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

 Content: 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 Lluisa 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, Eulalia 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, Sandor 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
 Abstract:             \"While many individuals have discovered discrete connections among origami, mathematics, science, technology, and education during the twentieth century, the field really took off when previously isolated individuals began to make stronger connections with each other, exploring the links between origami and \"the outside world.\" This volume brings together an unprecedented number of researchers who discuss topics ranging from mathematics to technology to educational uses of origami to fine art to computer programs for the design of origami\"--
\"Select proceedings from the Fifth International Meeting of Origami Science, Mathematics, and Education (5OSME), to be held July 13-17, 2010, in Singapore. The conference focuses on the mathematics of origami; applications of origami to science, engineering, and technology; use of origami in education; and the art and design of origami\"