vertex Foldability Local Flat Foldability is Easy Global Flat Foldability is Hard All-Positive Not-All-Equal 3-Satisfiability Reduction Overview Wire Not-All-Equal Clause Splitting and Routing Putting It Together Overlap Order from Valid Mountain-Valley Assignment Continuous Foldability Introduction Definitions Folded States: Overview Well-Behaved Folded States Folded States: Isometry Folded States: Order Folded States: Noncrossing Folding Motions Rolling between Flat-Folded States Unfurling on f(P) One-Dimensional Origami Equivalence of Folded States and Crimps Connection to Linkages Map Folding: Sequence of Simple Folds Origami Design Silhouettes and Gift Wrapping Strip Folding Hamiltonian Triangulation Seam Placement Tree Method Origami bases Uniaxial bases One Complete Straight Cut History Result Straight-Skeleton Method Straight Skeleton Perpendiculars Strange Behavior Spiraling Density Corridors Folded State for Linear Corridors

46. The World's First Origami Folding Robot origami, the geometry of paper folding, looks simple when you re a kid. Robot building a paper hat, This one comes from another film showing the robot http://www.primidi.com/2004/05/14.html

How new technologies are modifying our way of life vendredi 14 mai 2004 The World's First Origami Folding Robot 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.

47. AnyWho: Internet Directory Assistance; Yellow Pages, White Pages, Toll-Free Numb geometry and Modulars (12) Money folding (4), - origamic Architecture (18) Gift boxes hand made by folding paper or fabric using origami techniques. http://www.anywho.com/cgi-bin/webdrill?catkey=gwd/Top/Arts/Crafts/Origami

48. Origami & Catastrophe Theory Similarly, the 3D paper folding equivalents of the Cusp, Swallowtail and Butterfly The origami 3D Cusp fold has one cusp, the Swallowtail 2 cusps, http://www.paperfolding.com/chengchit/3d.php

Origami and Catastrophe Theory by Leong Cheng Chit In flat folding, the folds of a model and the model itself are collapsible onto a flat surface. However, some folds, normally formed towards the end, cannot be collapsed onto a plane without having to create additional folds. Examples are the crimp fold and the fold at a corner of a cube model. Whether the folds and the model itself are collapsible or not, the fold lines are straight. In the case of the crimp fold, the fold lines and the surface or surfaces formed by the fold may be curved. The current origami terminology is inadequate for curved 3D origami folds. A convenient and practical way is to borrow the terms applied to the manifolds of Catastrophe Theory, a branch of mathematics. In Catastrophe Theory, manifolds are used to explain sudden changes in the course of an event due to shifts in environmental factors. The first four catastrophe geometries are: Fold Cusp Swallowtail Butterfly catastrophe Without going into the mathematics of their geometry, we need only to observe that the Cusp manifold has one cusp point, which is the point of coming together of two folds in a sharp spike-like intersection. The Swallowtail manifold has two cusp points and the Butterfly manifold three. See diagram. We can translate the first four manifolds of Catastrophe Theory into origami folds. The first one, the Fold manifold, is the equivalent, in flat origami, of the mountain/valley fold. It has no cusp point. The second catastrophe geometry, the Cusp manifold, is the equivalent, in flat folding, of the reverse fold; third, the Swallowtail manifold, is the equivalent of the double reverse fold; and fourth, the Butterfly manifold, the triangular sink fold.

49. Origami -- From MathWorld The Japanese art of paper folding. In traditional origami, constructions are done Row, TS Geometric Exercises in paper folding. New York Dover, 1966. http://mathworld.wolfram.com/Origami.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Recreational Mathematics Folding Origami ... Lang Origami The Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square. In modular origami, a number of individual "units," each folded from a single sheet of paper, are combined to form a compound structure. Origami is an extremely rich art form, and constructions for thousands of objects, from dragons to buildings to vegetables have been devised. Many mathematical shapes can also be constructed, especially using modular origami. The images above show a number of modular polyhedral origami constructed by E. K. Herrstrom, together with an animated crane constructed in Mathematica by L. Zamiatina. Cube duplication and angle trisection can be solved using origami, although they cannot be solved using the traditional rules for

50. Folding -- From MathWorld origami, the Japanese art of paper folding, is one wellknown example. Sundra Row, T. Geometric Exercises in paper folding. New York Dover, 1966. http://mathworld.wolfram.com/Folding.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Recreational Mathematics Folding General Folding ... Mathematical Records Folding There are many mathematical and recreational problems related to folding. Origami , the Japanese art of paper folding, is one well-known example. It is possible to make a surprising variety of shapes by folding a piece of paper multiple times, making one complete straight cut, the unfolding. For example, a five-pointed star can be cut out after four folds (Demaine and Demaine 2004, p. 23), as can a polygonal swan, butterfly, and angelfish (Demaine and Demaine 2004, p. 29). Amazingly, every polygonal shape can be produced this way, as can any disconnected combination of polygonal shapes (Demaine and Demaine 2004, p. 25). Furthermore, algorithms for determining the patterns of folds for a given shape have been devised by Bern et al.

51. Paper Folding - Books paper folding Books 3-D Geometric origami $6.95 By Rona Gurkewitz and Bennett Arnstein. Contains step-by-step instructions and diagrams for building http://www.mathartfun.com/shopsite_sc/store/html/OrigamiBooks.html

Paper Folding - Books The Complete Book of Origami By Robert J. Lang. Includes a brief history of Origami, guide to folding techniques, illustrated list of folding symbols, plus step-by-step folding diagrams for 48 projects ranging from simple to complex. Over 1000 drawings and diagrams. [Add to Cart] [View Cart] Unfolding Mathematics with Unit Origami By Betsy Franco. A book of blackline activity masters designed for algebra and geometry students in high schoool or middle school. Contains 16 activities arranged in order of increasing difficulty. The book's primary purpose is to teach mathematics, but it also introduces students to the art of origami. 136 pages. [Add to Cart] [View Cart] 3-D Geometric Origami By Rona Gurkewitz and Bennett Arnstein. Contains step-by-step instructions and diagrams for building over 60 different polyhedra-based models from origami units. 80 pages. [Add to Cart] [View Cart] Origami for Beginners By Vincent Palacios. An easy-to-follow guide book with 57 models. Each is illustrated with step-by-step diagrams and captions that take you through their construction. 80 pages. [Add to Cart] [View Cart] Patty Paper Geometry 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.

52. Paper Folding Links Einsteins origami Fold paper into a series of geometric shapes faster than the other players. Site includes rules, and print outs of the shapes. http://www.shambles.net/pages/learning/MathsP/PaperFold/

(best viewed at 800 x 600) document.write(""+doClock("W0","%20","D1","%20","M0","%20","Y0","%20")+""); http://www.shambles.net Paper Folding Links Add a link Top of page 10 Paper Airplanes http://www.10PaperAirplanes.com Free animated paper airplane folding instructions for 10 cool paper airplanes. Einsteins Origami http://www.geocities.com/snowflakegame/tableofcontents.html Einsteins Origami Fold paper into a series of geometric shapes faster than the other players. Site includes rules, and print outs of the shapes. Robert Lang : Origami http://www.langorigami.com/index.htm Robert Lang : Origami Robert J. Lang has been an avid student of origami for over thirty years and is now recognized as one of the world? leading masters of the art, with over 400 designs catalogued and diagrammed. He is noted for designs of great detail and realism, and includes in his repertoire some of the most complex origami designs ever created. He has consulted on applications of origami to engineering problems ranging from air-bag design to expandable space telescopes. African Elephant http://tinyurl.com/3khf7

53. Origami Special thanks to origami Garden for this info. In the East. The art of paper folding is thought to have had its beginnings in China during the first or http://www.tuvy.com/resource/origami.htm

Home About Books Authors ... Household Special thanks to Origami Garden for this info. In the East The art of paper folding is thought to have had its beginnings in China during the first or second century A.D. By the sixth century, it was being practiced in Japan. In this small island country, paper was a scarce and treasured material. Because of this, the practice of paper folding was originally confined to the wealthy nobility. Origami appealed to the same aesthetic which created the tea ceremony, which one scholar has described as "essentially a worship of the Imperfect, as it is a tender attempt to accomplish something possible in this impossible thing we know as life...it is moral geometry, inasmuch as it defines our sense of proportion to the universe." (Kakuzo Okakura, The Book of Tea) Increasing trade eventually led to the widespread availability of affordable paper, and origami grew into a popular pastime among rich and poor alike. Because of their culture which emphasizes respect for the economy of nature, however, Asian practitioners of this art have never lost the impulse to save even the tiniest scraps of paper to fold into miniature origami models. Hiden Senbazuru Orikata ("How to Fold One Thousand Cranes") was published in 1797, and is the oldest origami publication which survives. Kan no modo ("Window on Midwinter"), the first published collection of origami models, appeared in 1845. In the West The Moors, who were Muslims from West Africa, brought paper folding with them to Spain when they invaded in the eighth century. Although Islam proscribed the making of representational figures, Islamic mathematicians and astronomers were fascinated with pattern, symmetry, and space. Their explorations included studies on the geometry of tessellation and on the folding patterns hidden within the square. These investigations of pattern were often given form in architecture.

54. No. 1110: Origami origami Where there is paper, it will be folded. In fact, a lot of Euclidean geometry can be done in folded paper. When the English first translated http://www.uh.edu/engines/epi1110.htm

No. 1110: ORIGAMI by John H. Lienhard Click here for audio of Episode 1110. Today, we fold paper. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. I linger after my History of Technology class to chat with a student, Michael Adcock. Adcock has just handed in his term paper on a seemingly marginal topic. He's written about origami the so-called "Japanese" art of paper-folding. As he explains origami to me, his fingers work on a small square of paper. I'd never seen myself as an origami folder, but as he talks and as I skim-read his paper, my childhood (dare I say) unfolds before me: the paper boats I sailed each spring in rivulets of melting snow; folded-paper hats; folded gliders that got me into trouble in my grade-school classroom; the paper water-bombs we threw at one another in the hot summer. Today, I still like to fold paper swans with flapping wings. As we talk, I remember how blank pages of paper lured me. I was dyslexic. Paper was little use to me as material to write upon. But paper, more than any other material, is foldable. Adcock suddenly hands me the figure he's been making. It's a clearly recognizable model of Alfred Hitchcock. He picks up another piece of paper. His fingers move again, and the conversation continues.

55. Focus On Learning Problems In Mathematics: A Survey Of Paper Cutting, Folding An origami or the art of paper folding receives substantial endorsement from Among the geometric concepts that are embedded in origami are similarity, http://www.findarticles.com/p/articles/mi_m0NVC/is_1_25/ai_105477685

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Home Advanced Search IN free articles only all articles this publication Automotive Sports FindArticles Focus on Learning Problems in Mathematics Wntr 2003 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Related Searches Geometry / Study and teaching Mathematics / Study and teaching Mathematics teachers / Training National Council of Teachers of Mathematics / Standards Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports A survey of paper cutting, folding and tearing in mathematics textbooks for prospective elementary school teachers Focus on Learning Problems in Mathematics Wntr, 2003 by Jack A. Carter Beverly J. Ferrucci Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it.

56. Fractal Geometry Panorama paperfolding provides a wonderful physical example of how iterative processes generate fractal shapes. Could more steps be done using origami paper? http://classes.yale.edu/fractals/Panorama/Art/PaperFolding/PaperFolding.html

Fractal Paperfolding Paperfolding provides a wonderful physical example of how iterative processes generate fractal shapes. Uribe's book has clear instructions on making some fascinating examples. Simmt and Davis give clear descriptions of several such constructions, along with examples of the mathematical questions students are led to ask while making these "fractal cards." Moreover, once the basic examples are grasped, students can easily construct their own examples. Any project that gives students creative control is pedagogically valuable, and this is yet another instance of these projects in fractal geometry. Valentine's Day and Christmas have been especially effective times to introduce this exercise. Here we give one example. What other fractal cards can you produce? Begin with a piece of paper. Fold it once. The unfolding stage involves reversing the directions of some folds, so repeat each fold several times, reversing the direction with each repetition. Now make two cuts, each about 1/4 of the side length from each edge and about half way to the other edge. Fold up the middle flap formed by these cuts. For the fold just formed, repeat the previous step. Now make two cuts, each about 1/4 of the side length from each edge and about half way to the other edge. Fold up the middle flap formed by these cuts.

57. Origami What Is Origami? Origami Is The Japanese Name For The Art After the Arabs left Spain, paper folding became more geometric in designs In class we learned the art of paper folding. A Chinese origami artist showed http://everyschool.org/u/logan/culturalmath/origami.htm

Origami What is origami? Origami is the Japanese name for the art of paper folding. In the word origami, oru means to fold and kami means paper. An origami figure that is completed is called a model. The only tool needed in order to do origami is the paper. The paper is usually cut into 15 cm squares. The most common technique in origami is the folding. The folds have different names. In the valley fold, a flat piece of paper is folded towards the paper folder. In the mountain fold, the paper is folded away from the paper folder. After a person makes these folds, there are a series of basic folds that follow. The four most common bases are the kite base, the fish base, the bird base, and the frog base. These show that origami artists like to use animals as their models in this art, Origami can be used to make almost anything such as animals, faces, plants, vehicles and buildings. Many people fold abstract or mathematical shapes, others specialize in modular origami . In modular origami many copies of a simple folded shape are assembled to form larger structures. The paper artists have different occupations like artists, scientists, and therapists. The scientists, architects, and mathematicians love the geometry of origami. Many people just do it because it is fun.

58. Exploratorium Magazine: Paper: Page 2 Volume 23, Number 2 Exploring origami Page 2 of 5 The art of paper folding, like the art of papermaking, began in China, but it spread to Japan by the http://www.exploratorium.edu/exploring/paper/paper2.html

Volume 23, Number 2 Exploring Origami - Page 2 of 5 In Japan, legend says that a person who makes a thousand origami cranes will live a long life. The legend took on new meaning in 1955, when Sadako Sasaki (shown above and below), a twelve-year-old girl who was exposed to radiation during the bombing of Hiroshima, contracted leukemia. While in the hospital, she tried to fold 1,000 cranes but died before she could finish. Sadako's statue now stands in Hiroshima's Peace Memorial Park, where it is decorated every year with thousands of origami cranes, folded by children from around the world, as a symbol of peace. Click here for a larger image of Sadako Sasaki. Click here to visit www.sadako.com he art of paper folding, like the art of papermaking, began in China, but it spread to Japan by the sixth century A.D. Over the centuries, it became an integral part of Japanese culture. Paper butterflies symbolized the bride and groom at weddings; folding a thousand paper cranes became a traditional way to ensure a long and healthy life. Animals were an especially popular theme, as "folders" developed more and more ingenious ways to make a little diamond of folded paper sprout legs or wings—and even to make it float, hop, or fly. Even so, Japanese origami evolved very slowly. According to American origami expert Peter Engel, Japanese folders invented about 150 traditional origami figures in a millennium of folding.

59. Math Forum Electronic Newsletter When paper is folded, an origami geometry is at work. Contents include a tutorial on origami geometric constructions that presents Humiaki http://mathforum.org/electronic.newsletter/mf.intnews2.45.html

Volume 2, Number 45 Back to Table of Contents http://www.math.uri.edu/~hull/OrigamiMath.html When paper is folded, an origami geometry is at work. Tom Hull provides information on investigations into the mathematics of origami as carried out by mathematicians, scientists, and artists. Contents include: - a tutorial on origami geometric constructions that presents Humiaki Huzita's origami axiom list and compares it to traditional straightedge and compass constructions, with instructions for trisecting angles and doubling cubes - a model: five intersecting tetrahedra - an origami math bibliography - a listing of upcoming origami math events Hull's bibliography on origami geometry and education includes articles from such widely available publications as "Mathematics Teacher" and "Mathematical Intelligencer." http://www.math.uri.edu/~hull/Geombib.html http://www.sanger.ac.uk/~agb/Origami/origami.html Directions for folding Alex Bateman's "square dance," "honeycomb," and "linked circles," with postscript files to be downloaded. Other models by Dino Andreozzi, Nick Robinson, and Edwin Corrie are also provided. HELENA'S ORIGAMI - H. A. VERRILL http://www.mast.queensu.ca/~helena/origami/

60. David Lister On Folding From Non-square Paper So it is easy to produce square origami paper, but impossible for manufacturers and origami is fascinating, not only from the point of view of folding, http://www.britishorigami.org.uk/academic/lister/nosquare.htm

Folding from non-square paper I thought I would set down a few random thoughts on folding from non-square as opposed to square paper, but I don't intend it to be a reasoned thesis! 1.A few months ago, I wrote in Origami-L about John Smith's ideas on "Origami Profiles" which analyses how each individual's preferences in folding fit into the general scheme of things. The theory accepts that everyone is entitles to adopt whatever rules for folding he or she chooses. 2. Following from this a folder can choose to fold from a square or from a triangle or from A4 or a pentagon or a rectangle or a rhombus or a long ribbon of paper half and inch wide and ten yards long. He may even prefer silk ribbon or even string. Whether other people would include in their own concepts of Origami is another thing. 3. If you accept that cutting is legitimate (and cutting, too, fits into John Smith's Profiles of Origami), your can convert a square of paper into any shape you like. Or you can trim your dollar bill into a square. Or you can chop off any of those surplus bits of paper that get in the way. (No, I accept that most people who like to use scissors don't look at it in this extreme way, but I assert the possibility.) 4. Without even using scissors, you can convert most simple shapes of paper into most other shapes by folding alone. You can fold a square to make a triangle, or a hexagon or a 3 X 7 rectangle, even A4. So having done that, in theory, you can go on to fold anything that can be folded from a square equally from a Dollar bill or anything that can be folded from a Dollar bill from a square. I write "in theory" advisedly, because all the preliminary folding to get the shape makes the model bulky and difficult or even impossible to fold in practice.

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