DOCSLIB.ORG

Above the Fold New Expressions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Above the Fold New Expressions Erik Demaine & Martin Demaine, Destructors III, 2013 New Expressions above the fold in Origami Traveling Exhibitions New Expressions above the fold in Origami Yuko Nishimura, Wave, 2013 bove the Fold demonstrates the extraordinary power “To most, the real beauty of and potential of contemporary origami. In the hands Aof nine international artists, what was once considered origami lies in its simplicity, a children’s craft becomes a sophisticated global art form. Paper is transformed into breathtaking sculpture, large-scale allowing everyone to create installations and conceptual works that express contemporary social, political, aesthetic, and cultural dialogues. Above the their interpretation of the Fold is the first traveling exhibition to bring origami installations world in paper.” from around the world to North American audiences. Visionary master folders—such as Erik Demaine and Martin Demaine (Canada/USA), Vincent Floderer (France), —VANESSA GOULD, director, Between the Folds Miri Golan (Israel), Paul Jackson (UK/Israel), Dr. Robert J. Lang (USA), Yuko Nishimura (Japan), Richard Sweeney (UK), and Jiangmei Wu (China/USA)—push the boundaries of paper as a medium to create bold, provocative works. International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 2 New Expressions above the fold in Origami Paul Jackson, Untitled, 2014 Each artist will create pieces specifically for this tour—their collective works have never been seen before anywhere in “Even DNA is folded—you the world. and I are born from folding.” These nine internationally celebrated folders comprise a cross- section of contemporary origami artists, ranging in age from —PAUL JACKSON, Above the Fold artist 29 to 71, hailing from four different continents, and working in seven different countries. Their origami creations will present original, “above the fold” commentaries on diverse aspects of modern life and art. increasingly elaborate and provocative sculptural works, while scientists and mathematicians are using origami to Origami, literally meaning “paper folding,” has evolved from unlock the mysteries of the universe. Since even our DNA a Japanese craft into a highly expressive, global art form is folded, origami artist Paul Jackson has expressed, “You that intersects and impacts the realms of art and science. and I are born from folding.” We are all, in essence, works Today, artists from all over the world are folding paper into of origami. International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 3 New Expressions above the fold in Origami Detail of Vincent Floderer, Unidentified Flying Origami, 2002-2014 The exhibition celebrates these artists who are redefining a traditional Japanese craft as a modern global genre, inventing “This transformation of unexpected forms of artistic expression. Their works exemplify not only innovative methods of working with paper, flat paper into swirling but also the power of origami to unite disciplines as diverse as sculpture and geometry, physics and religion, mathematics surfaces creates sculpture and the global peace movement. that feels alive.” Above the Fold was developed by International Arts & Artists and independent curator, author, and educator Meher McArthur, former curator of East Asian Art at Pacific Asia —ERIK DEMAINE, Above the Fold artist Museum in Pasadena, California and curator of the traveling exhibition, Folding Paper: The Infinite Possibilities of Origami. International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 4 New Expressions above the fold in Origami Richard Sweeney, Air, 2014 International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 5 New Expressions above the fold in Origami Detail of Jiangmei Wu, Ruga Swan, 2014 Jiangmei Wu works to illustrate how folding can be expressed mathmatically, physically, and asethetically, how it can be done with different materials and techniques, and how these aspects work together with the conceptual space in which they occur. In her folded works like Ruga Swan (ruga is the Latin word fo “a fold, crease, or wrinkle”), the folded forms have rigid properties and at the same time are flexible; they are deployable and can be collapsed again into smaller compressed forms. This installation, created from two folded sections joined together, unites her fascination with interior skin, natural forms, and the effects of light and shadow. There are many examples of folding-inspired design in architecture; however, folded architectural structures rarely make use of one of the main characteristic of folding design – the kinetic ability to morph from a two dimensional surface to a three-dimensional surface. Ruga Swan seeks to construct a deployable three dimensional semi-rigid structure that comes from fabricating two dimensional materials, that can be collapsed into, again, smaller compressed forms. International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 6 New Expressions above the fold in Origami Installation of Jiangmei Wu’s Ruga Swan (2014) at Springfield Museums, 2014 Installation of Jiangmei Wu’s Ruga Swan (2014) at Springfield Museums, 2014 International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 7 New Expressions above the fold in Origami Detail of Robert Lang, Vertical Pond II, 2014 About the Curator Meher McArthur is a freelance Asian art curator, author Values Through Art (2008-9), and Japan in Blue and White and educator, and curator of the traveling exhibition, Folding (March 2010-March 2011). She lectures and advises at several Paper: The Infinite Possibilities of Origami. She received a BA museums in Southern California, including the Santa Barbara in Japanese Studies from Cambridge University and a MA in Museum of Art, the Huntington Library, Art Collections, and Japanese art history from the School of Oriental and African Botanical Gardens, and the Bowers Museum of Cultural Art Studies (SOAS), London University. She worked for nine in Santa Ana, and has advised on Buddhist Art installations years as Curator of East Asian Art at Pacific Asia Museum in for the Victoria and Albert Museum in London. She is also a Pasadena, CA, where she curated 15 exhibitions, including visiting professor at Scripps College in Claremont, California. Gods and Goblins: Japanese Folk Paintings from Otsu (1999), Her publications include Gods and Goblins: Japanese Folk Constructing the Cosmos in the Religious Arts of Asia (2001), Paintings from Otsu (Pacific Asia Museum, 1999), Reading Paintings, Prints, and Drawings by Hokusai (2001), The Nature Buddhist Art: An Illustrated Guide to Buddhist Signs and of the Beast: Portrayals of Animals in Japanese Paintings Symbols (Thames & Hudson, 2002), The Arts of Asia: Materials, (2001), Visions of Enlightenment: Understanding the Art of Techniques, Styles (Thames & Hudson, 2005), Confucius Buddhism (2002) and Kampai! The Arts of Japanese Sake (Quercus, London, 2010), published in the USA as Confucius: (2004). She also curated the museum’s permanent Chinese A Throneless King (Pegasus Books, 2011), and Folding Paper: Ceramics Galleries (2000) and Gallery of Japanese Art (2006). The Infinite Possibilities of Origami (International Arts & Artists, As a guest curator at Pacific Asia Museum, she curated Jade, 2012). She has also published two children’s books about art: Silk, Porcelain…: An Introduction to the Materials of Asian Michael and the Magical Museum (Pacific Asia Museum, 2003) Art (2007), The Religious Arts of Japan (2007), Lotus Moon: and An ABC of What Art Can Be (The Getty Museum, 2010). The Arts of Otagaki Rengetsu (2008), Confucius: Shaping International Arts & Artists • 9 Hillyer Court NW, Washington, DC 20008 Phone 202.338.0680 • Fax 202.333.0758 • www.artsandartists.org | 8 New Expressions above the fold in Origami Detail of Erik Demaine and Martin Demaine, Greene Recycling/De- Miri Golan, Twisted Holy Book, 2014 structors VIII, 2013 Artists air flow. The models will show the creative process Floderer Erik Demaine and Martin Demaine (Canada/USA) uses to develop his crumpling techniques. Each model derives A father-son collaborative team, the Demaines fold, pleat, and from classical, modular, box-pleated origami forms that he twist paper into powerful sculptural forms that illustrate the transforms into otherworldly creations. The installation will intriguing and profound connections between mathematics adapt to each venue’s gallery space, changing aesthetically and origami. They use mathematical calculations to create with each presentation. unconventional works that challenge the direction of paper foldling. For years, the Demaines have been exploring the Miri Golan (Israel) potential of curved folding, in which paper is folded along a A peace activist, educator, and origami artist, Golan will create curved, rather than a straight line. The Demaines plan to fold a a series of book sculptures, based on her conceptual Folding series of their signature, abstract “Curved-Crease Sculptures” Paper piece, Two Books, in which origami figures emerge from using modular techniques to increase sculptural size. They the pages of two sacred texts, the Torah and the Koran,
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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].
    [Show full text]
  • 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.
    [Show full text]
  • Algorithmic Folding Complexity∗
    Algorithmic Folding Complexity∗ Jean Cardinal1, Erik D. Demaine2, Martin L. Demaine2, Shinji Imahori3, Tsuyoshi Ito4, Masashi Kiyomi5, Stefan Langerman1, Ryuhei Uehara5, Takeaki Uno6 1 D´epartement d'Informatique, Universit´eLibre de Bruxelles, CP 212, B-1050 Brussels, Belgium. e-mail: fjcardin,[email protected] 2 Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technol- ogy, Cambridge, MA 02139, USA. e-mail: fedemaine,[email protected] 3 Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan. e-mail: [email protected] 4 Institute for Quantum Computing and School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada. e-mail: [email protected] 5 School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan. e-mail: fmkiyomi,[email protected] 6 National Institute of Informatics, Chiyoda-ku, Tokyo 101-8430, Japan. e-mail: [email protected] Abstract. How do we most quickly fold a paper strip (modeled as a line) to obtain a desired mountain-valley pattern of equidistant creases (viewed as a binary string)? Define the folding complexity of a mountain-valley string as the minimum number of simple folds required to construct it. We first show that the folding complexity of a length-n uniform string (all mountains or all valleys), and hence of a length-n pleat (alternating mountain/valley), is O(lg2 n). We also show that a lower bound of the complexity of the problems is Ω(lg2 n= lg lg n). Next we show that almost all mountain-valley patterns require Ω(n= lg n) folds, which means that the uniform and pleat foldings are relatively easy problems.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Folding Concave Polygons Into Convex Polyhedra: the L-Shape
    Rose- Hulman Undergraduate Mathematics Journal Folding concave polygons into convex polyhedra: The L-Shape Emily Dinana Alice Nadeaub Isaac Odegardc Kevin Hartshornd Volume 16, No. 1, Spring 2015 Sponsored by Rose-Hulman Institute of Technology Department of Mathematics aUniversity of Washington Terre Haute, IN 47803 bUniversity of Minnesota c Email: [email protected] University of North Dakota d http://www.rose-hulman.edu/mathjournal Moravian College Rose-Hulman Undergraduate Mathematics Journal Volume 16, No. 1, Spring 2015 Folding concave polygons into convex polyhedra: The L-Shape Emily Dinan Alice Nadeau Issac Odegard Kevin Hartshorn Abstract. Mathematicians have long been asking the question: Can a given convex polyhedron can be unfolded into a polygon and then refolded into any other convex polyhedron? One facet of this question investigates the space of polyhedra that can be realized from folding a given polygon. While convex polygons are relatively well understood, there are still many open questions regarding the foldings of non-convex polygons. We analyze these folded realizations and their volumes derived from the polygonal family of ‘L-shapes,’ parallelograms with another parallelogram removed from a corner. We investigate questions of maximal volume, diagonalflipping, and topological connectedness and discuss the family of polyhedra that share a L-shape polygonal net. Acknowledgements: We gratefully acknowledge support from NSF grant DMS-1063070 and the 2012 Lafayette College Research Experience for Undergraduates, where the majority of this research was undertaken. We would like to thank our research advisor, Dr. Kevin Hartshorn, who helped us with his great ideas, feedback, problem solving abilities and support throughout the project.
    [Show full text]
  • Annual Report 2010–11
    ANNUAL REPORT 2010–11 ANNUAL REPORT 2010–11 The National Gallery of Australia is a Commonwealth (cover) authority established under the National Gallery Act 1975. Thapich Gloria Fletcher Dhaynagwidh (Thaynakwith) people The vision of the National Gallery of Australia is the Eran 2010 cultural enrichment of all Australians through access aluminium to their national art gallery, the quality of the national 270 cm (diam) collection, the exceptional displays, exhibitions and National Gallery of Australia, Canberra programs, and the professionalism of Gallery staff. acquired through the Founding Donors 2010 Fund, 2010 Photograph: John Gollings The Gallery’s governing body, the Council of the National Gallery of Australia, has expertise in arts administration, (back cover) corporate governance, administration and financial and Hans Heysen business management. Morning light 1913 oil on canvas In 2010–11, the National Gallery of Australia received 118.6 x 102 cm an appropriation from the Australian Government National Gallery of Australia, Canberra totalling $50.373 million (including an equity injection purchased with funds from the Ruth Robertson Bequest Fund, 2011 of $15.775 million for development of the national in memory of Edwin Clive and Leila Jeanne Robertson collection and $2 million for the Stage 1 South Entrance and Australian Indigenous Galleries project), raised $27.421 million, and employed 262 full‑time equivalent staff. © National Gallery of Australia 2011 ISSN 1323 5192 All rights reserved. No part of this publication can be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system, without permission in writing from the publisher.
    [Show full text]
  • The Geometry Junkyard: Origami
    Table of Contents Table of Contents 1 Origami 2 Origami The Japanese art of paper folding is obviously geometrical in nature. Some origami masters have looked at constructing geometric figures such as regular polyhedra from paper. In the other direction, some people have begun using computers to help fold more traditional origami designs. This idea works best for tree-like structures, which can be formed by laying out the tree onto a paper square so that the vertices are well separated from each other, allowing room to fold up the remaining paper away from the tree. Bern and Hayes (SODA 1996) asked, given a pattern of creases on a square piece of paper, whether one can find a way of folding the paper along those creases to form a flat origami shape; they showed this to be NP-complete. Related theoretical questions include how many different ways a given pattern of creases can be folded, whether folding a flat polygon from a square always decreases the perimeter, and whether it is always possible to fold a square piece of paper so that it forms (a small copy of) a given flat polygon. Krystyna Burczyk's Origami Gallery - regular polyhedra. The business card Menger sponge project. Jeannine Mosely wants to build a fractal cube out of 66048 business cards. The MIT Origami Club has already made a smaller version of the same shape. Cardahedra. Business card polyhedral origami. Cranes, planes, and cuckoo clocks. Announcement for a talk on mathematical origami by Robert Lang. Crumpling paper: states of an inextensible sheet. Cut-the-knot logo.
    [Show full text]
  • A Salamander Sculpture Barn Raising
    BRIDGES Mathematical Connections in Art, Music, and Science A Salamander Sculpture Barn Raising George W. Hart Computer Science Department. Stony Brook University Stony Brook, NY 11794-4400, USA E-mrul:[email protected] Abstract Salamanders is a thirty-piece wooden sculpture that was group assembled by thirty volunteers in an exciting sculpture "barn raising" when I was artist-in-residence at M.I.T. in OctoberlNovember 2003. It is composed of laser-cut salamander-shaped components which lie in the planes of a rhombic triacontahedron and were mathematically designed to weave through each other and exactly fit together on the outside. 1. Introduction M.e. Escher playfully incorporated chameleons and other reptiles or amphibians in his two-dimensional geometric artwork [1]. In homage to his creative spirit, I designed my sculpture Salamanders to feature flat salamanders which interweave in three dimensions. Figure 1 shows it hanging temporarily inside a window overlooking the construction of Frank O. Gehry's new Stata Center at M.I.T. [2], where the sculpture will eventually reside. Figure 1: Salamanders 54 2004 Bridges Proceedings My ultimate concept, if funding can be found, is for a large metal double sphere as shown in Figure 2. The inner and outer spheres are each made of thirty identical two-headed salamander shapes. Each part is parallel to an identical part similarly oriented in the other sphere. I find it visually interesting to show that the same salamander parts can be joined in these two contrasting arrangements---one very open and one very interlocked. It is a puzzle with two very different solutions.
    [Show full text]
  • Use of Origami in Mathematics Teaching: an Exemplary Activity
    Asian Journal of Education and Training Vol. 6, No. 2, 284-296, 2020 ISSN(E) 2519-5387 DOI: 10.20448/journal.522.2020.62.284.296 © 2020 by the authors; licensee Asian Online Journal Publishing Group Use of Origami in Mathematics Teaching: An Exemplary Activity Davut Köğce Niğde Ömer Halisdemir University, Faculty of Education, Department of Elementary Mathematics Education Turkey. Abstract Students’ attitudes and motivations toward mathematics decrease as they intensively confront cognitive information along the process of mathematics teaching in general. One of the most important reasons for this is the lack of activities for affective and psychomotor domains in the mathematics teaching process. One way to overcome this problem is to include activities through which students can participate effectively in the teaching process. For example, activities performed using origami can be one of them in teaching the attainments covered by the field of geometry learning in mathematics curriculum. Therefore, this study was carried out to present an exemplary activity about how origami can be used when teaching mathematics in secondary schools and to identify preservice teacher opinions on this activity. The activity presented in this study was performed with 32 preservice elementary mathematics teachers attending the faculty of education at a university and taking the Mathematics Teaching with Origami course, and their opinions were taken afterwards. At the end of the application, the preservice teachers stated that such activities would have very positive contributions to students’ mathematics learning. In addition, the preservice teachers communicated and exchanged ideas with each other during the application. It is therefore recommended to use such activities in mathematics teaching.
    [Show full text]
  • Paper Pentasia: an Aperiodic Surface in Modular Origami
    Paper Pentasia: An Aperiodic Surface in Modular Origami a b Robert J. Lang ∗ and Barry Hayes † aLangorigami.com, Alamo, California, USA, bStanford University, Stanford, CA 2013-05-26 Origami, the Japanese art of paper-folding, has numerous connections to mathematics, but some of the most direct appear in the genre of modular origami. In modular origami, one folds many sheets into identical units (or a few types of unit), and then fits the units together into larger constructions, most often, some polyhedral form. Modular origami is a diverse and dynamic field, with many practitioners (see, e.g., [12, 3]). While most modular origami is created primarily for its artistic or decorative value, it can be used effectively in mathematics education to provide physical models of geometric forms ranging from the Platonic solids to 900-unit pentagon-hexagon-heptagon torii [5]. As mathematicians have expanded their catalog of interesting solids and surfaces, origami designers have followed not far behind, rendering mathematical forms via folding, a notable recent example being a level-3 Menger Sponge folded from 66,048 business cards by Jeannine Mosely and co-workers [10]. In some cases, the origami explorations themselves can lead to new mathematical structures and/or insights. Mosely’s developments of business-card modulars led to the discovery of a new fractal polyhedron with a novel connection to the famous Snowflake curve [11]. One of the most popular geometric mathematical objects has been the sets of aperiodic tilings developed by Roger Penrose [14, 15], which acquired new significance with the dis- covery of quasi-crystals, their three-dimensional analogs in the physical world, in 1982 by Daniel Schechtman, who was awarded the 2011 Nobel Prize in Chemistry for his discovery.
    [Show full text]