Folding Paper: the Infinite Possibilities of Origami Educator Guide January 31, 2014 – April 27, 2014
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Understanding Matboard
FRAMING FUNDAMENTALS by Jared Davis, MCPF, GCF Understanding Matboard Being the best frame shop in your area starts with the best products. atboard is a fundamental compo- Mnent of almost every framed pic- ture. However, understanding the vast range of information and choices avail- able in matboards can be daunting. In this article, I aim to provide some useful insights about matboard to help you to dispel some of the myths and decipher some of the facts about this vital aspect of our profession. The two primary purposes for matboard that the introduction of a matboard can in- Different grades of matboard are are to provide protection for the artwork and crease both the size and level of value in the designed for to enhance the framing design. sale of a frame. different appli- cations. Under- 1) Protect. The last consumer survey con- standing which choice to make is ducted by the Professional Picture Fram- How Matboard is Made important to both ers Association found that the num- Matboards are comprised of layers of pa- your customer and your business. ber-one reason why a consumer chose to per of various thickness, laminated together. custom frame an artwork was to protect The papers and core of a matboard are made the item. Preservation, clearly, is of prima- from either unpurified wood pulp, purified al- ry importance to your customer. pha-cellulose wood pulp, or in the case of mu- 2) Enhance. A matboard can help the view- seum-grade board, cotton linter pulp. er to focus correctly on the image. -
Simple Origami for Cub Scouts and Leaders
SIMPLE ORIGAMI FOR CUB SCOUTS AND LEADERS Sakiko Wehrman (408) 296-6376 [email protected] ORIGAMI means paper folding. Although it is best known by this Japanese name, the art of paper folding is found all over Asia. It is generally believed to have originated in China, where paper- making methods were first developed two thousand years ago. All you need is paper (and scissors, sometimes). You can use any kind of paper. Traditional origami patterns use square paper but there are some patterns using rectangular paper, paper strips, or even circle shaped paper. Typing paper works well for all these projects. Also try newspaper, gift-wrap paper, or magazine pages. You may even want to draw a design on the paper before folding it. If you want to buy origami paper, it is available at craft stores and stationary stores (or pick it up at Japan Town or China Town when you go there on a field trip). Teach the boys how to make a square piece from a rectangular sheet. Then they will soon figure out they can keep going, making smaller and smaller squares. Then they will be making small folded trees or cups! Standard origami paper sold at a store is 15cm x 15 cm (6”x6”) but they come as small as 4cm (1.5”) and as large as 24cm (almost 9.5”). They come in different colors either single sided or double sided. They also come in different patterns, varying from traditional Japanese patterns to sparkles. When you make an origami, take your time. -
Geometry of Transformable Metamaterials Inspired by Modular Origami
Geometry of Transformable Metamaterials Inspired by Yunfang Yang Department of Engineering Science, Modular Origami University of Oxford Magdalen College, Oxford OX1 4AU, UK Modular origami is a type of origami where multiple pieces of paper are folded into mod- e-mail: [email protected] ules, and these modules are then interlocked with each other forming an assembly. Some 1 of them turn out to be capable of large-scale shape transformation, making them ideal to Zhong You create metamaterials with tuned mechanical properties. In this paper, we carry out a fun- Department of Engineering Science, damental research on two-dimensional (2D) transformable assemblies inspired by modu- Downloaded from http://asmedigitalcollection.asme.org/mechanismsrobotics/article-pdf/10/2/021001/6404042/jmr_010_02_021001.pdf by guest on 25 September 2021 University of Oxford, lar origami. Using mathematical tiling and patterns and mechanism analysis, we are Parks Road, able to develop various structures consisting of interconnected quadrilateral modules. Oxford OX1 3PJ, UK Due to the existence of 4R linkages within the assemblies, they become transformable, e-mail: [email protected] and can be compactly packaged. Moreover, by the introduction of paired modules, we are able to adjust the expansion ratio of the pattern. Moreover, we also show that trans- formable patterns with higher mobility exist for other polygonal modules. The design flex- ibility among these structures makes them ideal to be used for creation of truly programmable metamaterials. [DOI: 10.1115/1.4038969] Introduction be made responsive to external loading conditions. These struc- tures and materials based on such structures can find their usage Recently, there has been a surge of interest in creating mechani- in automotive, aerospace structures, and body armors. -
Ununfoldable Polyhedra with Convex Faces
Ununfoldable Polyhedra with Convex Faces Marshall Bern¤ Erik D. Demainey David Eppsteinz Eric Kuox Andrea Mantler{ Jack Snoeyink{ k Abstract Unfolding a convex polyhedron into a simple planar polygon is a well-studied prob- lem. In this paper, we study the limits of unfoldability by studying nonconvex poly- hedra with the same combinatorial structure as convex polyhedra. In particular, we give two examples of polyhedra, one with 24 convex faces and one with 36 triangular faces, that cannot be unfolded by cutting along edges. We further show that such a polyhedron can indeed be unfolded if cuts are allowed to cross faces. Finally, we prove that \open" polyhedra with triangular faces may not be unfoldable no matter how they are cut. 1 Introduction A classic open question in geometry [5, 12, 20, 24] is whether every convex polyhedron can be cut along its edges and flattened into the plane without any overlap. Such a collection of cuts is called an edge cutting of the polyhedron, and the resulting simple polygon is called an edge unfolding or net. While the ¯rst explicit description of this problem is by Shephard in 1975 [24], it has been implicit since at least the time of Albrecht Durer,Ä circa 1500 [11]. It is widely conjectured that every convex polyhedron has an edge unfolding. Some recent support for this conjecture is that every triangulated convex polyhedron has a vertex unfolding, in which the cuts are along edges but the unfolding only needs to be connected at vertices [10]. On the other hand, experimental results suggest that a random edge cutting of ¤Xerox Palo Alto Research Center, 3333 Coyote Hill Rd., Palo Alto, CA 94304, USA, email: [email protected]. -
Mathematics of Origami
Mathematics of Origami Angela Kohlhaas Loras College February 17, 2012 Introduction Origami ori + kami, “folding paper” Tools: one uncut square of paper, mountain and valley folds Goal: create art with elegance, balance, detail Outline History Applications Foldability Design History of Origami 105 A.D.: Invention of paper in China Paper-folding begins shortly after in China, Korea, Japan 800s: Japanese develop basic models for ceremonial folding 1200s: Origami globalized throughout Japan 1682: Earliest book to describe origami 1797: How to fold 1,000 cranes published 1954: Yoshizawa’s book formalizes a notational system 1940s-1960s: Origami popularized in the U.S. and throughout the world History of Origami Mathematics 1893: Geometric exercises in paper folding by Row 1936: Origami first analyzed according to axioms by Beloch 1989-present: Huzita-Hatori axioms Flat-folding theorems: Maekawa, Kawasaki, Justin, Hull TreeMaker designed by Lang Origami sekkei – “technical origami” Rigid origami Applications from the large to very small Miura-Ori Japanese solar sail “Eyeglass” space telescope Lawrence Livermore National Laboratory Science of the small Heart stents Titanium hydride printing DNA origami Protein-folding Two broad categories Foldability (discrete, computational complexity) Given a pattern of creases, when does the folded model lie flat? Design (geometry, optimization) How much detail can added to an origami model, and how efficiently can this be done? Flat-Foldability of Crease Patterns 훗 Three criteria for 훗: Continuity, Piecewise isometry, Noncrossing 2-Colorable Under the mapping 훗, some faces are flipped while others are only translated and rotated. Maekawa-Justin Theorem At any interior vertex, the number of mountain and valley folds differ by two. -
3.2.1 Crimpable Sequences [6]
JAIST Repository https://dspace.jaist.ac.jp/ Title 折り畳み可能な単頂点展開図に関する研究 Author(s) 大内, 康治 Citation Issue Date 2020-03-25 Type Thesis or Dissertation Text version ETD URL http://hdl.handle.net/10119/16649 Rights Description Supervisor:上原 隆平, 先端科学技術研究科, 博士 Japan Advanced Institute of Science and Technology Doctoral thesis Research on Flat-Foldable Single-Vertex Crease Patterns by Koji Ouchi Supervisor: Ryuhei Uehara Graduate School of Advanced Science and Technology Japan Advanced Institute of Science and Technology [Information Science] March, 2020 Abstract This paper aims to help origami designers by providing methods and knowledge related to a simple origami structure called flat-foldable single-vertex crease pattern.A crease pattern is the set of all given creases. A crease is a line on a sheet of paper, which can be labeled as “mountain” or “valley”. Such labeling is called mountain-valley assignment, or MV assignment. MV-assigned crease pattern denotes a crease pattern with an MV assignment. A sheet of paper with an MV-assigned crease pattern is flat-foldable if it can be transformed from the completely unfolded state into the flat state that all creases are completely folded without penetration. In applications, a material is often desired to be flat-foldable in order to store the material in a compact room. A single-vertex crease pattern (SVCP for short) is a crease pattern whose all creases are incident to the center of the sheet of paper. A deep insight of SVCP must contribute to development of both basics and applications of origami because SVCPs are basic units that form an origami structure. -
Pleat Folding, 6.849 Fall 2010
Demaine, Demaine, Lubiw Courtesy of Erik D. Demaine, Martin L. Demaine, and Anna Lubiw. Used with permission. 1999 1 Hyperbolic Paraboloid Courtesy of Jenna Fizel. Used with permission. [Albers at Bauhaus, 1927–1928] 2 Circular Variation from Bauhaus [Albers at Bauhaus, 1927–1928] 3 Courtesy of Erik Demaine, Martin Demaine, Jenna Fizel, and John Ochsendorf. Used with permission. Virtual Origami Demaine, Demaine, Fizel, Ochsendorf 2006 4 Virtual Origami Demaine, Demaine, Fizel, Ochsendorf 2006 Courtesy of Erik Demaine, Martin Demaine, Jenna Fizel, and John Ochsendorf. Used with permission. 5 “Black Hexagon” Demaine, Demaine, Fizel 2006 Courtesy of Erik Demaine, Martin Demaine, and Jenna Fizel. Used with permission. 6 Hyparhedra: Platonic Solids [Demaine, Demaine, Lubiw 1999] 7 Courtesy of Erik Demaine, Martin Demaine, Jenna Fizel, and John Ochsendorf. Used with permission. Virtual Origami Demaine, Demaine, Fizel, Ochsendorf 2006 8 “Computational Origami” Erik & Martin Demaine MoMA, 2008– Elephant hide paper ~9”x15”x7” Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/Computational/. 9 Peel Gallery, Houston Nov. 2009 Demaine & Demaine 2009 Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/Limit/. 10 “Natural Cycles” Erik & Martin Demaine JMM Exhibition of Mathematical Art, San Francisco, 2010 Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/NaturalCycles/. 11 Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/BlindGlass/. Demaine & Demaine 2010 12 Hyperbolic Paraboloid Courtesy of Jenna Fizel. Used with permission. [Demaine, Demaine, Hart, Price, Tachi 2009/2010] 13 θ = 30° n = 16 Courtesy of Erik D. -
WASHI TRANSFORMED New Expressions in Japanese Paper 2 WASHI TRANSFORMED INTRODUCTION
WASHI TRANSFORMED New Expressions in Japanese Paper 2 WASHI TRANSFORMED INTRODUCTION nique for its strong natural fibers and its Despite the increased mechanization of papermaking U painstaking production techniques, which in Japan over the last century, contemporary Japanese have been passed down from one generation to artists have turned to this supple yet sturdy paper the next, washi stands out as a nexus of tradition to express their artistic visions. The thirty-seven and innovation. Its continuing, and ever-evolving, artworks and installations in Washi Transformed: importance as an artistic medium is due primarily to New Expressions in Japanese Paper epitomize the the ingenuity of Japanese contemporary artists, who potential of this traditional medium in the hands of have pushed washi beyond its historic uses to create these innovative artists, who have made washi their highly textured two-dimensional works, expressive own. Using a range of techniques—layering, weaving, sculptures, and dramatic installations. Washi, which and dyeing to shredding, folding, and cutting—nine translates to “Japanese paper,” has been integral to artists embrace the seemingly infinite possibilities of Japanese culture for over a thousand years, and the washi. Bringing their own idiosyncratic techniques to strength, translucency, and malleability of this one- the material, their extraordinary creations—abstract of-a-kind paper have made it extraordinarily versatile paper sculptures, lyrical folding screens, highly as well as ubiquitous. Historically, washi has been textured wall pieces, and other dramatic installations— used as a base for Japanese calligraphy, painting, demonstrate the resilience and versatility of washi as and printmaking; but when oiled, lacquered, or a medium, as well as the unique stature this ancient otherwise altered, it has other fascinating applications art form has earned in the realm of international in architecture, religious ritual, fashion, and art. -
Read a Book, Make a Book, CBF, April 2012 Sarah C
Read A Book, Make A Book, CBF, April 2012 Sarah C. Campbell and Julie Owen Why make a book as reader response? To promote reflection and higher order thinking To assess mastery of content or skills To encourage creativity To practice the writing process To synthesize math skills in measurement, geometry, spatial reasoning To move beyond standard pencil/paper assignments To engage in process-oriented learning To create an attractive display that encourages literacy and participation in programming To have fun and take pride in writing and making one’s own book Online Resources http://www.bookmakingwithkids.com/ (a blog with organizational lists by grade level, topic, and book structure) http://www.makingbooks.com/ (website with links to videos for making different book types in- cluding the instant book, called a hot-dog book here) www.Pinterest.com (Pinterest is a social network of virtual pinboards where people post images they find on the web to pinboards of their own, organize them by topic, and follow pinboards of other people. After joining for free, you can search “bookmaking” and related terms to find ideas). www.YouTube.com (Search for video tutorials for bookmaking and bookbinding) http://angrychicken.typepad.com/angry_chicken/2011/04/hardback-sketchbook-tutorial.html (Video for an easy book bound with staples and duct-tape) http://robertsabuda.com/popmake/index.asp (Instructions for simple pop-ups categorized by be- ginner, intermediate, and advanced) Books Diehn, Gwen. Making Books That Fly, Fold, Wrap, Hide, Pop Up, Twist & Turn. New York: Lark Books, 1998. Fennimore, Flora. The Art of the Handmade Book: Designing, Decorating, and Binding One-of- a-Kind Books. -
Wenwu Chang, Exploring Space Filling Origami
Exploring space-filling origami Wenwu Chang [email protected] Shanghai Putuo Modern Educational Technology Center, China Abstract A new tetrahedra origami model was discussed in this paper. Sommerville in 1922 found four kinds of tetrahedron can fill space. This model starts from a rectangle paper, whose shape ratio is 1:√2, to produce one Sommerville’s main tetrahedron. It is proved that as long as the original paper is big enough, one can produce by this origami method more and more so-called Sommerville-tetrahedrons without cutting or pasting. Furthermore, these tetrahedrons fill three-dimension space in the same time. Just like Peano curve fills two-dimensional space, the original paper (two dimensional manifold) used in producing tetrahedrons fills the three-dimensional space. This article also introduces some interesting models in the lower number cases. Introduction In 1922, D.M.Y Sommerville found Aristotle, a famous philosopher during Ancient Greek Times, made a mistake. Aristotle stated there were two kinds of regular polyhedron, including regular tetrahedra could tile space. In fact, cube is the only regular polyhedron that can fill space. Sommerville in his paper ended this mistake and pointed out that several general tetrahedra could fill space indeed. Resulting from the way of cutting and reassembling a cube, he found 4 kinds of tetrahedra. The most important tetrahedron was the one made up of four triangles whose edge ratios are 2:√3:√3. I will call it Sommerville-tetrahedron within this paper. Another three kinds of tetrahedra were developed by dissection or reassembling of the dissection to this original tetrahedron. -
Jitterbug ★★★✩✩ Use 12 Squares Finished Model Ratio 1.0
Jitterbug ★★★✩✩ Use 12 squares Finished model ratio 1.0 uckminister Fuller gave the name Jitterbug to this transformation. I first came across B the Jitterbug in Amy C. Edmondson’s A Fuller Explanation (1987).As I didn’t have dowels and four-way rubber connectors, I made several cuboctahedra that worked as Jitterbugs but were not very reversible. Some were from paper and others from drinking straws and elastic thread. My first unit,Triangle Unit, was partly successful as a Jitterbug.A better result came from using three units per triangular face (or one unit per vertex) which was published in 2000. This improved version is slightly harder to assemble but has a stronger lock.The sequence is pleasingly rhythmical and all steps have location points.The pleats in step 18 form the spring that make the model return to its cuboctahedral shape. Module ★★★ Make two folds in half. Do Fold the sides to the centre. Fold the bottom half behind. 1 not crease the middle for 2 Unfold the right flap. 3 the vertical fold. Fold the top right corner to This creates a 60 degree Fold the right edge to the 4 lie on the left edge whilst the 5 angle. Unfold. 6 centre. fold starts from the original centre of the square. Reproduced with permission from Tarquin Group publication Action Modular Origami (ISBN 978-1-911093-94-7) 978-1-911093-95-4 (ebook). © 2018 Tung Ken Lam. All rights reserved. 90 ° Fold the bottom half Repeat step 4 and unfold, Fold the left edge to the 7 behind. -
Stem+Visual Art
STEM+VISUAL ART A Curricular Resource for K-12 Idaho Teachers a r t Drew Williams, M.A., Art Education Boise State University + Table of Contents Introduction 1 Philosophy 2 Suggestions 2 Lesson Plan Design 3 Tips for Teaching Art 4 Artist Catalogue 5 Suggestions for Classroom Use 9 Lesson Plans: K-3 10 Lesson Plans: 4-6 20 Lesson Plans: 6-9 31 Lesson Plans: 9-12 42 Sample Images 52 Resources 54 References 55 STEM+VISUAL ART A Curricular Resource for K-12 Idaho Teachers + Introduction: Finding a Place for Art in Education Art has always been an integral part of students’ educational experiences. How many can remember their first experiences as a child manipulating crayons, markers and paintbrushes to express themselves without fear of judgement or criticism? Yet, art is more than a fond childhood memory. Art is creativity, an outlet of ideas, and a powerful tool to express the deepest thoughts and dreams of an individual. Art knows no language or boundary. Art is always innovative, as each image bears the unique identity of the artist who created it. Unfortunately as many art educators know all too well, in schools art is the typically among the first subjects on the chopping block during budget shortfalls or the last to be mentioned in a conversation about which subjects students should be learning. Art is marginalized, pushed to the side and counted as an “if-we-have-time” subject. You may draw…if we have time after our math lesson. We will have time art in our class…after we have prepared for the ISAT tests.