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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. -
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. -
Origami Design Secrets Reveals the Underlying Concepts of Origami and How to Create Original Origami Designs
SECOND EDITION PRAISE FOR THE FIRST EDITION “Lang chose to strike a balance between a book that describes origami design algorithmically and one that appeals to the origami community … For mathematicians and origamists alike, Lang’s expository approach introduces the reader to technical aspects of folding and the mathematical models with clarity and good humor … highly recommended for mathematicians and students alike who want to view, explore, wrestle with open problems in, or even try their own hand at the complexity of origami model design.” —Thomas C. Hull, The Mathematical Intelligencer “Nothing like this has ever been attempted before; finally, the secrets of an origami master are revealed! It feels like Lang has taken you on as an apprentice as he teaches you his techniques, stepping you through examples of real origami designs and their development.” —Erik D. Demaine, Massachusetts Institute of Technology ORIGAMI “This magisterial work, splendidly produced, covers all aspects of the art and science.” —SIAM Book Review The magnum opus of one of the world’s leading origami artists, the second DESIGN edition of Origami Design Secrets reveals the underlying concepts of origami and how to create original origami designs. Containing step-by-step instructions for 26 models, this book is not just an origami cookbook or list of instructions—it introduces SECRETS the fundamental building blocks of origami, building up to advanced methods such as the combination of uniaxial bases, the circle/river method, and tree theory. With corrections and improved Mathematical Methods illustrations, this new expanded edition also for an Ancient Art covers uniaxial box pleating, introduces the new design technique of hex pleating, and describes methods of generalizing polygon packing to arbitrary angles. -
Marvelous Modular Origami
www.ATIBOOK.ir Marvelous Modular Origami www.ATIBOOK.ir Mukerji_book.indd 1 8/13/2010 4:44:46 PM Jasmine Dodecahedron 1 (top) and 3 (bottom). (See pages 50 and 54.) www.ATIBOOK.ir Mukerji_book.indd 2 8/13/2010 4:44:49 PM Marvelous Modular Origami Meenakshi Mukerji A K Peters, Ltd. Natick, Massachusetts www.ATIBOOK.ir Mukerji_book.indd 3 8/13/2010 4:44:49 PM Editorial, Sales, and Customer Service Office A K Peters, Ltd. 5 Commonwealth Road, Suite 2C Natick, MA 01760 www.akpeters.com Copyright © 2007 by A K Peters, Ltd. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photo- copying, recording, or by any information storage and retrieval system, without written permission from the copyright owner. Library of Congress Cataloging-in-Publication Data Mukerji, Meenakshi, 1962– Marvelous modular origami / Meenakshi Mukerji. p. cm. Includes bibliographical references. ISBN 978-1-56881-316-5 (alk. paper) 1. Origami. I. Title. TT870.M82 2007 736΄.982--dc22 2006052457 ISBN-10 1-56881-316-3 Cover Photographs Front cover: Poinsettia Floral Ball. Back cover: Poinsettia Floral Ball (top) and Cosmos Ball Variation (bottom). Printed in India 14 13 12 11 10 10 9 8 7 6 5 4 3 2 www.ATIBOOK.ir Mukerji_book.indd 4 8/13/2010 4:44:50 PM To all who inspired me and to my parents www.ATIBOOK.ir Mukerji_book.indd 5 8/13/2010 4:44:50 PM www.ATIBOOK.ir Contents Preface ix Acknowledgments x Photo Credits x Platonic & Archimedean Solids xi Origami Basics xii -
Artistic Origami Design, 6.849 Fall 2012
F-16 Fighting Falcon 1.2 Jason Ku, 2012 Courtesy of Jason Ku. Used with permission. 1 Lobster 1.8b Jason Ku, 2012 Courtesy of Jason Ku. Used with permission. 2 Crab 1.7 Jason Ku, 2012 Courtesy of Jason Ku. Used with permission. 3 Rabbit 1.3 Courtesy of Jason Ku. Used with permission. Jason Ku, 2011 4 Convertible 3.3 Courtesy of Jason Ku. Used with permission. Jason Ku, 2010 5 Bicycle 1.8 Jason Ku, 2009 Courtesy of Jason Ku. Used with permission. 6 Origami Mathematics & Algorithms • Explosion in technical origami thanks in part to growing mathematical and computational understanding of origami “Butterfly 2.2” Jason Ku 2008 Courtesy of Jason Ku. Used with permission. 7 Evie 2.4 Jason Ku, 2006 Courtesy of Jason Ku. Used with permission. 8 Ice Skate 1.1 Jason Ku, 2004 Courtesy of Jason Ku. Used with permission. 9 Are there examples of origami folding made from other materials (not paper)? 10 Puppy 2 Lizard 2 Buddha Penguin 2 Swan Velociraptor Alien Facehugger Courtesy of Marc Sky. Used with permission. Mark Sky 11 “Toilet Paper Roll Masks” Junior Fritz Jacquet Courtesy of Junior Fritz Jacquet. Used with permission. 12 To view video: http://vimeo.com/40307249. “Hydro-Fold” Christophe Guberan 13 stainless steel cast “White Bison” Robert Lang “Flight of Folds” & Kevin Box Robert Lang 2010 & Kevin Box Courtesy of Robert J. Lang and silicon bronze cast 2010 Kevin Box. Used with permission. 14 “Flight of Folds” Robert Lang 2010 Courtesy of Robert J. Lang. Used with permission. 15 To view video: http://www.youtube.com/watch?v=XEv8OFOr6Do. -
Paper-Fold Physics: Newton’S Three Laws of Motion Lisa (Yuk Kuen) Yau Revised Date: Monday, July 30, 2018
Unit Title: Paper-fold Physics: Newton’s Three Laws of Motion Lisa (Yuk Kuen) Yau Revised Date: Monday, July 30, 2018 1. Abstract Can you teach physics effectively using only paper and the simple act of folding? This interdisciplinary curriculum unit is designed for a 5th grade class focusing on how to unpack Newton’s Three Laws of Motion using paper folding (i.e. origami) as a teaching tool to promote inquiry and project-based learning. Students will learn scientific concepts by making paper models, testing them to form hypotheses, analyzing the collected data with graphs, researching supporting theories of Newton, making real-world connections, writing scientific conclusions, and applying their new understandings to solve challenges such as how to design a paper container to protect a fragile egg from cracking under a stressful landing. Can paper folding be a teaching strategy to promote an equitable and competitive learning environment for all students from the hyperactive to the hypersensitive, from the “underachievers” to the “overachievers”, and all other biased labels in between? Folding in solitude is a calming activity that builds concentration and focus (i.e., mindfulness), allows each student multiple opportunities to fail and succeed. In the repeating actions of folding in order to gain mastery, student can retain the learned knowledge better and longer. From my own experience, I have witnessed how powerful origami can help students to verbalize what they are learning to each other. Students gain a better sense of self and community as they make personal connections to real problems and situations with their hands “thinking out loud.” Of course, origami is not the magic pill but if uses properly, it can open many doors of positive learning for both students and teachers from all walks of life. -
Mortality Statistics and Paper Folding
Welcome to Issue 79 of the Secondary Magazine. Contents From the editor In order to focus clearly on our mathematical thinking, it is helpful sometimes to address questions and problems that require a minimum of mathematical background. It’s in the News! Mortality Statistics Each year the Office for National Statistics publishes a set of data showing the causes of death for the previous year. In January 2011 the data for 2009 was released, showing some interesting statistics which might challenge our intuitive understanding of, and the way that the media presents, the dangers facing us. This is used as a context for students to explore the way that data is presented and interpreted. The Interview – James Grime Dr James Grime is the Enigma Project Officer of the Millennium Mathematics Project in the Department of Mathematics and Theoretical Physics at the University of Cambridge. He travels the UK, and the world, talking to schools and adult audiences about mathematical ideas and their histories. Focus on…paper folding Paper folding explorations include the generation of mathematical objects, the doing of mathematical actions and the proving of relationships. 5 things to do Will you be arranging to be at a STEM careers conference, or at a meeting about algebra without equations, or at a workshop on using origami in the classroom? There is still time to apply for a Media Fellowship, and respond to the Call for Evidence relating to the National Curriculum Review. Or you could just relax by watching Tung Ken Lam fold a cuboctahedron! Subject Leadership Diary Sometimes a subject leader may seize an opportunity to convey messages to the whole school, for example by taking a school assembly. -
In the Fold: Origami Meets Mathematics
from SIAM News, Volume 34, Number 8 In the Fold: Origami Meets Mathematics By Barry A. Cipra Say “origami” and most people picture birds, fish, or frogs made of sharply creased paper, an amusing exercise for children. But for participants in the Third International Meeting of Origami, Science, Math, and Education, held March 9–11 in Pacific Grove, California, the ancient Japanese word conjures up images of fantastically complex organic and geometric shapes, of axioms and algorithms, and of applications ranging from safer airbags in cars to the deployment in outer space of telescopes 100 meters or more in diameter. “There’s a particular appeal of origami to mathematicians,” says Tom Hull, a mathematician at Merrimack College in Andover, Massachusetts, and the organizer of the conference. Paperfolding offers innumerable challenges, both theoretical and practical— and does so in a way that appeals to mathematicians’ aesthetic sensibilities. “I tend to view origami as being latent mathematics,” Hull says. Unlimited Possibilities Traditional origami starts with a square sheet of paper, typically white on one side and colored on the other. The origamist makes a sequence of “mountain” and “valley” folds, creating a network of creases that turn the square into a mosaic of polygonal facets. And as computer graphics enthusiasts know, you can do a lot with polygons. Erik Demaine, a computer scientist at the University of Waterloo, described some of the amazing polygonal and polyhedral possibilities. A square of origami paper that’s black on one side and white on the other, for example, can be folded to create a checkerboard pattern. -
Tienda AEP Libros.Pdf
Asociación Española de Papiroflexia El precio que figura en este documento es orientativo, puede no estar actualizado y nocompromete en ningún caso a la A.E.P. El precio definitivo será suministrado por el encargado del Servicio. Los envíos realizan mediante la empresa de mensajería MRW. Tienen un importe de 8,71 tarifa plana, sea cual sea su peso o volumen. Para cualquier duda o consulta puede escribir a [email protected] 001 001-Sirgorigami - Manuel Sirgo 13,00 € 002 002-VOG 2 30,00 € 003 003-Star Wars Origami - Chris Alexander 20,00 € 004 004-Practigami - Neorigami 6,50 € 005 005-The Mask - Tomoko Fuse 39,00 € 006 006-Mooser's Train - Emmanuel Mooser 8,00 € 007 007-Origami Twelve Days of Christmas - John Montroll 10,00 € 008 008-Easy Origami - Montroll 11,00 € 009 009-Works of Satoshi Kamiya 50,00 € 010 010-Curlicue: Kinetic Origami - Asia Brill 18,00 € 011 011-Spirits of Origami - Gen Hagiwara 30,00 € 012 012-Favorite Animals in Origami - Montroll 10,00 € 013 013-Aviones Voladores - Franco Pavarin 12,00 € 014-17 Modelos inéditos de Aviones Voladores - Franco 014 Pavarin 15,00 € 015 015-Origami Flowers - Kazuo Kobayashi (4021906444) 18,00 € 016 016-Building With Butterflies - David Mitchell 19,00 € 017 017-Origami Insects vol.2 - Robert Lang 47,00 € 018-Small Boxes in Origami 2 - Tomoko Fuse 018 (4529052850) 23,00 € 019-Origami Ornaments - Makoto Yamaguchi 019 (4883379140) 28,00 € 020 020-Origami Sculptures- John Montroll 17,00 € 021 021-Prehistoric Origami - John Montroll 17,00 € 022-The Amazing Art Work Folding by One Piece of -
Poetry in Paper Poezija U Papiru
Pučko otvoreno učilište Krapina, Open University Krapina, Galerija grada Krapine Krapina City Gallery Magistratska 25 Magistratska 25 5. - 20. lipnja 2008. June 5 - 20, 2008 A ORIGAMIR T POEZIJA U PAPIRU POETRY IN PAPER Prva izložba origami arta u Hrvatskoj The first origami art exhibition sa svjetskim majstorima in Croatia with international origamija origami masters Zahvale Acknowledgments Izložbu "Poezija u papiru" organizirali su Pučko otvoreno učilište Krapina, Ga- The exhibition "Poetry in Paper" was organized by the Open University lerija grada Krapine, u suradnji sa Veleposlanstvom Japana u Zagrebu. Krapina, Krapina City Gallery, in conjunction with the Japanese Embassy in Zagreb. Željeli bismo izraziti zahvalnost za fiancijsku potporu tvrtki Baotić Rotus d.o.o., tvrtki Profil multimedijalne knjižare d.o.o., gradu Krapini, Hrvatskom društvu We would like to gratefully acknowledge the financial support of: Baotic znanstvenih i tehničkih prevoditelja te Prevoditeljskom centru. Rotus d.o.o., Profil multimedijalne knjižare d.o.o., the City of Krapina, the Croatian Association of Scientific and the Technical Translators and Croatian Posebno zahvaljujemo svim autorima i origamistima koji su poslali svoje radove Translation Agency. za ovu izložbu ili dozvolili drugim origamistima da ih predstave te na taj način We are particularly grateful to all the origami authors and folders who sent pomogli promoviranju origami arta u Hrvatskoj. their art models or permitted other folders to fold their models for this exhibi- Galerija grada Krapine sa zahvalnošću i poštovanjem prima origami art modele tion and thus helped promoting origami art in Croatia. donirane od: Petera Budaia, Joela Coopera, Dragutina Gerića, Mirjane Go- Krapina City Gallery is honoured and grateful for the donated origami art letić, Roberta Grettera, Gorana Konjevoda, Michaela G. -
Origami - Von Der Kunst Und Der Wissenschaft Des Papierfaltens
Origami - von der Kunst und der Wissenschaft des Papierfaltens NORBERT HUNGERBUHLER¨ (ETH ZURICH¨ ) Origami gehort¨ zu den skalierbaren Themen des Mathematikunterrichts. Das heisst, die Beschaftigung¨ mit dem Falten von Papier halt¨ Aspekte vom Kindergartenniveau bis hin zu aktueller Forschung bereit. Dieser Text bietet einen kurzen Uberblick¨ uber¨ die Geschichte und die Anwendungen von Origami, uber¨ Origami-Geometrie und deren Axiomatik. Gleichzeitig werden einige etwas speziellere mathematische Probleme im Zusammenhang mit Origami vorgestellt. Wir gehen auch der Frage nach, wie die Mathematik beim Design der beeindruckenden Faltfiguren der Origamikunstler¨ hilft. Origami ist viel mehr als nur ein Spiel fur¨ Kinderhande.¨ 1. Was ist Origami? Origami ist ein Sammelbegriff fur¨ die vielfaltigen¨ Aspekte des Faltens von Papier. Die folgende (unvoll- standige)¨ Liste gibt einen groben Uberblick¨ uber¨ die Gebiete: Klassisches Origami: Aus einem quadratischen Stuck¨ Papier wird (ohne Verwendung von Schere oder Leim) eine Figur gefaltet. Die Abbildung rechts zeigt eine Ta- rantel von Robert Lang. Modulares Origami: Das gefaltete Objekt setzt sich aus mehreren Komponenten zusammen. Die Abbildung rechts zeigt einen dreidimensionalen Stern aus ver- schrankten¨ Tetraedern von Thomas Hull. Rigid Origami: Beim industriellen Falten von Metall anstelle von Papier stellt sich die Frage, welche Origami-Modelle starr (also ohne Verbiegen der Flachenst¨ ucke)¨ gefaltet und allenfalls wieder geoffnet¨ werden konnen.¨ Origami-Parkettierungen: Es werden regulare¨ Parket- tierungen der Ebene gefaltet. Die Abbildung rechts zeigt Beispiele von Origami-Parkettierungen im Durchlicht. Zweidimensionales Origami vs. dreidimensionales Origami: Hier geht es um die Untersuchung der Unterschiede beim Falten von Figuren, die in die Ebene gefaltet werden konnen¨ im Vergleich zu solchen, welche dreidimensionale Objekte bilden. -
1 a Program for Origami Design
Copyright ©1994–1998 by Robert J. Lang. All rights reserved. Portions (CFSQP) Copyright ©1993-1998 by Craig T. Lawrence, Jian L. Zhou, and Andre L. Tits. Use and distribution of this program is subject to restrictions described in the TreeMaker documentation. A Program for Origami Design Thanks for suggestions and algorithmic insight to: Alex Bateman, Toshiyuki Meguro, Tom Hull, Jun Maekawa, Fumiaki Kawahata, Erik Demaine, Barry Hayes, and Marshall Bern. Programmed with Metrowerks CodeWarrior ™ and Metrowerks PowerPlant™. Copyright ©1994–1998 by Robert J. Lang. All rights reserved. Portions (CFSQP) copyright @1993–1998 by Craig T. Lawrence, Jian L. Zhou, and Andre L. Tits. All Rights Reserved. Terms of License TreeMaker contains copyrighted code (CFSQP) that may only be used for non-profit purposes. TreeMaker may not be freely distributed. CFSQP's Conditions for External Use include the following 1. The CFSQP routines may not be distributed to third parties. Interested parties should contact the authors directly. 2. Due acknowledgment must be made of the use of the CFSQP routines in research reports or publications. Whenever such reports are released for public access, a copy should be forwarded to the authors of CFSQP. 3. The CFSQP routines may only be used for research and development, unless it has been agreed otherwise with the authors in writing. For more information on CFSQP, see http://www.isr.umd.edu/Labs/CACSE/FSQP/fsqp.html To obtain a copy of the TreeMaker executable, please provide the following information: Your name Your affiliation (must be a non-profit organization) Your e-mail address An affirmation that you will abide by CFSQP’s Conditions for External Use.