Origami 5 : Fifth International Meeting of Origami Science, Mathematics, and Education book cover
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Origami 5
Fifth International Meeting of Origami Science, Mathematics, and Education




ISBN 9781568817149
Published June 21, 2011 by A K Peters/CRC Press
668 Pages

 
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Book Description

Origami5 continues in the excellent tradition of its four previous incarnations, documenting work presented at an extraordinary series of meetings that explored the connections between origami, mathematics, science, technology, education, and other academic fields.

The fifth such meeting, 5OSME (July 13–17, 2010, Singapore Management University) followed the precedent previous meetings to explore the interdisciplinary connections between origami and the real world. This book begins with a section on origami history, art, and design. It is followed by sections on origami in education and origami science, engineering, and technology, and culminates with a section on origami mathematics—the pairing that inspired the original meeting.

Within this one volume, you will find a broad selection of historical information, artists’ descriptions of their processes, various perspectives and approaches to the use of origami in education, mathematical tools for origami design, applications of folding in engineering and technology, as well as original and cutting-edge research on the mathematical underpinnings of origami.

Table of Contents

Origami History, Art, and Design

History of Origami in the East and the West before Interfusion, Koshiro Hatori
Introduction
Origin of Origami: Many Misunderstandings and Some Suppositions
The East and the West: Different Styles, Different Traditions
Conclusion
Bibliography

Deictic Properties of Origami Technical Terms and Translatability, Koichi Tateishi
Introduction
Previous Studies on Origami Terms
Theoretical Backgrounds
Maze of (Un)Translatability
Referentiality/Deictic versus Similarity: The Role of a Japanese Verbal Noun Ori
Why Don’t the Japanese Use Verbs?
Further Considerations
Conclusion
Bibliography

Betsy Ross Revisited: General Fold and One-Cut Regular and Star Polygons, Arnold Tubis and Crystal Elaine Mills
Introduction
Historical Sources for the Story
Folding and One-Cut of the Pattern for Stars Artifact
Generalizing the Betsy Ross Method to Fold and One-Cut Any Regular and Star Polygons
Discussion
Bibliography

Reconstructing David Huffman’s Legacy in Curved-Crease Folding, Erik D. Demaine, Martin L. Demaine, and Duks Koschitz
Introduction
Approach
Reconstructions
Conclusion
Bibliography

Simulation of Nonzero Gaussian Curvature in Origami by Curved-Crease Couplets, Cheng Chit Leong
Introduction
Geometry of a Curved Surface
Representation of Curved Surfaces by Paper Folding
Ruled Surfaces
Radial Formed Rotational Symmetric Models
Cylindrical Formed Rotational Symmetric Models
Applications of Couplets to Folding Animal Models
Conclusion
Bibliography

Compression and Rotational Limitations of Curved Corrugations, Christine E. Edison
Introduction
Method
Discussion of Results
Conclusions
Bibliography

Polygon Symmetry Systems, Andrew Hudson
Introduction
Polygon Construction
Unified Algorithm for Polygon Construction
Polygonal Grids and Their Properties
Symmetrical Twist-Fold Constructions
Generalizing Folding Algorithms to Different
Polygons
Conclusion
Bibliography

New Collaboration on Modular Origami and LED, Miyuki Kawamura and Hiroyuki Moriwaki
Introduction
AKARI-ORIGAMI: Some Modular Works
Workshop
Future of AKARI-ORIGAMI
Bibliography

Using the Snapology Technique to Teach Convex Polyhedra, Faye Goldman
Introduction
Polyhedra Review
Snapology Technique
Brief Introduction to General Snapology
Observations
Conclusions
Bibliography

A Systematic Approach to Twirl Design, Krystyna Burczyk and Wojciech Burczyk
Introduction
The First Attempt: Small (Change) Is Beautiful
A Square Is a Rectangle: Metamorphosis
Planar Decorative Area: From Octahedron to Cube, Mosaic Twirls
Shapes and Lengths: Different Spirals
Minimal Folding: No Crease Origami
Consensus Building: Spirals Work Together with Flaps-and-Pockets, Macro-modules
Conclusion
Bibliography

Oribotics: The Future Unfolds, Matthew Gardiner
Introduction
Industrial Evolution of Oribotics
Crease Pattern and Mechanical Design
Paper versus Fabric
Interaction Design
Conclusion and Further Work
Bibliography

Origami in Education

Origametria and the van Hiele Theory of Teaching Geometry, Miri Golan
Introduction
The van Hiele Theory of Geometric Teaching
Origami and the Van Hiele Theory
Time of Learning
Gradually Building Knowledge and Concepts
Using Origametria to Eliminate Misconceptions
Origametria and van Hiele: An Example from the Classroom
Conclusion: The Benefits of Using Origametria in the van Hiele System
Bibliography

Student-Teachers Introduce Origami in Kindergarten and Primary Schools, Maria Lluïsa Fiol, Neus Dasquens, and Montserrat Prat
Introduction
Objectives
Review of the Literature
Problem Statements
Data Collection, Analysis, and Discussion
Conclusion and Next Steps
Bibliography

Narratives of Success: Teaching Origami in Low-Income Urban Communities, Christine Edison
Introduction
Origami in Mathematics
Origami in Art Class
Origami in Elementary School
Discussion
Bibliography

Origami and Spatial Thinking of College-Age Students, Norma Boakes
Introduction
Design and Purpose
Results
Conclusion
Bibliography

Close Observation and Reverse Engineering of Origami Models, James Morrow and Charlene Morrow
Introduction
Rationale/Goals
Origins and Context
An Approach to Close Observation and Reverse Engineering
An Example
Close Observation and Reverse Engineering in Learning and Problem Solving
Our Observations of CORE
Challenges, a Question, and Next Steps
Conclusion
Bibliography

Origami and Learning Mathematics, Sue Pope and Tung Ken Lam
Introduction
Using Origami in Mathematics Lessons
Using Origami to Teach Conceptually Demanding Mathematics
Conclusions
Bibliography

Hands-On Geometry with Origami, Michael J. Winckler, Kathrin D. Wolf, and Hans-Georg Bock
Introduction
New Trends in Teaching
Design of the Coursework
Evaluation and Lessons Learned

My Favorite Origamics Lessons on the Volume of Solids, Shi-Pui Kwan
Introduction
Exploration: Origami Masu Cubic Box
Exploration: Origami CK-Octahedron
Exploration: The Building Block of CK and KC
Exploration: Origami KC-Heptahedron
Exploration: Tessellating Solids
Origami, Science, Mathematics, and Education
Conclusion
Bibliography

Origami Science, Engineering, and Technology

Rigid-Foldable Thick Origami, Tomohiro Tachi
Introduction
Problem Description
Proposed Method
Application for Designs
Conclusion
Bibliography

Folding a Patterned Cylinder by Rigid Origami, Kunfeng Wang and Yan Chen
Introduction
Kinematics of SphericalR Linkage and Its One DoF Assembly
Rigid Origami Patterns to Form Cylindrical Structures
Conclusions and Discussion
Bibliography

The Origami Crash Box, Jiayao Ma and Zhong You
Introduction
Description of the Origami Pattern Design
Finite Element Modeling
Results and Discussion
Conclusion
Bibliography

Origami Folding: A Structural Engineering Approach, Mark Schenk and Simon D. Guest
Introduction
Folded Textured Sheets
Mechanical Modeling Method
Conclusion
Bibliography

Designing Technical Tessellations, Yves Klett and Klaus Drechsler
Introduction: Paper as Technical Material
Lightweight Construction with Paper
Modular Isometric Origami
Design Strategies
Not So Serious—Some Fun
Conclusion
Bibliography

A Simulator for Origami-Inspired Self-Reconfigurable Robots, Steven Gray, Nathan J. Zeichner, Mark Yim, and Vijay Kumar
Introduction
Foldable Programmable Matter
Representing Programmable Matter
Editor Implementation and Usage
PhysX Simulator and Integration
Conclusion
Bibliography

A CAD System for Diagramming Origami with Prediction of Folding Processes, Naoya Tsuruta, Jun Mitani, Yoshihiro Kanamori, and Yukio Fukui
Introduction
Related Work
Our Proposed System
Results and Discussion
Conclusion and Future Work
Bibliography

Development of an Intuitive Algorithm for Diagramming and 3D Animated…, Hugo Akitaya, Matheus Ribeiro, Carla Koike, and Jose Ralha
Introduction
Computational Origami
Basic Definitions on Technical Origami
Turning a CP into a Folding Sequence
Applicability Scope
Example
Software Implementation
Conclusion
Bibliography

Hands-Free Microscale Origami, Noy Bassik, George M. Stern, Alla Brafman, Nana Y. Atuobi, and David H. Gracias
Introduction
Stress-Based Microscale Folding
Miniaturized Microscale Origami Structures:
Unidirectional Folding
Bidirectional Microscale Folding Using
Thin Metal Films
Conclusion and Future Possibilities
Bibliography

Foldable Parylene Origami Sheets Covered with Cells: Toward Applications…, Kaori Kuribayashi-Shigetomi and Shoji Takeuchi
Introduction
Materials and Methods
Results and Discussion
Conclusions
Bibliography

Mathematics of Origami

Introduction to the Study of Tape Knots, Jun Maekawa
Introduction
Why a Knot in a Tape Forms a Regular Pentagon
Regular Odd-Sided Polygonal Knots
Regular Even-Sided Polygonal Knots
Regular Decagonal Knots
Stability of Knots
Nonregular Polygonal Knots
Conclusion and Further Research
Bibliography

Universal Hinge Patterns for Folding Orthogonal Shapes, Nadia M. Benbernou, Erik D. Demaine, Martin L. Demaine, and Aviv Ovadya
Introduction
Definitions
Cube Gadgets
Folding Polycubes
Implementation
Rigid Foldability and Self-Folding Sheets
Bibliography

A General Method of Drawing Biplanar Crease Patterns, Cheng Herng Yi
Introduction
Mathematical Conventions
Defining the Biplanar
Drawing the Net
Drawing the Crease Pattern
Conclusion
Bibliography

A Design Method for Axisymmetric Curved Origami with Triangular Prism Protrusions, Jun Mitani
Introduction
Shape of the TargetD Origami
Designing the Crease Pattern
Examples and Discussions
Conclusion
Bibliography

Folding Any Orthogonal Maze, Erik D. Demaine, Martin L. Demaine, and Jason Ku
Introduction
Algorithm
Bibliography

Every Spider Web Has a Simple Flat Twist Tessellation, Robert J. Lang and Alex Bateman
Introduction
Shrink and Rotate
Nonregular Polygons
Maxwell’s Reciprocal Figures
Bibliography

Flat-Unfoldability and Woven Origami Tessellations, Robert J. Lang
Introduction
Woven Tessellations
Simple Woven Patterns
Flat-Unfoldability
Parameterizing the Woven Tessellation
Conclusion
Bibliography

Degenerative Coordinates in 22.5° Grid System, Tomohiro Tachi and Erik D. Demaine
Introduction
Model
Construction
Degeneracy
Conclusion
Bibliography

Two Folding Constructions, Robert Orndorff
Introduction
Method A: Descartes’ Construction
Method B: My Construction
Conclusion
Bibliography

Variations on a Theorem of Haga, Emma Frigerio
Introduction
Haga’s Theorem
Variation
Variation
A Comparison
Variations on the Variations
Conclusion
Bibliography

Precise Division of Rectangular Paper into an Odd Number of Equal Parts. . ., Kazuo Haga
Introduction
Preparation
Trisection
Five-Section
Seven-Section
Pendulum Symmetry
Nine-section
Individual Line for Higher-Number Sections
Conclusions
Bibliography

The Speed of Origami Constructions Versus Other Construction Tools, Eulália Tramuns
Introduction
Geometric Tools
Constructions and Measures
Optimal Constructions
Conclusions
Bibliography

A Note on Operations of Spherical Origami Construction, Toshikazu Kawasaki
Introduction
The Eight Operations of Planar Origami
Construction
Notation
Spherical Origami
Operations of Spherical Origami Construction
Conclusion
Bibliography

Origami Alignments and Constructions in the Hyperbolic Plane, Roger C. Alperin
Introduction
Basic Alignments and Folds
Relations between the Alignment Axioms
Trigonometry and More Folding in H2
The Non-Euclidean Parabola
H6
Bibliography

A Combinatorial Definition of 1D Flat-Folding, Hidefumi Kawasaki
Introduction
Flat-Foldable 3D Origami
Mingling
Proof of the Flat-Foldability Theorem
Bibliography85

Stamp Foldings with a Given Mountain-Valley Assignment, Ryuhei Uehara
Introduction
Preliminaries
Universality of the Simple Folding Model
The Number of Folded States
Concluding Remarks
Bibliography

Flat Vertex Fold Sequences, Thomas C. Hull and Eric Chang
Introduction
The Basics of Flat Vertex Folds
Flat Vertex Fold Sequences
Conclusion
Bibliography

Circle Packing for Origami Design Is Hard, Erik D. Demaine, Sándor P. Fekete, and Robert J. Lang
Introduction
Circle-River Design
Packing and Complexity
Symmetric-Pockets
Triangular Paper
Rectangular Paper
Square Paper
Filling Gaps
Encoding the Input
A Positive Result
Conclusions
Bibliography
Contributors

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Editor(s)

Biography

Patsy Wang-Iverson is Vice President for Special Projects at the Gabriella and Paul Rosenbaum Foundation. Introduced to origami as a child by her mother, her personal interest in origami merged in recent years with her work in helping to improve students' interest in and success with mathematics. She co-organized, with Eileen Tan and Benjamin Tan, the 2010 Fifth International Meeting on Origami in Science, Mathematics and Education (5OSME) plus a Folding Convention (PLUS!) at the Singapore Management University in Singapore.

Robert J. Lang has been an avid student of origami for some forty years and is now recognized as one of the world’s leading masters of the art. He is one of the pioneers of the cross-disciplinary marriage of origami with mathematics and organized the 2006 Fourth International Meeting on Origami in Science, Mathematics, and Education at Caltech. He has consulted on applications of origami to medical devices, air-bag design, and space telescopes, is the author or co-author of twelve books and numerous articles on origami and lectures widely on the connections between origami, mathematics, science, and technology.

Mark Yim is a professor of mechanical engineering at the University of Pennsylvania. Previously, he was a Principal Scientist at the Palo Alto Research Center (formerly Xerox PARC). His group studies modular self-reconfigurable robots and has demonstrated robots that can transform into different shapes, jump, ride tricycles, climb stairs, poles and fences, manipulate objects and reassemble themselves. Collaborative work with researchers at Harvard, MIT and Berkeley include robotic self-folding origami. He has authored over 100 journal and conference papers and over 40 patents on topics ranging from robotics and videogame feedback devices to education and robotic performance art.

Reviews

I will readily admit I became engaged with, even engrossed in, this seminal volume on the multifaceted aspects of the art, history, science, and engineering of origami in almost four dozen short papers astutely organized, really threaded through, four main sections. … There is plenty of mathematics learning and teaching engagingly embedded within the covers. … There’s something for virtually everyone, students and teachers alike, those mathematically or artistically inclined or interested, and those not so much. … novices and the origami-ignorant like me can find starting points to commence their own personalized explorations of this fascinating field. So, pick up this volume and begin unfolding it to reveal all its intricacies. May you find your own treasure ship or sacred crane among its pages!
—John E. Hammett III, Professor of Mathematics, Saint Peter’s University, and President, New Jersey Association of Mathematics Teacher Educators

When I first visited Japan in 1983 I was curious to learn how origami was taught and developed in Japan. … My search for a connection of origami with mathematics was not successful at that time. I wished that I could have seen a book or even some articles as they are published now in this book … Until recently, the scientific view of origami was rather underdeveloped and [these] proceedings might change this.
—Wolfgang Polasek, International Statistical Review, 2012

Origami 5 continues in the excellent tradition of its four previous incarnations, documenting work presented at an extraordinary series of international meetings that explored the connections between origami, mathematics, science, technology, education, and other academic fields. … Within this one volume, you will find a broad selection of historical information, artists’ descriptions of their processes, various perspectives and approaches to the use of origami in education, mathematical tools for origami design, applications of folding in engineering and technology, as well as original and cutting-edge research on the underpinnings of origami.
L’Enseignement Mathematique (2) 57, 2011

… fascinating … With Origami 5 you can make everything from an origami angel to a full-sized baseball cap and learn all the associated mathematics along the way.
—Kay Gilliland, NCSM Newsletter, Winter 2011

Praise for the Previous Volume:
Wow! Fantastic book! It will create new folds in your brain whether you are an artist, scientist, inventor, educator, or simply like to be amazed. The balance between mathematical theory and manipulative practice, and between artistic and educational applications makes this a book for everyone. I look forward to using this book personally and professionally.
—Robert Root-Bernstein, Ph.D., co-author of Sparks of Genius: The Thirteen Thinking Tools of the World's Most Creative People