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Origami 5

Fifth International Meeting of Origami Science, Mathematics, and Education

Edited by Patsy Wang-Iverson, Robert J. Lang, Mark YIM

A K Peters/CRC Press – 2011 – 660 pages

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    978-1-56881-714-9
    June 21st 2011

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.

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

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

Author Bio

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.

Name: Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (Paperback)A K Peters/CRC Press 
Description: Edited by Patsy Wang-Iverson, Robert J. Lang, Mark YIM. 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...
Categories: Mathematics & Statistics, Geometry, Foundations & Theorems